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<title>Linear Mixed-Effect Modeling with R</title>
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<script src="data:application/javascript;base64,/* slidy.js

   Copyright (c) 2005-2013 W3C (MIT, ERCIM, Keio), All Rights Reserved.
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   http://www.w3.org/Consortium/Legal/copyright-software

   Defines single name "w3c_slidy" in global namespace
   Adds event handlers without trampling on any others
*/

// the slidy object implementation
var w3c_slidy = {
  // classify which kind of browser we're running under
  ns_pos: (typeof window.pageYOffset!='undefined'),
  khtml: ((navigator.userAgent).indexOf("KHTML") >= 0 ? true : false),
  opera: ((navigator.userAgent).indexOf("Opera") >= 0 ? true : false),
  ipad: ((navigator.userAgent).indexOf("iPad") >= 0 ? true : false),
  iphone: ((navigator.userAgent).indexOf("iPhone") >= 0 ? true : false),
  android: ((navigator.userAgent).indexOf("Android") >= 0 ? true : false),
  ie: (typeof document.all != "undefined" && !this.opera),
  ie6: (!this.ns_pos && navigator.userAgent.indexOf("MSIE 6") != -1),
  ie7: (!this.ns_pos && navigator.userAgent.indexOf("MSIE 7") != -1),
  ie8: (!this.ns_pos && navigator.userAgent.indexOf("MSIE 8") != -1),
  ie9: (!this.ns_pos && navigator.userAgent.indexOf("MSIE 9") != -1),

  // data for swipe and double tap detection on touch screens
  last_tap: 0,
  prev_tap: 0,
  start_x: 0,
  start_y: 0,
  delta_x: 0,
  delta_y: 0,

  // are we running as XHTML? (doesn't work on Opera)
  is_xhtml: /xml/.test(document.contentType),

  slide_number: 0, // integer slide count: 0, 1, 2, ...
  slide_number_element: null, // element containing slide number
  slides: [], // set to array of slide div's
  notes: [], // set to array of handout div's
  backgrounds: [], // set to array of background div's
  observers: [], // list of observer functions
  toolbar: null, // element containing toolbar
  title: null, // document title
  last_shown: null, // last incrementally shown item
  eos: null,  // span element for end of slide indicator
  toc: null, // table of contents
  outline: null, // outline element with the focus
  selected_text_len: 0, // length of drag selection on document
  view_all: 0,  // 1 to view all slides + handouts
  want_toolbar: true,  // user preference to show/hide toolbar
  mouse_click_enabled: true, // enables left click for next slide
  scroll_hack: 0, // IE work around for position: fixed
  disable_slide_click: false,  // used by clicked anchors

  lang: "en", // updated to language specified by html file

  help_anchor: null, // used for keyboard focus hack in showToolbar()
  help_page: "http://www.w3.org/Talks/Tools/Slidy2/help/help.html",
  help_text: "Navigate with mouse click, space bar, Cursor Left/Right, " +
             "or Pg Up and Pg Dn. Use S and B to change font size.",

  size_index: 0,
  size_adjustment: 0,
  sizes:  new Array("10pt", "12pt", "14pt", "16pt", "18pt", "20pt",
                    "22pt", "24pt", "26pt", "28pt", "30pt", "32pt"),

  // needed for efficient resizing
  last_width: 0,
  last_height: 0,


  // Needed for cross browser support for relative width/height on
  // object elements. The work around is to save width/height attributes
  // and then to recompute absolute width/height dimensions on resizing
   objects: [],

  // attach initialiation event handlers
  set_up: function () {
    var init = function() { w3c_slidy.init(); };
    if (typeof window.addEventListener != "undefined")
      window.addEventListener("load", init, false);
    else
      window.attachEvent("onload", init);
  },

  hide_slides: function () {
    if (document.body && !w3c_slidy.initialized)
      document.body.style.visibility = "hidden";
    else
      setTimeout(w3c_slidy.hide_slides, 50);
  },

  // hack to persuade IE to compute correct document height
  // as needed for simulating fixed positioning of toolbar
  ie_hack: function () {
    window.resizeBy(0,-1);
    window.resizeBy(0, 1);
  },

  init: function () {
    //alert("slidy starting test 10");
    document.body.style.visibility = "visible";
    this.init_localization();
    this.add_toolbar();
    this.wrap_implicit_slides();
    this.collect_slides();
    this.collect_notes();
    this.collect_backgrounds();
    this.objects = document.body.getElementsByTagName("object");
    this.patch_anchors();
    this.slide_number = this.find_slide_number(location.href);
    window.offscreenbuffering = true;
    this.size_adjustment = this.find_size_adjust();
    this.time_left = this.find_duration();
    this.hide_image_toolbar();  // suppress IE image toolbar popup
    this.init_outliner();  // activate fold/unfold support
    this.title = document.title;
    this.keyboardless = (this.ipad||this.iphone||this.android);

    if (this.keyboardless)
    {
      w3c_slidy.remove_class(w3c_slidy.toolbar, "hidden")
      this.want_toolbar = 0;
    }

    // work around for opera bug
    this.is_xhtml = (document.body.tagName == "BODY" ? false : true);

    if (this.slides.length > 0)
    {
      var slide = this.slides[this.slide_number];
   
      if (this.slide_number > 0)
      {
        this.set_visibility_all_incremental("visible");
        this.last_shown = this.previous_incremental_item(null);
        this.set_eos_status(true);
      }
      else
      {
        this.last_shown = null;
        this.set_visibility_all_incremental("hidden");
        this.set_eos_status(!this.next_incremental_item(this.last_shown));
      }

      this.set_location();
      this.add_class(this.slides[0], "first-slide");
      w3c_slidy.show_slide(slide);
    }

    this.toc = this.table_of_contents();

    this.add_initial_prompt();

    // bind event handlers without interfering with custom page scripts
    // Tap events behave too weirdly to support clicks reliably on
    // iPhone and iPad, so exclude these from click handler

    if (!this.keyboardless)
    {
      this.add_listener(document.body, "click", this.mouse_button_click);
      this.add_listener(document.body, "mousedown", this.mouse_button_down);
    }

    this.add_listener(document, "keydown", this.key_down);
    this.add_listener(document, "keypress", this.key_press);
    this.add_listener(window, "resize", this.resized);
    this.add_listener(window, "scroll", this.scrolled);
    this.add_listener(window, "unload", this.unloaded);

    this.add_listener(document, "gesturechange", function ()
    {
      return false;
    });

    this.attach_touch_handers(this.slides);

    // this seems to be a debugging hack
    //if (!document.body.onclick)
    //  document.body.onclick = function () { };

    this.single_slide_view();

    //this.set_location();

    this.resized();

    if (this.ie7)
      setTimeout(w3c_slidy.ie_hack, 100);

    this.show_toolbar();

    // for back button detection
    setInterval(function () { w3c_slidy.check_location(); }, 200);
    w3c_slidy.initialized = true;
  },

  // create div element with links to each slide
  table_of_contents: function () {
    var toc = this.create_element("div");
    this.add_class(toc, "slidy_toc hidden");
    //toc.setAttribute("tabindex", "0");

    var heading = this.create_element("div");
    this.add_class(heading, "toc-heading");
    heading.innerHTML = this.localize("Table of Contents");

    toc.appendChild(heading);
    var previous = null;

    for (var i = 0; i < this.slides.length; ++i)
    {
      var title = this.has_class(this.slides[i], "title");
      var num = document.createTextNode((i + 1) + ". ");

      toc.appendChild(num);

      var a = this.create_element("a");
      a.setAttribute("href", "#(" + (i+1) + ")");

      if (title)
        this.add_class(a, "titleslide");

      var name = document.createTextNode(this.slide_name(i));
      a.appendChild(name);
      a.onclick = w3c_slidy.toc_click;
      a.onkeydown = w3c_slidy.toc_key_down;
      a.previous = previous;

      if (previous)
        previous.next = a;

      toc.appendChild(a);

      if (i == 0)
        toc.first = a;

      if (i < this.slides.length - 1)
      {
        var br = this.create_element("br");
        toc.appendChild(br);
      }

      previous = a;
    }

    toc.focus = function () {
      if (this.first)
        this.first.focus();
    }

    toc.onmouseup = w3c_slidy.mouse_button_up;

    toc.onclick = function (e) {
      e||(e=window.event);

      if (w3c_slidy.selected_text_len <= 0)
         w3c_slidy.hide_table_of_contents(true);

      w3c_slidy.stop_propagation(e);
    
      if (e.cancel != undefined)
        e.cancel = true;
      
      if (e.returnValue != undefined)
        e.returnValue = false;
      
      return false;
    };

    document.body.insertBefore(toc, document.body.firstChild);
    return toc;
  },

  is_shown_toc: function () {
    return !w3c_slidy.has_class(w3c_slidy.toc, "hidden");
  },

  show_table_of_contents: function () {
    w3c_slidy.remove_class(w3c_slidy.toc, "hidden");
    var toc = w3c_slidy.toc;
    toc.focus();

    if (w3c_slidy.ie7 && w3c_slidy.slide_number == 0)
      setTimeout(w3c_slidy.ie_hack, 100);
  },

  hide_table_of_contents: function (focus) {
    w3c_slidy.add_class(w3c_slidy.toc, "hidden");

    if (focus && !w3c_slidy.opera &&
        !w3c_slidy.has_class(w3c_slidy.toc, "hidden"))
      w3c_slidy.set_focus();
  },

  toggle_table_of_contents: function () {
    if (w3c_slidy.is_shown_toc())
      w3c_slidy.hide_table_of_contents(true);
    else
      w3c_slidy.show_table_of_contents();
  },

  // called on clicking toc entry
  toc_click: function (e) {
    if (!e)
      e = window.event;

    var target = w3c_slidy.get_target(e);

    if (target && target.nodeType == 1)
    {
      var uri = target.getAttribute("href");

      if (uri)
      {
        //alert("going to " + uri);
        var slide = w3c_slidy.slides[w3c_slidy.slide_number];
        w3c_slidy.hide_slide(slide);
        w3c_slidy.slide_number = w3c_slidy.find_slide_number(uri);
        slide = w3c_slidy.slides[w3c_slidy.slide_number];
        w3c_slidy.last_shown = null;
        w3c_slidy.set_location();
        w3c_slidy.set_visibility_all_incremental("hidden");
        w3c_slidy.set_eos_status(!w3c_slidy.next_incremental_item(w3c_slidy.last_shown));
        w3c_slidy.show_slide(slide);
        //target.focus();

        try
        {
          if (!w3c_slidy.opera)
            w3c_slidy.set_focus();
        }
        catch (e)
        {
        }
      }
    }

    w3c_slidy.hide_table_of_contents(true);
    if (w3c_slidy.ie7) w3c_slidy.ie_hack();
    w3c_slidy.stop_propagation(e);
    return w3c_slidy.cancel(e);
  },

  // called onkeydown for toc entry
  toc_key_down: function (event) {
    var key;

    if (!event)
      var event = window.event;

    // kludge around NS/IE differences 
    if (window.event)
      key = window.event.keyCode;
    else if (event.which)
      key = event.which;
    else
      return true; // Yikes! unknown browser

    // ignore event if key value is zero
    // as for alt on Opera and Konqueror
    if (!key)
      return true;

    // check for concurrent control/command/alt key
    // but are these only present on mouse events?

    if (event.ctrlKey || event.altKey)
      return true;

    if (key == 13)
    {
      var uri = this.getAttribute("href");

      if (uri)
      {
        //alert("going to " + uri);
       var slide = w3c_slidy.slides[w3c_slidy.slide_number];
        w3c_slidy.hide_slide(slide);
        w3c_slidy.slide_number = w3c_slidy.find_slide_number(uri);
        slide = w3c_slidy.slides[w3c_slidy.slide_number];
        w3c_slidy.last_shown = null;
        w3c_slidy.set_location();
        w3c_slidy.set_visibility_all_incremental("hidden");
        w3c_slidy.set_eos_status(!w3c_slidy.next_incremental_item(w3c_slidy.last_shown));
        w3c_slidy.show_slide(slide);
        //target.focus();

        try
        {
          if (!w3c_slidy.opera)
            w3c_slidy.set_focus();
        }
        catch (e)
        {
        }
      }

      w3c_slidy.hide_table_of_contents(true);

      if (self.ie7)
       w3c_slidy.ie_hack();

      return w3c_slidy.cancel(event);
    }

    if (key == 40 && this.next)
    {
      this.next.focus();
      return w3c_slidy.cancel(event);
    }

    if (key == 38 && this.previous)
    {
      this.previous.focus();
      return w3c_slidy.cancel(event);
    }

    return true;
  },

  touchstart: function (e)
  {
    // a double touch often starts with a
    // single touch due to fingers touching
    // down at slightly different times
    // thus avoid calling preventDefault here
    this.prev_tap = this.last_tap;
    this.last_tap = (new Date).getTime();

    var tap_delay = this.last_tap - this.prev_tap;

    if (tap_delay <= 200)
    {
      // double tap
    }

    var touch = e.touches[0];

    this.pageX = touch.pageX;
    this.pageY = touch.pageY;
    this.screenX = touch.screenX;
    this.screenY = touch.screenY;
    this.clientX = touch.clientX;
    this.clientY = touch.clientY;

    this.delta_x = this.delta_y = 0;
  },

  touchmove: function (e)
  {
    // override native gestures for single touch
    if (e.touches.length > 1)
      return;

    e.preventDefault();
    var touch = e.touches[0];
    this.delta_x = touch.pageX - this.pageX;
    this.delta_y = touch.pageY - this.pageY;
  },

  touchend: function (e)
  {
    // default behavior for multi-touch
    if (e.touches.length > 1)
      return;

    var delay = (new Date).getTime() - this.last_tap;
    var dx = this.delta_x;
    var dy = this.delta_y;
    var abs_dx = Math.abs(dx);
    var abs_dy = Math.abs(dy);

    if (delay < 500 && (abs_dx > 100 || abs_dy > 100))
    {
      if (abs_dx > 0.5 * abs_dy)
      {
        e.preventDefault();

        if (dx < 0)
          w3c_slidy.next_slide(true);
        else
          w3c_slidy.previous_slide(true);
      }
      else if (abs_dy > 2 * abs_dx)
      {
        e.preventDefault();
        w3c_slidy.toggle_table_of_contents();
      }
    }
  },

  // ### OBSOLETE ###
  before_print: function () {
    this.show_all_slides();
    this.hide_toolbar();
    alert("before print");
  },

  // ### OBSOLETE ###
  after_print: function () {
    if (!this.view_all)
    {
      this.single_slide_view();
      this.show_toolbar();
    }
    alert("after print");
  },

  // ### OBSOLETE ###
  print_slides: function () {
    this.before_print();
    window.print();
    this.after_print();
  },

  // ### OBSOLETE ?? ###
  toggle_view: function () {
    if (this.view_all)
    {
      this.single_slide_view();
      this.show_toolbar();
      this.view_all = 0;
    }
    else
    {
      this.show_all_slides();
      this.hide_toolbar();
      this.view_all = 1;
    }
  },

  // prepare for printing  ### OBSOLETE ###
  show_all_slides: function () {
    this.remove_class(document.body, "single_slide");
    this.set_visibility_all_incremental("visible");
  },

  // restore after printing  ### OBSOLETE ###
  single_slide_view: function () {
    this.add_class(document.body, "single_slide");
    this.set_visibility_all_incremental("visible");
    this.last_shown = this.previous_incremental_item(null);
  },

  // suppress IE's image toolbar pop up
  hide_image_toolbar: function () {
    if (!this.ns_pos)
    {
      var images = document.getElementsByTagName("IMG");

      for (var i = 0; i < images.length; ++i)
        images[i].setAttribute("galleryimg", "no");
    }
  },

  unloaded: function (e) {
    //alert("unloaded");
  },

  // Safari and Konqueror don't yet support getComputedStyle()
  // and they always reload page when location.href is updated
  is_KHTML: function () {
    var agent = navigator.userAgent;
    return (agent.indexOf("KHTML") >= 0 ? true : false);
  },

  // find slide name from first h1 element
  // default to document title + slide number
  slide_name: function (index) {
    var name = null;
    var slide = this.slides[index];

    var heading = this.find_heading(slide);

    if (heading)
      name = this.extract_text(heading);

    if (!name)
      name = this.title + "(" + (index + 1) + ")";

    name.replace(/\&/g, "&amp;");
    name.replace(/\</g, "&lt;");
    name.replace(/\>/g, "&gt;");

    return name;
  },

  // find first h1 element in DOM tree
  find_heading: function (node) {
    if (!node || node.nodeType != 1)
      return null;

    if (node.nodeName == "H1" || node.nodeName == "h1")
      return node;

    var child = node.firstChild;

    while (child)
    {
      node = this.find_heading(child);

      if (node)
        return node;

      child = child.nextSibling;
    }

    return null;
  },

  // recursively extract text from DOM tree
  extract_text: function (node) {
    if (!node)
      return "";

    // text nodes
    if (node.nodeType == 3)
      return node.nodeValue;

    // elements
    if (node.nodeType == 1)
    {
      node = node.firstChild;
      var text = "";

      while (node)
      {
        text = text + this.extract_text(node);
        node = node.nextSibling;
      }

      return text;
    }

    return "";
  },

  // find copyright text from meta element
  find_copyright: function () {
    var name, content;
    var meta = document.getElementsByTagName("meta");

    for (var i = 0; i < meta.length; ++i)
    {
      name = meta[i].getAttribute("name");
      content = meta[i].getAttribute("content");

      if (name == "copyright")
        return content;
    }

    return null;
  },

  find_size_adjust: function () {
    var name, content, offset;
    var meta = document.getElementsByTagName("meta");

    for (var i = 0; i < meta.length; ++i)
    {
      name = meta[i].getAttribute("name");
      content = meta[i].getAttribute("content");

      if (name == "font-size-adjustment")
        return 1 * content;
    }

    return 1;
  },

  // <meta name="duration" content="20" />  for 20 minutes
  find_duration: function () {
    var name, content, offset;
    var meta = document.getElementsByTagName("meta");

    for (var i = 0; i < meta.length; ++i)
    {
      name = meta[i].getAttribute("name");
      content = meta[i].getAttribute("content");

      if (name == "duration")
        return 60000 * content;
    }

    return null;
  },

  replace_by_non_breaking_space: function (str) {
    for (var i = 0; i < str.length; ++i)
      str[i] = 160;
  },

  // ### CHECK ME ### is use of "li" okay for text/html?
  // for XHTML do we also need to specify namespace?
  init_outliner: function () {
    var items = document.getElementsByTagName("li");

    for (var i = 0; i < items.length; ++i)
    {
      var target = items[i];

      if (!this.has_class(target.parentNode, "outline"))
        continue;

      target.onclick = this.outline_click;
/* ### more work needed for IE6
      if (!this.ns_pos)
      {
        target.onmouseover = this.hover_outline;
        target.onmouseout = this.unhover_outline;
      }
*/
      if (this.foldable(target))
      {
        target.foldable = true;
        target.onfocus = function () {w3c_slidy.outline = this;};
        target.onblur = function () {w3c_slidy.outline = null;};

        if (!target.getAttribute("tabindex"))
          target.setAttribute("tabindex", "0");

        if (this.has_class(target, "expand"))
          this.unfold(target);
        else
          this.fold(target);
      }
      else
      {
        this.add_class(target, "nofold");
        target.visible = true;
        target.foldable = false;
      }
    }
  },

  foldable: function (item) {
    if (!item || item.nodeType != 1)
      return false;

    var node = item.firstChild;

    while (node)
    {
      if (node.nodeType == 1 && this.is_block(node))
        return true;

      node = node.nextSibling;
    }

    return false;
  },

  // ### CHECK ME ### switch to add/remove "hidden" class
  fold: function (item) {
    if (item)
    {
      this.remove_class(item, "unfolded");
      this.add_class(item, "folded");
    }

    var node = item ? item.firstChild : null;

    while (node)
    {
      if (node.nodeType == 1 && this.is_block(node)) // element
      {
         w3c_slidy.add_class(node, "hidden");
      }

      node = node.nextSibling;
    }

    item.visible = false;
  },

  // ### CHECK ME ### switch to add/remove "hidden" class
  unfold: function (item) {
    if (item)
    {
      this.add_class(item, "unfolded");
      this.remove_class(item, "folded");
    }

    var node = item ? item.firstChild : null;

    while (node)
    {
      if (node.nodeType == 1 && this.is_block(node)) // element
      {
        w3c_slidy.remove_class(node, "hidden");
      }

      node = node.nextSibling;
    }

    item.visible = true;
  },

  outline_click: function (e) {
    if (!e)
      e = window.event;

    var rightclick = false;
    var target = w3c_slidy.get_target(e);

    while (target && target.visible == undefined)
      target = target.parentNode;

    if (!target)
      return true;

    if (e.which)
      rightclick = (e.which == 3);
    else if (e.button)
      rightclick = (e.button == 2);

    if (!rightclick && target.visible != undefined)
    {
      if (target.foldable)
      {
        if (target.visible)
          w3c_slidy.fold(target);
        else
          w3c_slidy.unfold(target);
      }

      w3c_slidy.stop_propagation(e);
      e.cancel = true;
      e.returnValue = false;
    }

    return false;
  },

  add_initial_prompt: function () {
    var prompt = this.create_element("div");
    prompt.setAttribute("class", "initial_prompt");

    var p1 = this.create_element("p");
    prompt.appendChild(p1);
    p1.setAttribute("class", "help");

    if (this.keyboardless)
      p1.innerHTML = "swipe left to move to next slide";
    else
      p1.innerHTML = "Space, Right Arrow or swipe left to move to " +
                     "next slide, click help below for more details";

    this.add_listener(prompt, "click", function (e) {
      document.body.removeChild(prompt);
      w3c_slidy.stop_propagation(e);
    
      if (e.cancel != undefined)
        e.cancel = true;
      
      if (e.returnValue != undefined)
        e.returnValue = false;
      
      return false;
    });

    document.body.appendChild(prompt);
    this.initial_prompt = prompt;
    setTimeout(function() {document.body.removeChild(prompt);}, 5000);
  },

  add_toolbar: function () {
    var counter, page;

     this.toolbar = this.create_element("div");
     this.toolbar.setAttribute("class", "toolbar");

     // a reasonably behaved browser
     if (this.ns_pos || !this.ie6)
     {
       var right = this.create_element("div");
       right.setAttribute("style", "float: right; text-align: right");

       counter = this.create_element("span")
       counter.innerHTML = this.localize("slide") + " n/m";
       right.appendChild(counter);
       this.toolbar.appendChild(right);

       var left = this.create_element("div");
       left.setAttribute("style", "text-align: left");

       // global end of slide indicator
       this.eos = this.create_element("span");
       this.eos.innerHTML = "* ";
       left.appendChild(this.eos);

       var help = this.create_element("a");
       help.setAttribute("href", this.help_page);
       help.setAttribute("title", this.localize(this.help_text));
       help.innerHTML = this.localize("help?");
       left.appendChild(help);
       help.style.display="none"; 
       this.help_anchor = help;  // save for focus hack

       var gap1 = document.createTextNode(" ");
       left.appendChild(gap1);

       var contents = this.create_element("a");
       contents.setAttribute("href", "javascript:w3c_slidy.toggle_table_of_contents()");
       contents.setAttribute("title", this.localize("table of contents"));
       contents.innerHTML = this.localize("Contents");
       left.appendChild(contents);

       var gap2 = document.createTextNode(" ");
       left.appendChild(gap2);

       var copyright = this.find_copyright();

       if (copyright)
       {
         var span = this.create_element("span");
         span.className = "copyright";
         span.innerHTML = copyright;
         left.appendChild(span);
       }

       this.toolbar.setAttribute("tabindex", "0");
       this.toolbar.appendChild(left);
     }
     else // IE6 so need to work around its poor CSS support
     {
       this.toolbar.style.position = (this.ie7 ? "fixed" : "absolute");
       this.toolbar.style.zIndex = "200";
       this.toolbar.style.width = "99.9%";
       this.toolbar.style.height = "1.2em";
       this.toolbar.style.top = "auto";
       this.toolbar.style.bottom = "0";
       this.toolbar.style.left = "0";
       this.toolbar.style.right = "0";
       this.toolbar.style.textAlign = "left";
       this.toolbar.style.fontSize = "60%";
       this.toolbar.style.color = "red";
       this.toolbar.borderWidth = 0;
       this.toolbar.className = "toolbar";
       this.toolbar.style.background = "rgb(240,240,240)";

       // would like to have help text left aligned
       // and page counter right aligned, floating
       // div's don't work, so instead use nested
       // absolutely positioned div's.

       var sp = this.create_element("span");
       sp.innerHTML = "&nbsp;&nbsp;*&nbsp;";
       this.toolbar.appendChild(sp);
       this.eos = sp;  // end of slide indicator

       var help = this.create_element("a");
       help.setAttribute("href", this.help_page);
       help.setAttribute("title", this.localize(this.help_text));
       help.innerHTML = this.localize("help?");
       this.toolbar.appendChild(help);
       this.help_anchor = help;  // save for focus hack

       var gap1 = document.createTextNode(" ");
       this.toolbar.appendChild(gap1);

       var contents = this.create_element("a");
       contents.setAttribute("href", "javascript:toggleTableOfContents()");
       contents.setAttribute("title", this.localize("table of contents".localize));
       contents.innerHTML = this.localize("contents?");
       this.toolbar.appendChild(contents);

       var gap2 = document.createTextNode(" ");
       this.toolbar.appendChild(gap2);

       var copyright = this.find_copyright();

       if (copyright)
       {
         var span = this.create_element("span");
         span.innerHTML = copyright;
         span.style.color = "black";
         span.style.marginLeft = "0.5em";
         this.toolbar.appendChild(span);
       }

       counter = this.create_element("div")
       counter.style.position = "absolute";
       counter.style.width = "auto"; //"20%";
       counter.style.height = "1.2em";
       counter.style.top = "auto";
       counter.style.bottom = 0;
       counter.style.right = "0";
       counter.style.textAlign = "right";
       counter.style.color = "red";
       counter.style.background = "rgb(240,240,240)";

       counter.innerHTML = this.localize("slide") + " n/m";
       this.toolbar.appendChild(counter);
     }

     // ensure that click isn't passed through to the page
     this.toolbar.onclick =
         function (e) {
           if (!e)
             e = window.event;

           var target = e.target;

           if (!target && e.srcElement)
             target = e.srcElement;

           // work around Safari bug
           if (target && target.nodeType == 3)
             target = target.parentNode;

           w3c_slidy.stop_propagation(e);

           if (target && target.nodeName.toLowerCase() != "a")
             w3c_slidy.mouse_button_click(e);
         };

     this.slide_number_element = counter;
     this.set_eos_status(false);
     document.body.appendChild(this.toolbar);
  },

  // wysiwyg editors make it hard to use div elements
  // e.g. amaya loses the div when you copy and paste
  // this function wraps div elements around implicit
  // slides which start with an h1 element and continue
  // up to the next heading or div element
  wrap_implicit_slides: function () {
    var i, heading, node, next, div;
    var headings = document.getElementsByTagName("h1");

    if (!headings)
      return;

    for (i = 0; i < headings.length; ++i)
    {
      heading = headings[i];

      if (heading.parentNode != document.body)
        continue;

      node = heading.nextSibling;

      div = document.createElement("div");
      this.add_class(div, "slide");
      document.body.replaceChild(div, heading);
      div.appendChild(heading);

      while (node)
      {
        if (node.nodeType == 1) // an element
        {
           if (node.nodeName == "H1" || node.nodeName == "h1")
             break;

           if (node.nodeName == "DIV" || node.nodeName == "div")
           {
             if (this.has_class(node, "slide"))
               break;

             if (this.has_class(node, "handout"))
               break;
           }
        }

        next = node.nextSibling;
        node = document.body.removeChild(node);
        div.appendChild(node);
        node = next;
      } 
    }
  },

  attach_touch_handers: function(slides)
  {
    var i, slide;

    for (i = 0; i < slides.length; ++i)
    {
      slide = slides[i];
      this.add_listener(slide, "touchstart", this.touchstart);
      this.add_listener(slide, "touchmove", this.touchmove);
      this.add_listener(slide, "touchend", this.touchend);
    }
  },

// return new array of all slides
  collect_slides: function () {
    var slides = new Array();
    var divs = document.body.getElementsByTagName("div");

    for (var i = 0; i < divs.length; ++i)
    {
      div = divs.item(i);

      if (this.has_class(div, "slide"))
      {
        // add slide to collection
        slides[slides.length] = div;

        // hide each slide as it is found
        this.add_class(div, "hidden");

        // add dummy <br/> at end for scrolling hack
        var node1 = document.createElement("br");
        div.appendChild(node1);
        var node2 = document.createElement("br");
        div.appendChild(node2);
      }
      else if (this.has_class(div, "background"))
      {  // work around for Firefox SVG reload bug
        // which otherwise replaces 1st SVG graphic with 2nd
        div.style.display = "block";
      }
    }

    this.slides = slides;
  },

  // return new array of all <div class="handout">
  collect_notes: function () {
    var notes = new Array();
    var divs = document.body.getElementsByTagName("div");

    for (var i = 0; i < divs.length; ++i)
    {
      div = divs.item(i);

      if (this.has_class(div, "handout"))
      {
        // add note to collection
        notes[notes.length] = div;

        // and hide it
        this.add_class(div, "hidden");
      }
    }

    this.notes = notes;
  },

  // return new array of all <div class="background">
  // including named backgrounds e.g. class="background titlepage"
  collect_backgrounds: function () {
    var backgrounds = new Array();
    var divs = document.body.getElementsByTagName("div");

    for (var i = 0; i < divs.length; ++i)
    {
      div = divs.item(i);

      if (this.has_class(div, "background"))
      {
        // add background to collection
        backgrounds[backgrounds.length] = div;

        // and hide it
        this.add_class(div, "hidden");
      }
    }

    this.backgrounds = backgrounds;
  },

  // set click handlers on all anchors
  patch_anchors: function () {
    var self = w3c_slidy;
    var handler = function (event) {
      // compare this.href with location.href
      // for link to another slide in this doc

      if (self.page_address(this.href) == self.page_address(location.href))
      {
        // yes, so find new slide number
        var newslidenum = self.find_slide_number(this.href);

        if (newslidenum != self.slide_number)
        {
          var slide = self.slides[self.slide_number];
          self.hide_slide(slide);
          self.slide_number = newslidenum;
          slide = self.slides[self.slide_number];
          self.show_slide(slide);
          self.set_location();
        }
      }
      else
        w3c_slidy.stop_propagation(event);

//      else if (this.target == null)
//        location.href = this.href;

      this.blur();
      self.disable_slide_click = true;
    };

    var anchors = document.body.getElementsByTagName("a");

    for (var i = 0; i < anchors.length; ++i)
    {
      if (window.addEventListener)
        anchors[i].addEventListener("click", handler, false);
      else
        anchors[i].attachEvent("onclick", handler);
    }
  },

  // ### CHECK ME ### see which functions are invoked via setTimeout
  // either directly or indirectly for use of w3c_slidy vs this
  show_slide_number: function () {
    var timer = w3c_slidy.get_timer();
    w3c_slidy.slide_number_element.innerHTML = timer + w3c_slidy.localize("slide") + " " +
           (w3c_slidy.slide_number + 1) + "/" + w3c_slidy.slides.length;
  },

  // every 200mS check if the location has been changed as a
  // result of the user activating the Back button/menu item
  // doesn't work for Opera < 9.5
  check_location: function () {
    var hash = location.hash;

    if (w3c_slidy.slide_number > 0 && (hash == "" || hash == "#"))
      w3c_slidy.goto_slide(0);
    else if (hash.length > 2 && hash != "#("+(w3c_slidy.slide_number+1)+")")
    {
      var num = parseInt(location.hash.substr(2));

      if (!isNaN(num))
        w3c_slidy.goto_slide(num-1);
    }

    if (w3c_slidy.time_left && w3c_slidy.slide_number > 0)
    {
      w3c_slidy.show_slide_number();

      if (w3c_slidy.time_left > 0)
        w3c_slidy.time_left -= 200;
    } 
  },

  get_timer: function () {
    var timer = "";
    if (w3c_slidy.time_left)
    {
      var mins, secs;
      secs = Math.floor(w3c_slidy.time_left/1000);
      mins = Math.floor(secs / 60);
      secs = secs % 60;
      timer = (mins ? mins+"m" : "") + secs + "s ";
    }

    return timer;
  },

  // this doesn't push location onto history stack for IE
  // for which a hidden iframe hack is needed: load page into
  // the iframe with script that set's parent's location.hash
  // but that won't work for standalone use unless we can
  // create the page dynamically via a javascript: URL
  // ### use history.pushState if available
  set_location: function () {
     var uri = w3c_slidy.page_address(location.href);
     var hash = "#(" + (w3c_slidy.slide_number+1) + ")";

     if (w3c_slidy.slide_number >= 0)
       uri = uri + hash;

     if (typeof(history.pushState) != "undefined" && location.protocol !== "file:")
     {
       document.title = w3c_slidy.title + " (" + (w3c_slidy.slide_number+1) + ")";
       history.pushState(0, document.title, hash);
       w3c_slidy.show_slide_number();
       w3c_slidy.notify_observers();
       return;
     }

     if (w3c_slidy.ie && (w3c_slidy.ie6 || w3c_slidy.ie7))
       w3c_slidy.push_hash(hash);

     if (uri != location.href) // && !khtml
        location.href = uri;

     if (this.khtml)
        hash = "(" + (w3c_slidy.slide_number+1) + ")";

     if (!this.ie && location.hash != hash && location.hash != "")
       location.hash = hash;

     document.title = w3c_slidy.title + " (" + (w3c_slidy.slide_number+1) + ")";
     w3c_slidy.show_slide_number();
     w3c_slidy.notify_observers();
  },

  notify_observers: function ()
  {
    var slide = this.slides[this.slide_number];

    for (var i = 0; i < this.observers.length; ++i)
      this.observers[i](this.slide_number+1, this.find_heading(slide).innerText, location.href);
  },

  add_observer: function (observer)
  {
    for (var i = 0; i < this.observers.length; ++i)
    {
      if (observer == this.observers[i])
        return;
    }

    this.observers.push(observer);
  },

  remove_observer: function (o)
  {
    for (var i = 0; i < this.observers.length; ++i)
    {
      if (observer == this.observers[i])
      {
        this.observers.splice(i,1);
        break;
      }
    }
  },

  page_address: function (uri) {
    var i = uri.indexOf("#");

    if (i < 0)
      i = uri.indexOf("%23");

    // check if anchor is entire page

    if (i < 0)
      return uri;  // yes

    return uri.substr(0, i);
  },

  // only used for IE6 and IE7
  on_frame_loaded: function (hash) {
    location.hash = hash;
    var uri = w3c_slidy.page_address(location.href);
    location.href = uri + hash;
  },

  // history hack with thanks to Bertrand Le Roy
  push_hash: function (hash) {
    if (hash == "") hash = "#(1)";
      window.location.hash = hash;

    var doc = document.getElementById("historyFrame").contentWindow.document;
    doc.open("javascript:'<html></html>'");
    doc.write("<html><head><script type=\"text/javascript\">window.parent.w3c_slidy.on_frame_loaded('"+
      (hash) + "');</script></head><body>hello mum</body></html>");
      doc.close();
  },

  // find current slide based upon location
  // first find target anchor and then look
  // for associated div element enclosing it
  // finally map that to slide number
  find_slide_number: function (uri) {
    // first get anchor from page location

    var i = uri.indexOf("#");

    // check if anchor is entire page
    if (i < 0)
      return 0;  // yes

    var anchor = unescape(uri.substr(i+1));

    // now use anchor as XML ID to find target
    var target = document.getElementById(anchor);

    if (!target)
    {
      // does anchor look like "(2)" for slide 2 ??
      // where first slide is (1)
      var re = /\((\d)+\)/;

      if (anchor.match(re))
      {
        var num = parseInt(anchor.substring(1, anchor.length-1));

        if (num > this.slides.length)
          num = 1;

        if (--num < 0)
          num = 0;

        return num;
      }

      // accept [2] for backwards compatibility
      re = /\[(\d)+\]/;

      if (anchor.match(re))
      {
         var num = parseInt(anchor.substring(1, anchor.length-1));

         if (num > this.slides.length)
            num = 1;

         if (--num < 0)
            num = 0;

         return num;
      }

      // oh dear unknown anchor
      return 0;
    }

    // search for enclosing slide

    while (true)
    {
      // browser coerces html elements to uppercase!
      if (target.nodeName.toLowerCase() == "div" &&
            this.has_class(target, "slide"))
      {
        // found the slide element
        break;
      }

      // otherwise try parent element if any

      target = target.parentNode;

      if (!target)
      {
        return 0;   // no luck!
      }
    };

    for (i = 0; i < slides.length; ++i)
    {
      if (slides[i] == target)
        return i;  // success
    }

    // oh dear still no luck
    return 0;
  },

  previous_slide: function (incremental) {
    if (!w3c_slidy.view_all)
    {
      var slide;

      if ((incremental || w3c_slidy.slide_number == 0) && w3c_slidy.last_shown != null)
      {
        w3c_slidy.last_shown = w3c_slidy.hide_previous_item(w3c_slidy.last_shown);
        w3c_slidy.set_eos_status(false);
      }
      else if (w3c_slidy.slide_number > 0)
      {
        slide = w3c_slidy.slides[w3c_slidy.slide_number];
        w3c_slidy.hide_slide(slide);

        w3c_slidy.slide_number = w3c_slidy.slide_number - 1;
        slide = w3c_slidy.slides[w3c_slidy.slide_number];
        w3c_slidy.set_visibility_all_incremental("visible");
        w3c_slidy.last_shown = w3c_slidy.previous_incremental_item(null);
        w3c_slidy.set_eos_status(true);
        w3c_slidy.show_slide(slide);
      }

      w3c_slidy.set_location();

      if (!w3c_slidy.ns_pos)
        w3c_slidy.refresh_toolbar(200);
    }
  },

  next_slide: function (incremental) {
    if (!w3c_slidy.view_all)
    {
      var slide, last = w3c_slidy.last_shown;

      if (incremental || w3c_slidy.slide_number == w3c_slidy.slides.length - 1)
         w3c_slidy.last_shown = w3c_slidy.reveal_next_item(w3c_slidy.last_shown);

      if ((!incremental || w3c_slidy.last_shown == null) &&
             w3c_slidy.slide_number < w3c_slidy.slides.length - 1)
      {
         slide = w3c_slidy.slides[w3c_slidy.slide_number];
         w3c_slidy.hide_slide(slide);

         w3c_slidy.slide_number = w3c_slidy.slide_number + 1;
         slide = w3c_slidy.slides[w3c_slidy.slide_number];
         w3c_slidy.last_shown = null;
         w3c_slidy.set_visibility_all_incremental("hidden");
         w3c_slidy.show_slide(slide);
      }
      else if (!w3c_slidy.last_shown)
      {
         if (last && incremental)
           w3c_slidy.last_shown = last;
      }

      w3c_slidy.set_location();

      w3c_slidy.set_eos_status(!w3c_slidy.next_incremental_item(w3c_slidy.last_shown));

      if (!w3c_slidy.ns_pos)
         w3c_slidy.refresh_toolbar(200);
     }
  },

  // to first slide with nothing revealed
  // i.e. state at start of presentation
  first_slide: function () {
     if (!w3c_slidy.view_all)
     {
       var slide;

       if (w3c_slidy.slide_number != 0)
       {
         slide = w3c_slidy.slides[w3c_slidy.slide_number];
         w3c_slidy.hide_slide(slide);

         w3c_slidy.slide_number = 0;
         slide = w3c_slidy.slides[w3c_slidy.slide_number];
         w3c_slidy.last_shown = null;
         w3c_slidy.set_visibility_all_incremental("hidden");
         w3c_slidy.show_slide(slide);
       }

       w3c_slidy.set_eos_status(
         !w3c_slidy.next_incremental_item(w3c_slidy.last_shown));
       w3c_slidy.set_location();
     }
  },

  // goto last slide with everything revealed
  // i.e. state at end of presentation
  last_slide: function () {
    if (!w3c_slidy.view_all)
    {
      var slide;

      w3c_slidy.last_shown = null; //revealNextItem(lastShown);

      if (w3c_slidy.last_shown == null &&
          w3c_slidy.slide_number < w3c_slidy.slides.length - 1)
      {
         slide = w3c_slidy.slides[w3c_slidy.slide_number];
         w3c_slidy.hide_slide(slide);
         w3c_slidy.slide_number = w3c_slidy.slides.length - 1;
         slide = w3c_slidy.slides[w3c_slidy.slide_number];
         w3c_slidy.set_visibility_all_incremental("visible");
         w3c_slidy.last_shown = w3c_slidy.previous_incremental_item(null);

         w3c_slidy.show_slide(slide);
      }
      else
      {
         w3c_slidy.set_visibility_all_incremental("visible");
         w3c_slidy.last_shown = w3c_slidy.previous_incremental_item(null);
      }

      w3c_slidy.set_eos_status(true);
      w3c_slidy.set_location();
    }
  },


  // ### check this and consider add/remove class
  set_eos_status: function (state) {
    if (this.eos)
      this.eos.style.color = (state ? "rgb(240,240,240)" : "red");
  },

  // first slide is 0
  goto_slide: function (num) {
    //alert("going to slide " + (num+1));
    var slide = w3c_slidy.slides[w3c_slidy.slide_number];
    w3c_slidy.hide_slide(slide);
    w3c_slidy.slide_number = num;
    slide = w3c_slidy.slides[w3c_slidy.slide_number];
    w3c_slidy.last_shown = null;
    w3c_slidy.set_visibility_all_incremental("hidden");
    w3c_slidy.set_eos_status(!w3c_slidy.next_incremental_item(w3c_slidy.last_shown));
    document.title = w3c_slidy.title + " (" + (w3c_slidy.slide_number+1) + ")";
    w3c_slidy.show_slide(slide);
    w3c_slidy.show_slide_number();
  },


  show_slide: function (slide) {
    this.sync_background(slide);
    this.remove_class(slide, "hidden");

    // work around IE9 object rendering bug
    setTimeout("window.scrollTo(0,0);", 1);
  },

  hide_slide: function (slide) {
    this.add_class(slide, "hidden");
  },

  set_focus: function (element)
  {
    if (element)
      element.focus();
    else
    {
      w3c_slidy.help_anchor.focus();

      setTimeout(function() {
        w3c_slidy.help_anchor.blur();
      }, 1);
    }
  },

  // show just the backgrounds pertinent to this slide
  // when slide background-color is transparent
  // this should now work with rgba color values
  sync_background: function (slide) {
    var background;
    var bgColor;

    if (slide.currentStyle)
      bgColor = slide.currentStyle["backgroundColor"];
    else if (document.defaultView)
    {
      var styles = document.defaultView.getComputedStyle(slide,null);

      if (styles)
        bgColor = styles.getPropertyValue("background-color");
      else // broken implementation probably due Safari or Konqueror
      {
        //alert("defective implementation of getComputedStyle()");
        bgColor = "transparent";
      }
    }
    else
      bgColor == "transparent";

    if (bgColor == "transparent" ||
        bgColor.indexOf("rgba") >= 0 ||
        bgColor.indexOf("opacity") >= 0)
    {
      var slideClass = this.get_class_list(slide);

      for (var i = 0; i < this.backgrounds.length; i++)
      {
        background = this.backgrounds[i];

        var bgClass = this.get_class_list(background);

        if (this.matching_background(slideClass, bgClass))
          this.remove_class(background, "hidden");
        else
          this.add_class(background, "hidden");
      }
    }
    else // forcibly hide all backgrounds
      this.hide_backgrounds();
  },

  hide_backgrounds: function () {
    for (var i = 0; i < this.backgrounds.length; i++)
    {
      background = this.backgrounds[i];
      this.add_class(background, "hidden");
    }
  },

  // compare classes for slide and background
  matching_background: function (slideClass, bgClass) {
    var i, count, pattern, result;

    // define pattern as regular expression
    pattern = /\w+/g;

    // check background class names
    result = bgClass.match(pattern);

    for (i = count = 0; i < result.length; i++)
    {
      if (result[i] == "hidden")
        continue;

      if (result[i] == "background")
	continue;

      ++count;
    }

    if (count == 0)  // default match
      return true;

    // check for matches and place result in array
    result = slideClass.match(pattern);

    // now check if desired name is present for background
    for (i = count = 0; i < result.length; i++)
    {
      if (result[i] == "hidden")
        continue;

      if (this.has_token(bgClass, result[i]))
        return true;
    }

    return false;
  },

  resized: function () {
     var width = 0;

     if ( typeof( window.innerWidth ) == 'number' )
       width = window.innerWidth;  // Non IE browser
     else if (document.documentElement && document.documentElement.clientWidth)
       width = document.documentElement.clientWidth;  // IE6
     else if (document.body && document.body.clientWidth)
       width = document.body.clientWidth; // IE4

     var height = 0;

     if ( typeof( window.innerHeight ) == 'number' )
       height = window.innerHeight;  // Non IE browser
     else if (document.documentElement && document.documentElement.clientHeight)
       height = document.documentElement.clientHeight;  // IE6
     else if (document.body && document.body.clientHeight)
       height = document.body.clientHeight; // IE4

     if (height && (width/height > 1.05*1024/768))
     {
       width = height * 1024.0/768;
     }

     // IE fires onresize even when only font size is changed!
     // so we do a check to avoid blocking < and > actions
     if (width != w3c_slidy.last_width || height != w3c_slidy.last_height)
     {
       if (width >= 1100)
         w3c_slidy.size_index = 5;    // 4
       else if (width >= 1000)
         w3c_slidy.size_index = 4;    // 3
       else if (width >= 800)
         w3c_slidy.size_index = 3;    // 2
       else if (width >= 600)
         w3c_slidy.size_index = 2;    // 1
       else if (width)
         w3c_slidy.size_index = 0;

       // add in font size adjustment from meta element e.g.
       // <meta name="font-size-adjustment" content="-2" />
       // useful when slides have too much content ;-)

       if (0 <= w3c_slidy.size_index + w3c_slidy.size_adjustment &&
             w3c_slidy.size_index + w3c_slidy.size_adjustment < w3c_slidy.sizes.length)
         w3c_slidy.size_index = w3c_slidy.size_index + w3c_slidy.size_adjustment;

       // enables cross browser use of relative width/height
       // on object elements for use with SVG and Flash media
       w3c_slidy.adjust_object_dimensions(width, height);

       if (document.body.style.fontSize != w3c_slidy.sizes[w3c_slidy.size_index])
       {
         document.body.style.fontSize = w3c_slidy.sizes[w3c_slidy.size_index];
       }

       w3c_slidy.last_width = width;
       w3c_slidy.last_height = height;

       // force reflow to work around Mozilla bug
       if (w3c_slidy.ns_pos)
       {
         var slide = w3c_slidy.slides[w3c_slidy.slide_number];
         w3c_slidy.hide_slide(slide);
         w3c_slidy.show_slide(slide);
       }

       // force correct positioning of toolbar
       w3c_slidy.refresh_toolbar(200);
     }
  },

  scrolled: function () {
    if (w3c_slidy.toolbar && !w3c_slidy.ns_pos && !w3c_slidy.ie7)
    {
      w3c_slidy.hack_offset = w3c_slidy.scroll_x_offset();
      // hide toolbar
      w3c_slidy.toolbar.style.display = "none";

      // make it reappear later
      if (w3c_slidy.scrollhack == 0 && !w3c_slidy.view_all)
      {
        setTimeout(function () {w3c_slidy.show_toolbar(); }, 1000);
        w3c_slidy.scrollhack = 1;
      }
    }
  },

  hide_toolbar: function () {
    w3c_slidy.add_class(w3c_slidy.toolbar, "hidden");
    window.focus();
  },

  // used to ensure IE refreshes toolbar in correct position
  refresh_toolbar: function (interval) {
    if (!w3c_slidy.ns_pos && !w3c_slidy.ie7)
    {
      w3c_slidy.hide_toolbar();
      setTimeout(function () {w3c_slidy.show_toolbar();}, interval);
    }
  },

  // restores toolbar after short delay
  show_toolbar: function () {
    if (w3c_slidy.want_toolbar)
    {
      w3c_slidy.toolbar.style.display = "block";

      if (!w3c_slidy.ns_pos)
      {
        // adjust position to allow for scrolling
        var xoffset = w3c_slidy.scroll_x_offset();
        w3c_slidy.toolbar.style.left = xoffset;
        w3c_slidy.toolbar.style.right = xoffset;

        // determine vertical scroll offset
        //var yoffset = scrollYOffset();

        // bottom is doc height - window height - scroll offset
        //var bottom = documentHeight() - lastHeight - yoffset

        //if (yoffset > 0 || documentHeight() > lastHeight)
        //   bottom += 16;  // allow for height of scrollbar

        w3c_slidy.toolbar.style.bottom = 0; //bottom;
      }

      w3c_slidy.remove_class(w3c_slidy.toolbar, "hidden");
    }

    w3c_slidy.scrollhack = 0;


    // set the keyboard focus to the help link on the
    // toolbar to ensure that document has the focus
    // IE doesn't always work with window.focus()
    // and this hack has benefit of Enter for help

    try
    {
      if (!w3c_slidy.opera)
        w3c_slidy.set_focus();
    }
    catch (e)
    {
    }
  },

// invoked via F key
  toggle_toolbar: function () {
    if (!w3c_slidy.view_all)
    {
      if (w3c_slidy.has_class(w3c_slidy.toolbar, "hidden"))
      {
        w3c_slidy.remove_class(w3c_slidy.toolbar, "hidden")
        w3c_slidy.want_toolbar = 1;
      }
      else
      {
        w3c_slidy.add_class(w3c_slidy.toolbar, "hidden")
        w3c_slidy.want_toolbar = 0;
      }
    }
  },

  scroll_x_offset: function () {
    if (window.pageXOffset)
      return self.pageXOffset;

    if (document.documentElement && 
             document.documentElement.scrollLeft)
      return document.documentElement.scrollLeft;

    if (document.body)
      return document.body.scrollLeft;

    return 0;
  },

  scroll_y_offset: function () {
    if (window.pageYOffset)
      return self.pageYOffset;

    if (document.documentElement && 
             document.documentElement.scrollTop)
      return document.documentElement.scrollTop;

    if (document.body)
      return document.body.scrollTop;

    return 0;
  },

  // looking for a way to determine height of slide content
  // the slide itself is set to the height of the window
  optimize_font_size: function () {
    var slide = w3c_slidy.slides[w3c_slidy.slide_number];

    //var dh = documentHeight(); //getDocHeight(document);
    var dh = slide.scrollHeight;
    var wh = getWindowHeight();
    var u = 100 * dh / wh;

    alert("window utilization = " + u + "% (doc "
      + dh + " win " + wh + ")");
  },

  // from document object
  get_doc_height: function (doc) {
    if (!doc)
      doc = document;

    if (doc && doc.body && doc.body.offsetHeight)
      return doc.body.offsetHeight;  // ns/gecko syntax

    if (doc && doc.body && doc.body.scrollHeight)
      return doc.body.scrollHeight;

    alert("couldn't determine document height");
  },

  get_window_height: function () {
    if ( typeof( window.innerHeight ) == 'number' )
      return window.innerHeight;  // Non IE browser

    if (document.documentElement && document.documentElement.clientHeight)
      return document.documentElement.clientHeight;  // IE6

    if (document.body && document.body.clientHeight)
      return document.body.clientHeight; // IE4
  },

  document_height: function () {
    var sh, oh;

    sh = document.body.scrollHeight;
    oh = document.body.offsetHeight;

    if (sh && oh)
    {
      return (sh > oh ? sh : oh);
    }

    // no idea!
    return 0;
  },

  smaller: function () {
    if (w3c_slidy.size_index > 0)
    {
      --w3c_slidy.size_index;
    }

    w3c_slidy.toolbar.style.display = "none";
    document.body.style.fontSize = w3c_slidy.sizes[w3c_slidy.size_index];
    var slide = w3c_slidy.slides[w3c_slidy.slide_number];
    w3c_slidy.hide_slide(slide);
    w3c_slidy.show_slide(slide);
    setTimeout(function () {w3c_slidy.show_toolbar(); }, 50);
  },

  bigger: function () {
    if (w3c_slidy.size_index < w3c_slidy.sizes.length - 1)
    {
      ++w3c_slidy.size_index;
    }

    w3c_slidy.toolbar.style.display = "none";
    document.body.style.fontSize = w3c_slidy.sizes[w3c_slidy.size_index];
    var slide = w3c_slidy.slides[w3c_slidy.slide_number];
    w3c_slidy.hide_slide(slide);
    w3c_slidy.show_slide(slide);
    setTimeout(function () {w3c_slidy.show_toolbar(); }, 50);
  },

  // enables cross browser use of relative width/height
  // on object elements for use with SVG and Flash media
  // with thanks to Ivan Herman for the suggestion
  adjust_object_dimensions: function (width, height) {
    for( var i = 0; i < w3c_slidy.objects.length; i++ )
    {
      var obj = this.objects[i];
      var mimeType = obj.getAttribute("type");

      if (mimeType == "image/svg+xml" || mimeType == "application/x-shockwave-flash")
      {
        if ( !obj.initialWidth ) 
          obj.initialWidth = obj.getAttribute("width");

        if ( !obj.initialHeight ) 
          obj.initialHeight = obj.getAttribute("height");

        if ( obj.initialWidth && obj.initialWidth.charAt(obj.initialWidth.length-1) == "%" )
        {
          var w = parseInt(obj.initialWidth.slice(0, obj.initialWidth.length-1));
          var newW = width * (w/100.0);
          obj.setAttribute("width",newW);
        }

        if ( obj.initialHeight &&
             obj.initialHeight.charAt(obj.initialHeight.length-1) == "%" )
        {
          var h = parseInt(obj.initialHeight.slice(0, obj.initialHeight.length-1));
          var newH = height * (h/100.0);
          obj.setAttribute("height", newH);
        }
      }
    }
  },

  // needed for Opera to inhibit default behavior
  // since Opera delivers keyPress even if keyDown
  // was cancelled
  key_press: function (event) {
    if (!event)
      event = window.event;

    if (!w3c_slidy.key_wanted)
      return w3c_slidy.cancel(event);

    return true;
  },

  //  See e.g. http://www.quirksmode.org/js/events/keys.html for keycodes
  key_down: function (event) {
    var key, target, tag;

    w3c_slidy.key_wanted = true;

    if (!event)
      event = window.event;

    // kludge around NS/IE differences 
    if (window.event)
    {
      key = window.event.keyCode;
      target = window.event.srcElement;
    }
    else if (event.which)
    {
      key = event.which;
      target = event.target;
    }
    else
      return true; // Yikes! unknown browser

    // ignore event if key value is zero
    // as for alt on Opera and Konqueror
    if (!key)
       return true;

    // avoid interfering with keystroke
    // behavior for non-slidy chrome elements
    if (!w3c_slidy.slidy_chrome(target) &&
        w3c_slidy.special_element(target))
      return true;

    // check for concurrent control/command/alt key
    // but are these only present on mouse events?

    if (event.ctrlKey || event.altKey || event.metaKey)
       return true;

    // dismiss table of contents if visible
    if (w3c_slidy.is_shown_toc() && key != 9 && key != 16 && key != 38 && key != 40)
    {
      w3c_slidy.hide_table_of_contents(true);

      if (key == 27 || key == 84 || key == 67)
        return w3c_slidy.cancel(event);
    }

    if (key == 34) // Page Down
    {
      if (w3c_slidy.view_all)
        return true;

      w3c_slidy.next_slide(false);
      return w3c_slidy.cancel(event);
    }
    else if (key == 33) // Page Up
    {
      if (w3c_slidy.view_all)
        return true;

      w3c_slidy.previous_slide(false);
      return w3c_slidy.cancel(event);
    }
    else if (key == 32) // space bar
    {
      w3c_slidy.next_slide(true);
      return w3c_slidy.cancel(event);
    }
    else if (key == 37) // Left arrow
    {
      w3c_slidy.previous_slide(!event.shiftKey);
      return w3c_slidy.cancel(event);
    }
    else if (key == 36) // Home
    {
      w3c_slidy.first_slide();
      return w3c_slidy.cancel(event);
    }
    else if (key == 35) // End
    {
      w3c_slidy.last_slide();
      return w3c_slidy.cancel(event);
    }
    else if (key == 39) // Right arrow
    {
      w3c_slidy.next_slide(!event.shiftKey);
      return w3c_slidy.cancel(event);
    }
    else if (key == 13) // Enter
    {
      if (w3c_slidy.outline)
      {
        if (w3c_slidy.outline.visible)
          w3c_slidy.fold(w3c_slidy.outline);
        else
          w3c_slidy.unfold(w3c_slidy.outline);
          
       return w3c_slidy.cancel(event);
      }
    }
    else if (key == 188)  // < for smaller fonts
    {
      w3c_slidy.smaller();
      return w3c_slidy.cancel(event);
    }
    else if (key == 190)  // > for larger fonts
    {
      w3c_slidy.bigger();
      return w3c_slidy.cancel(event);
    }
    else if (key == 189 || key == 109)  // - for smaller fonts
    {
      w3c_slidy.smaller();
      return w3c_slidy.cancel(event);
    }
    else if (key == 187 || key == 191 || key == 107)  // = +  for larger fonts
    {
      w3c_slidy.bigger();
      return w3c_slidy.cancel(event);
    }
    else if (key == 83)  // S for smaller fonts
    {
      w3c_slidy.smaller();
      return w3c_slidy.cancel(event);
    }
    else if (key == 66)  // B for larger fonts
    {
      w3c_slidy.bigger();
      return w3c_slidy.cancel(event);
    }
    else if (key == 90)  // Z for last slide
    {
      w3c_slidy.last_slide();
      return w3c_slidy.cancel(event);
    }
    else if (key == 70)  // F for toggle toolbar
    {
      w3c_slidy.toggle_toolbar();
      return w3c_slidy.cancel(event);
    }
    else if (key == 65)  // A for toggle view single/all slides
    {
      w3c_slidy.toggle_view();
      return w3c_slidy.cancel(event);
    }
    else if (key == 75)  // toggle action of left click for next page
    {
      w3c_slidy.mouse_click_enabled = !w3c_slidy.mouse_click_enabled;
      var alert_msg = (w3c_slidy.mouse_click_enabled ?
                "enabled" : "disabled") +  " mouse click advance";

      alert(w3c_slidy.localize(alert_msg));
      return w3c_slidy.cancel(event);
    }
    else if (key == 84 || key == 67)  // T or C for table of contents
    {
      if (w3c_slidy.toc)
        w3c_slidy.toggle_table_of_contents();

      return w3c_slidy.cancel(event);
    }
    else if (key == 72) // H for help
    {
      window.location = w3c_slidy.help_page;
      return w3c_slidy.cancel(event);
    }
    //else alert("key code is "+ key);

    return true;
  },

  // safe for both text/html and application/xhtml+xml
  create_element: function (name) {
    if (this.xhtml && (typeof document.createElementNS != 'undefined'))
      return document.createElementNS("http://www.w3.org/1999/xhtml", name)

    return document.createElement(name);
  },

  get_element_style: function (elem, IEStyleProp, CSSStyleProp) {
    if (elem.currentStyle)
    {
      return elem.currentStyle[IEStyleProp];
    }
    else if (window.getComputedStyle)
    {
      var compStyle = window.getComputedStyle(elem, "");
      return compStyle.getPropertyValue(CSSStyleProp);
    }
    return "";
  },

  // the string str is a whitespace separated list of tokens
  // test if str contains a particular token, e.g. "slide"
  has_token: function (str, token) {
    if (str)
    {
      // define pattern as regular expression
      var pattern = /\w+/g;

      // check for matches
      // place result in array
      var result = str.match(pattern);

      // now check if desired token is present
      for (var i = 0; i < result.length; i++)
      {
        if (result[i] == token)
          return true;
      }
    }

    return false;
  },

  get_class_list: function (element) {
    if (typeof element.className != 'undefined')
      return element.className;

    return element.getAttribute("class");
  },

  has_class: function (element, name) {
    if (element.nodeType != 1)
      return false;

    var regexp = new RegExp("(^| )" + name + "\W*");

    if (typeof element.className != 'undefined')
      return regexp.test(element.className);

    return regexp.test(element.getAttribute("class"));
  },

  remove_class: function (element, name) {
    var regexp = new RegExp("(^| )" + name + "\W*");
    var clsval = "";

    if (typeof element.className != 'undefined')
    {
      clsval = element.className;

      if (clsval)
      {
        clsval = clsval.replace(regexp, "");
        element.className = clsval;
      }
    }
    else
    {
      clsval = element.getAttribute("class");

      if (clsval)
      {
        clsval = clsval.replace(regexp, "");
        element.setAttribute("class", clsval);
      }
    }
  },

  add_class: function (element, name) {
    if (!this.has_class(element, name))
    {
      if (typeof element.className != 'undefined')
        element.className += " " + name;
      else
      {
        var clsval = element.getAttribute("class");
        clsval = clsval ? clsval + " " + name : name;
        element.setAttribute("class", clsval);
      }
    }
  },

  // HTML elements that can be used with class="incremental"
  // note that you can also put the class on containers like
  // up, ol, dl, and div to make their contents appear
  // incrementally. Upper case is used since this is what
  // browsers report for HTML node names (text/html).
  incremental_elements: null,
  okay_for_incremental: function (name) {
    if (!this.incremental_elements)
    {
      var inclist = new Array();
      inclist["p"] = true;
      inclist["pre"] = true;
      inclist["li"] = true;
      inclist["blockquote"] = true;
      inclist["dt"] = true;
      inclist["dd"] = true;
      inclist["h2"] = true;
      inclist["h3"] = true;
      inclist["h4"] = true;
      inclist["h5"] = true;
      inclist["h6"] = true;
      inclist["span"] = true;
      inclist["address"] = true;
      inclist["table"] = true;
      inclist["tr"] = true;
      inclist["th"] = true;
      inclist["td"] = true;
      inclist["img"] = true;
      inclist["object"] = true;
      this.incremental_elements = inclist;
    }
    return this.incremental_elements[name.toLowerCase()];
  },

  next_incremental_item: function (node) {
    var br = this.is_xhtml ? "br" : "BR";
    var slide = w3c_slidy.slides[w3c_slidy.slide_number];

    for (;;)
    {
      node = w3c_slidy.next_node(slide, node);

      if (node == null || node.parentNode == null)
        break;

      if (node.nodeType == 1)  // ELEMENT
      {
        if (node.nodeName == br)
          continue;

        if (w3c_slidy.has_class(node, "incremental")
             && w3c_slidy.okay_for_incremental(node.nodeName))
          return node;

        if (w3c_slidy.has_class(node.parentNode, "incremental")
             && !w3c_slidy.has_class(node, "non-incremental"))
          return node;
      }
    }

    return node;
  },

  previous_incremental_item: function (node) {
    var br = this.is_xhtml ? "br" : "BR";
    var slide = w3c_slidy.slides[w3c_slidy.slide_number];

    for (;;)
    {
      node = w3c_slidy.previous_node(slide, node);

      if (node == null || node.parentNode == null)
        break;

      if (node.nodeType == 1)
      {
        if (node.nodeName == br)
          continue;

        if (w3c_slidy.has_class(node, "incremental")
             && w3c_slidy.okay_for_incremental(node.nodeName))
          return node;

        if (w3c_slidy.has_class(node.parentNode, "incremental")
             && !w3c_slidy.has_class(node, "non-incremental"))
          return node;
      }
    }

    return node;
  },

  // set visibility for all elements on current slide with
  // a parent element with attribute class="incremental"
  set_visibility_all_incremental: function (value) {
    var node = this.next_incremental_item(null);

    if (value == "hidden")
    {
      while (node)
      {
        w3c_slidy.add_class(node, "invisible");
        node = w3c_slidy.next_incremental_item(node);
      }
    }
    else // value == "visible"
    {
      while (node)
      {
        w3c_slidy.remove_class(node, "invisible");
        node = w3c_slidy.next_incremental_item(node);
      }
    }
  },

  // reveal the next hidden item on the slide
  // node is null or the node that was last revealed
  reveal_next_item: function (node) {
    node = w3c_slidy.next_incremental_item(node);

    if (node && node.nodeType == 1)  // an element
      w3c_slidy.remove_class(node, "invisible");

    return node;
  },

  // exact inverse of revealNextItem(node)
  hide_previous_item: function (node) {
    if (node && node.nodeType == 1)  // an element
      w3c_slidy.add_class(node, "invisible");

    return this.previous_incremental_item(node);
  },

  // left to right traversal of root's content
  next_node: function (root, node) {
    if (node == null)
      return root.firstChild;

    if (node.firstChild)
      return node.firstChild;

    if (node.nextSibling)
      return node.nextSibling;

    for (;;)
    {
      node = node.parentNode;

      if (!node || node == root)
        break;

      if (node && node.nextSibling)
        return node.nextSibling;
    }

    return null;
  },

  // right to left traversal of root's content
  previous_node: function (root, node) {
    if (node == null)
    {
      node = root.lastChild;

      if (node)
      {
        while (node.lastChild)
          node = node.lastChild;
      }

      return node;
    }

    if (node.previousSibling)
    {
      node = node.previousSibling;

      while (node.lastChild)
        node = node.lastChild;

      return node;
    }

    if (node.parentNode != root)
      return node.parentNode;

    return null;
  },

  previous_sibling_element: function (el) {
    el = el.previousSibling;

    while (el && el.nodeType != 1)
      el = el.previousSibling;

    return el;
  },

  next_sibling_element: function (el) {
    el = el.nextSibling;

    while (el && el.nodeType != 1)
      el = el.nextSibling;

    return el;
  },

  first_child_element: function (el) {
    var node;

    for (node = el.firstChild; node; node = node.nextSibling)
    {
      if (node.nodeType == 1)
        break;
    }

    return node;
  },

  first_tag: function (element, tag) {
    var node;

    if (!this.is_xhtml)
      tag = tag.toUpperCase();

    for (node = element.firstChild; node; node = node.nextSibling)
    {
      if (node.nodeType == 1 && node.nodeName == tag)
        break;
    }

    return node;
  },

  hide_selection: function () {
    if (window.getSelection) // Firefox, Chromium, Safari, Opera
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<body>
<div class="slide titlepage">
<h1 class="title">Linear Mixed-Effect Modeling with R</h1>
<p class="author">
Clay Ford
</p>
<p class="date">spring 2022</p>
</div>
<div id="what-are-linear-mixed-effect-models" class="slide section level2">
<h1>What are Linear Mixed-Effect Models?</h1>
<ul>
<li><p>Linear models with fixed and random effects.</p></li>
<li><p>LME (<strong>L</strong>inear <strong>M</strong>ixed-<strong>E</strong>ffect) models are suitable for clustered, longitudinal or repeated-measures data in which the data are grouped by <em>random levels</em> and the dependent variable is continuous.</p></li>
<li><p>“Grouped by random levels” means there are several observations that belong to a single subject or group that can be thought of as a random sample from a population.</p></li>
<li><p>These groups are sometimes referred to as “random effects”.</p></li>
</ul>
</div>
<div id="candidate-for-linear-mixed-effect-modeling" class="slide section level2">
<h1>Candidate for linear mixed-effect modeling</h1>
<ul>
<li><p>We have a new medical treatment. We carry out an experiment where we randomly prescribe the treatment or placebo to patients and collect response data every week for two months to gauge efficacy.</p></li>
<li><p>Treatment is the <em>fixed effect</em>. Other fixed effects may include age, gender, weight, time, etc. If we were to replicate this study, we would use these variables again.</p></li>
<li><p>The data is grouped by patients, a sample from a population. We will likely have <em>random effects</em> associated with patients. If we were to replicate this study, we would not use the same patients again.</p></li>
</ul>
</div>
<div id="another-candidate-for-linear-mixed-effect-modeling" class="slide section level2">
<h1>Another candidate for linear mixed-effect modeling</h1>
<p>We have a new computer-based math curriculum. We carry out an experiment where we randomly prescribe either the new curriculum or current curriculum to teachers in various schools and measure change in student pre- and post-test scores.</p>
<ul>
<li><p>Curriculum is the <em>fixed effect</em>. Other fixed effects might include gender, race, etc. If we were to replicate this study, we would use these variables again.</p></li>
<li><p>The data is grouped by school, and teacher within school. We will likely have <em>random effects</em> associated with schools and teachers. If we were to replicate this study, we would not necessarily use the same teachers and schools again.</p></li>
</ul>
</div>
<div id="example-of-fixed-effect-vs-random-effect" class="slide section level2">
<h1>Example of fixed effect vs random effect</h1>
<p>In our medical treatment example, let’s say we add <code>age</code> to our model.</p>
<p>We get a coefficient for <code>age</code> that summarizes the relationship between <code>age</code> and the response.</p>
<p>If we think the relationship between <code>age</code> and the response <em>varies between patients</em>, we “add a random effect for <code>age</code>”. This produces an estimate of variability of how the <code>age</code> coefficient differs between patients.</p>
<p><strong>Fixed effects have coefficients.</strong><br />
<strong>Random effects have estimates of variation.</strong></p>
</div>
<div id="specification-of-a-linear-model" class="slide section level2">
<h1>Specification of a Linear Model</h1>
<p>Let’s review the specification for a basic linear model:</p>
<p><span class="math display">\[\boldsymbol{Y} = \boldsymbol{X\beta} + \epsilon \]</span> <span class="math display">\[\epsilon \sim N(0, \sigma)\]</span></p>
<p>where <span class="math inline">\(\boldsymbol{X\beta} = \beta_0 + \beta_1 X_{1} + \beta_2 X_{2} + ... + \beta_k X_{k}\)</span>.</p>
<p>This says our dependent variable (<span class="math inline">\(\boldsymbol{Y}\)</span>) is equal to our independent variables (<span class="math inline">\(\boldsymbol{X}\)</span>) multiplied by coefficients (<span class="math inline">\(\boldsymbol{\beta}\)</span>) and added up, plus some random error (<span class="math inline">\(\epsilon\)</span>) that comes from a Normal distribution with mean 0 and standard deviation <span class="math inline">\(\sigma\)</span>.</p>
<p>A key assumption is the independence of the random errors (ie, independent observations).</p>
</div>
<div id="simple-data-for-a-linear-model" class="slide section level2">
<h1>Simple data for a linear model</h1>
<p><img 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" width="768" /></p>
</div>
<div id="fitting-a-linear-model-in-r" class="slide section level2">
<h1>Fitting a linear model in R</h1>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>m1 <span class="ot"><-</span> <span class="fu">lm</span>(y <span class="sc">~</span> x)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">coef</span>(m1) <span class="co"># model coefficients</span></span></code></pre></div>
<pre><code>## (Intercept) x
## 0.5525 0.7940</code></pre>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m1)<span class="sc">$</span>sigma <span class="co"># estimate of error standard deviation</span></span></code></pre></div>
<pre><code>## [1] 0.3611</code></pre>
</div>
<div id="visualizing-a-linear-model" class="slide section level2">
<h1>Visualizing a linear model</h1>
<p><img 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YFv0UuRABgU5b8cU7GOBFBcGgDlFBdzOvUYAWP8ZJCBV/57YziUcfMvARSXBkA5xcGcTl1GQGszebskAVAotZgvfu0bJZiC1775ld8q3ZkbZdz8LwVw3SUJINEgh3JgAZxOfUZAYzOZuyQBUCiVmN88fbMIU/LiN6dfL9uZO2Xc/C8EcNslCSDRIIciAZRjmtZe71N47yQACqUOUzpHl1E+O5X8dbGgjJv/hwDu+7T8a8BHkQAoFAmgHNOy8nqnIrsnAVAoVZji39ELKZ/WGWDg/N8FsCxk/iWASooEUI5pWXm1U7H9G1YA759O7z2+/OLdl38n2fUXv/bS5ubD7U/vb8Y3Nl8n2vdu8f3l9HLZyc9ev/fN+/LHzPrpy0uiza5e/vmj7TePbwcacxe7lP/6tNirl/rN9TfeVBlg4Pz7BQDMvwRQSTmwAEY6CHav7e8/gT0cVgB/fVpO+W9WOgjUZ7c+nV+c3zgCWH4d3wv/FrcCuG/xN16++nyxwuev30wJ4LH9hwA+u24t0pi7+O9tN/y6i1dxfPH+cp8vsIrjAAPn3ysAZP4lgErKkQUw0Glw95pfAG8/Pa1nwN+Ivv55Mb/dZ7xrPSbsb2y+ju5FYIsbATz+pLi8brHrl79ckgK4b/8ugHfs26/nwcbii9+s9nH5uvuW3/i3GK+B8z+mAH76w6enD/7Zz0oHQEX/FSUBlFM2mB759zaTD1pkfm8B1Ob/8dFI3gdALxPety4fc6w+2Xi39nvBr6N7EdrirT6/zLkvv+W//Cr9eN3986s3l+8kBXDf/ueLNW+/nSd2I7D4Za++8VuXxb9+e903rp8XXfX0WaCxaA2cf+9B4L0F8MnTa33nz0sHAKUkgHLKbs2U/Kr1eO3OAqjO/+OTlKwPgF4scfsEZvV77eeOPVZfx/YiuMVbvX/ZwU9viz8/LT4EemF8dl2SFsBttr8J4PP1JzeR3Qgt/vS2zU8vs/wX7y/ezl931i0pTzMd5v+q/HtPA91ZAD//8IM/ePv2Fz98+l7pAKDU0efMHpS9monk2FOPV8bW6y6AhvzfJtbQ/Luux2+zb9YfbX/qfNK9+jq2F8EtPjb0jfXST29uuXwIdJ9zUwL4tXuHNwF8+nBeYjdSe3nb5Ge+v6Ky/rRyajcBpPPvvxAMmP8KAXz89IPLOPgd91egBDi+Y6g6+JzZhbJTM9HfZKIVWau7ABry/8X1Q6D3s45VPuZ154ONN85vuauvV3vx/nt5W7zU3Uvv3/30eN3rh0D3D7GWzTqQ15f+xv2VNwEsTg1K7EZi8esmX77tvg2vlfW3lVN7CSAj/6tbQTz+i8t//UHgrz6SAPpjOJTpBDDAhWBV+f/s9aORT/M+qH5McJ+vV3g3P/83rwdaf93zdUwAwS3etnOdeVcCeO++xuk/u3+VFMD9466rAG6fIWXsRmLx3RAve/kfXj9u+tZqWfFnQPMJYIQLwX7+4Xfdw2AJcHzHUHXsObMPZT4BRCgkAdTl/+UX1C/ezztV5f3lRPje4/vuyS/rr2MCCG3xUo/J/vG6xQc3lzODfmPZjRdyXX35cdfzTX05u5Fa/B/evx8CeO/T5ftwa6L4TNAJBRDeQZYA/uLDpx/d/v3ta9VuS2WzHgNg7z0pr8r8/3+Xyfrv5SDeTXD/7X2t9x7f/+vH+3b6hufr5SbeW38Z2OJt6W2//t/TdenL7t5f93LSzd/17ae7pXcr/Vev//27l71777LJl29m7EZ88eupoN+87du2778M7GRhUSKZkf/rosv/tv8F7EPdah8/PX3wx/evJABVVU07/9fn/y890/Sb06pu81doInzZxDffLfnL9y+Tqvv1okoE8NePuf5FKe+9k8Hrhbe1AvjLy95cN/sGJIDXS4RfX3ARwLecvv96+/bWFCeT6fwPKoCv/+U//fDpg3/ufjvxp0f8TxNUHftTkz6UKU4DzaUQPgJqyf+brDOAXur95XmT7/lfsT7l5eXr+EdAkS2+WWxsqaTb6z4r+wjodjz2+jHOm8e6qcaSfV82/PLJ1/WFi13//FR+JcAcp4EO9hHQ258u/gYuGQC96+hzZg/Kfs3A53/aMYDa/OdfqpT4LNzz/Zeva48BrI9M3AzwrfeXB4FP9yk3RwCXq928Amg5BvB8PTl1cTHd4nVzCaDgQjDvf30UlgDefvnkHgVLgOM7hqrDz5kdKJaaqQ88Jv/5AkieDeO9JPjtbd1lPc6rD27R2a/Lpz+/9fnyNNBv3E5jvXbjhzxm8Nf7XXgE0HoW0GXCX1zztXgfJhNACjSyALanQSTA8R1D1RjTDArDoVhqpj7wmPznC2B1Prz36qawAK4Vuw7A2aL/oqvPFheCvfvl/36OTc5fAJfPaj5/3F3otv1EY7l9v7+8/ve2D8vTTXNLAiipr398/dNXAiBgOBRLzRQHHpz/fAGEroh9/OZ7ecX665gAYtfY+s9NfbP8Zf75cQQjTwAvv6T/yvY00Morgd2Phu5XKS/f05lOA80ADSiAtx9fr4H/eHMtfAIc3zFUjTHNoDAciqVmygOPzb9HAM5HKbdfYEP3xHlz28L1xgzrr2MCiNyEZ/Vx+30fb5cG3D9vv30IlCeA64Hj957Xv5lX3gvozerjqOUdVRcHw7Nus+qUBFBUP//w6fd+9vbrP3v64E9qBkDvGmOaQWE4lO6Y12NdYzRTHnhs/gvuV/kihm/674r53t+/fEx/u3fn4+uYAEJbdHfret/NL97cZu3Hw2yuv2FnCuDitveu37wDwruR0/dnt7OR3r+87rP3F6L4NHDcOFb9BRDO/4QCePvl5W6IH7gnQUgAeAyH0htzPdu5M+VS/Y8BtOW/QACfP07FfJ3fbmc7Lv5i+PXN11EBhLa4/DxlvcX3rguXU/q7dXMF8HqV8m0b99e5u/Fr649tMvr+O+vXPfZ9yJvBRfI/owDe/uL338X/+z/ZfD8Bju8YqsaYZlAYDqUz5jZK+1KuRTgI3JT/kjvWOw/Ouk/Xb9bfX30dFUBwi+6n8atnby0fCHb9EChXAK/A967rPT7PWe/G5yfnoyDniWDbvr/hvO7xqMkRbwcdy/+UAghVAhzfMVQdY868YTiUvpjH72ldMdeinQVUmf+iR5asH537mK4vT+x9PFJ38XVcAMEturfWvDxs91uvq6ye8Xv5EChbAI/bc65uWr3ajS9Wz5BcLr6f07ru+++vX/feY13QA2GgAojmXwJA1yHmzDuGQ5EAlP9CSjlm8UjIbX3uP3WnmIJ5JKQEoAGQokgA2SUB5OwXqsaNzGeRT2c+8y8qpbyTDOCh8M8SgAZAiiIBZJcEkLNfqBo4Mp+GT9B53//HQSnlTcUHQBKABkAFRQLIL+b8LwFwKFWYN6EzdN68F8CUbf+zqvlfB4E1AMopEkBBXfI/RjPIwCv/heU3wBfvfzOEKdp65fyv00A1AMopEkBJvf7+M0YzyMAr/6VVOEcXUX7zFPJIitJbAAe7EEwDQAKownAoEgCDUov54tdKDFBCefMr5ef/XCndBfC6PYoAzhIAh2JpzkRhOBQJgEE5eGRmFcD5nNpzJ7MSQCVljgGQd+h1kmYyKRIAgzJHZKrzP6kAzi8COEe36GRWAqikTDEAMk++maOZXIoEwKBMEZn6/M8pgLMEoAGwqNzTL6doJpsiATAoM0SmIf9TCuB8EUB8T5zMSgCVlAkGQPYFWDM0k0+RABiUCSLTkn8JQAMgTjn4AOhRY/xkkIFX/ntjWla2JoCzBPDK4VAOPgB61Bg/GWTglf/emJaVjQngMv8n99zJrARQSTn4AOhRY/xkkIFX/ntjWla2JYDXw78SgAbAonQQ2Lu8WzXtF6rGeJdRmKa1LR0Evpz/c07vuZNZCaCSMsMA0Gmg3uXdqmm/UDXGu4zCtK1u5zTQxwmgEgCHMsUA0IVgvuXdqmm/UDXGu4zCNK5v5UKwxeFfCYBDmWMAZFIsNYMMvPLfG9O6gayJfHoBnCWABYdDmWQA5FEsNYMMvPLfG9O6AQnALSezEkAlZZIBkEex1Awy8Mp/b0zrBkwIYHX+jwTAoUwyAPIolppBBl75741p3YAFAazP/5EAOJRJBkAexVIzyMAr/70xrRswIICzBLDmcCiTDIA8iqVmkIFX/ntjWjdwfAG4J4BKABzKJAMgj2KpGWTglf/emNYNHF4Am8O/EgCHMskAyKNYagYZeOW/N6Z1A0cXwPb8HwmAQ5lkAORRLDWDDLzy3xvTuoGDC+AsAWw5HMokAyCPYqkZZOCV/96Y1g0cWwCX8z/Pvj8NguVkVgKopEwyAPIolppBBl75741p3cChBXC7AagEsOJwKJMMgDyKpWaQgVf+e2NaN3BkAdzP/5QAVhwOZZIBkEex1Awy8Mp/b0zrBg4sgMUT4CWAJYdDmWQA5FEsNYMMvPLfG9O6gcMLILA4XE5mJYBKyiQDII9iqRlk4JX/3pjWDUgAbjmZlQAqKZMMgDyKpWaQgVf+e2NaN3BUAZwlgCCHQ5lkAORRLDWDDLzy3xvTuoGDCuC8fgK8BLDkcCiTDIA8iqVmkIFX/ntjWjdwTAHc5n8JwMfhUCYZAHkUS80gA6/898a0buCQArjP/xKAj8OhTDIA8iiWmkEGXvnvjWndwIEFEFwc3xMnsxJAJWWSAZBHsdQMMvDKf29M6waOK4Dw4vieOJmVACopkwyAPIqlZpCBV/57Y1o3cDwB3O7/E1gsAWgAlFMsNYMMvPLfG9O6gcMJ4PH5v3exBKABUEGx1Awy8Mp/b0zrBo4mgPX8LwH4OBzKJAMgj2KpGWTglf/emNYNHEwAzvwvAfg4HMokAyCPYqkZZOCV/96Y1g0cUgDBxRkblABAlEkGQB5lkGZOJ8C4kwAolEEik6qpBODJv08A4cXuBn3lZFYCqKRMMgDyKGM0czohDCABUChjRCZZMwnAl3+PACKLnQ16y8msBFBJmWQA5FG4zQSm+dMJYgAJgEKZJP8jCmAV8sc/vflfzvC3538FFksAVw6HMskAyKNQmwlM86cTxgASAIUySf4HFMA65Pd/+fO/mOHdA8DOYgngxuFQJhkAeRRmM6FpXgLA1AEj01DjCcBJebYAfPO/BODjcCiTDIA8CrGZ4Dx/WlYLRQJgUCbJ/3ACcDPuEYDnE6LtCaDOYve/4XIyKwFUUiYZAHmU4QTQMPwkAAplkvxPKgD3E6LtCaDOYve/4XIyKwFUUiYZAHmUEQSAMoAEQKFMkv95BODP/1oAod2UAJYcDmWSAZBHGUIAIANIABTKJPmfSADe/F/+f96eALpaWwJYcjiUSQZAHmWEg8DPzgiopkgADMok+R9OAMGDwM/e/F/O//R//vMsAXg5HMokAyCPMsJpoMuFEkB9HTEy9TWeAEKngT4WuQIIz/8SgI/DoUwyAPIo3GZi07sE0FqHjEx1DSiA0IVgzwEBROZ/CcDH4VAmGQB5lIGaaZ3/JQAOZaDIxGpEATgf+6xftfmEKDb/SwA+DocyyQDIo4zUTOP8LwFwKCNFJlLTCWDzCVFs/pcAfBwOZZIBkEcZqpm2+V8C4FCGiky45hOA+wlRbP6XAHwcDmWSAZBHsdQMMvDKf29M6wYmFMDyW8HzP9drSwBLDocyyQDIo1hqBhl45b83pnUDswsg+vu/BODlcCiTDIA8iqVmkIFX/ntjWjcwtwBS878E4ONwKJMMgDyKpWaQgVf+e2NaNzC1AJLzvwTg43AokwyAPIqlZpCBV/57Y1o3MLMAoieArtaWAJYcDmWSAZBHecE0nnyTg+m7+Usl20AGXvnvjWndQL4A1sEZQAAZ879HAKX5lwAqKZMMgDzK2/bT73MwXbd+qXQbyMAr/70xrRvIFoATnP0FkDP/bwVQnH8JoJIyyQDIo7xtvwA3B9Nz45fKaAMZeOW/N6Z1A7kCcIOzuwCy5v+NAMrzLwFUUiYZAHmUt+234MnBdNz2pXLaQAZe+e+Nad1ApgA2wdlbAGfPE+ADm12sV5F/CaCSMskAyKPsIYAeMAlA+V/XuAK4wvwCOF8EkLXZZwlgzeFQJhkAeZQdBNCFJgEo/+saVgA3mlcA54sA8jb7LAGsORzKJAMgj8IXQB+cBKD8r2tUAdxxEQFkbvZZAlhzOJRJBkAehX4QuJdwMraKDLzy3xvTuoFBDwIH5upWAegg8LMGQA2Ffhpot7840htFBl75741p3cCgp4HGBHBuEIBOA9UAqKHQLwTr95FTcpvIwCv/vTGtGxj0QrCIAG7nf9YJQBeCaQBUUOjN9BOAbgXBoUyS/3wB+D6Nx1W2AO7n/1cKoDT/EkAlZZIBkEfhN9PvmIMEQKFMkv9BBRA8CPy4/ksCqCwNgHLKDs10O+YgAVAok+R/VAGETgN9XP8rAVSWBkA5ZY9meh1zkAAolEnyP6wAAheCPe7/IAFUlgZAOcVSM8jAK/+9Ma0bGFcAq//eFzzu/yMBVJYGQDnFUjPIwCv/vTGtG5hKAKv7/4N2ci8AACAASURBVEgAlaUBUE6x1Awy8Mp/b0zrBmYSwPoGoBJAZWkAlFMsNYMMvPLfG9O6gYkE4NwAWgKoLA2AcoqlZpCBV/57Y1o3MI8A3AcASACVpQFQTrHUDDLwyn9vTOsGphHA5gEwEkBlaQCUUyw1gwy88t8b07qBWQSwfQCYBFBZGgDlFEvNIAOv/PfGtG5gEgF4HgApAVSWBkA5xVIzyMAr/70xrRuYQwDn5QUAJXsgAXg4HMoYAwBzOe0gzYAoEgCDMkZkkvmfQgDeBwBLAJVlaQCAbqgzRjP1tXoTJAAKZYjIpPM/gwD8DwAuEMDqrhISAIcywgBA3VJziGbqa/0mSAAUygiRycj/BAIIPAA4XwDr+8pJABzKAAMAdlP9EZqpL+dNkAAolAEik5P/aQTgXSNrs86dpSUADmWSAZBHGaCZ6nLfBQmAQhkgMhLA8+m0eBckgAuHQ5lkAORRBmimuiQAh8OhDBCZIwgg/ABgCaCyNADKKQM0U10SgMPhUAaIzAEEEHkAsARQWXYGgA4Cv5QE4HA4lBEik5H/sQUQewCwBFBZhgaATgN9KWcakAAolCEik87/0AKIPgBYB4Ery9IA0IVgL7WeBiQACmWMyCTzP4EAAjidBlpZpgYAiDJ5M6tpQAKgUAaJTGqaHF8AIZwuBKssWwMAQ7HUDDLwyn9vTOoF8wrgnHgAcIEAVl9IABzKIAMAQ7HUDDLwyn9vTOoFswsgjJMAKsvWAMBQLDWDDLzy3xuTesG0Akg+/1ECqCxbAwBDsdQMMvDKf29M6gWzCiD9/EcJoLJsDQAMxVIzyMAr/70xqRdMKoCMBwBLAJVlawBgKJaaQQZe+e+NSb1gagFEcRJAZdkaABiKpWaQgVf+e2NSL5hZAHGcBFBZtgYAhmKpGWTglf/emNQLJhaAu9izRtZmnS8kAA5lkAGAoVhqBhl45b83JvWCGQWwfQC8BAAsWwMAQ7HUDDLwyn9vTOoFEwrAPQAcwEkAlWVrAGAolppBBl75741JvWA+AfjmfwkAWLYGAIZiqRlk4JX/3pjUC6YTgHf+lwCAZWsAYCiWmkEGXvnvjUm9YDYB+Od/CQBYtgYAhmKpGWTglf/emNQLJhNAYP6XAIBlawBgKJaaQQZe+e+NSb1gLgGE5n8JAFi2BgCGYqkZZOCV/96Y1AumEsB5dQdQd3H6W4n1JIALh0MZZABgKJaaQQZe+e+NSb1gJgGcLwIILU5/K7GeBHDhcCiDDAAMxVIzyMAr/70xqRdMJIDzRQChxRnfSqwnAVw4HMogAwBDsdQMMvDKf29M6gXzCOB8EUBocc63EutJABcOhzLIAMBQLDWDDLzy3xuTeoEE4H4hAXAogwwADMVSM8jAK/+9MakXSADuFxIAhzLIAMBQLDWDDLzy3xuTesEkArid/ykB9C9bAwBDsdQMMvDKf29M6gVzCOB+/r8E0L9sDQAMxVIzyMAr/70xqRdMIYDr/P9WAmCUrQGAoVhqBhl45b83JvWCGQRw+/1fAqCUrQGAoVhqBhl45b83JvWCCQRw//xHAqCUrQGAoWRgTqfmMTFGM8jAK/+9MakX0ARQnf/H/X8kAErZGgAYShpzOrUbIEwB2OVBkQAYlEHyzxJAdf4X938LC8C37RkFoDpqna7Vc+t9tq06dKViUxCr1Uud9arzf73/W3x3vNvOgsX2Oa/0F0AlZZDfgDCUFOZ0ryZMYust215Q9BcAgzJI/jl/AVTnf3X/t9BfAP5tz/gXQAKc0RCgbA0ADGVXAWA2/qBIAAzKIPkfWwDr+78FBBDYuARQWbYGAIYiASj/hZRB8j+0AJy7P0gAlLI1ADAUCUD5L6QMkv+RBXCWANbgjIYAZWsAYCgZ4wwwRRcJoJomAVAog+SfdBZQ/fxfK4A8mgTg4XAogwwADGXf00BD+a/jSQAUyiD5H/c00O3930oOAmfyJAAPh0MZZABgKDtfCBbKfxVRAqBQBsn/sBeC3c//SQugIf8SgIfDoQwyADCUvZsJ5b/GABIAhbJ3ZK7FuxVE+e//l/N/MgRQn38JwMPhUAYZABjKaM1IAPVlKzJjC2C9XlgAW5YEUF22BgCGMlozEkB92YrMoAI4SwAecEbngLI1ADCU0ZqRAOrLVmTGFMBZAvCBMzoHlK0BgKEM14wOAleXrcgMKYBzqwB0ELihbA0ADKUOUzpDl1B0GmhtDR2ZYkzqBXsKIJTQ6w3gnhsEoNNA68vWAMBQqjDFc3QRpfq0UwmAQhkk/zsKIJR/5wTQOgHoQrDqsjUAMJQaTPmnNGM0gwy88t8bk3rBfgII5d89AbRSAHklAXg4HMogAwBDqcBUHKcdoxlk4JX/3pjUC3YTQCj/m0//JYA7uLXbvLI1ADAUlADiPhijGWTglf/emNQLxhLA6fXDfwkgAG7tNq9sDQAMBSSAxF8EYzSDDLzy3xuTesFQArjN/xKAH9zabV7ZGgAYCkYAqc+ExmgGGXjlvzcm9YKRBHCf/58lAC+4tdu8sjUAMBTIQWD/p6KLr8doBhl45b83JvWCgQ4Cv8z/FwUsp/51/iWA/mVrAGAokNNAg0cFbt8Yoxlk4JX/3pjUCwY6DfRl8n8VwGkhACf/EkD/sjUAMJQ6jHeu90vhgmnYxfySACiUQfI/0IVgp8cFwHcBuPmXAPqXrQGAoUAwkaMC12giKMmSACiUQfK/pwCcb93n/4cANvmXAPqXrQGAoWAw4T8AJADlvw6TesE4AljM/xKAH9zabV7ZGgAYCggTOAIgAeTsF6rGeJdRmNQLhhHAcv6XAPzg1m7zytYAwFACGGc6T5e7ggSQv1+oGuNdRmFSL+gqAOfjzNjGr+f/nNYngEoAK3Brt3llawBgKH7M5hf68mIeBL5yJAAKZZD89xTAOv9RAdxuALpaQD4IXJd/CaCSsvcAaJ6blxQvZvuRfkUtN9H3LbuRJAAKZZD8dxSAk/+YAO43AF0t4J4GWpl/CaCSsvMAAMzNC4oPs/7ztboWG+j6lt13VgKgUAbJfz8BuPmPCOBxA9DVAvdjpK4CqM2/BFBJ2XcAQObmB6WjAJYY1IY89dhbCYBCGST/Iwhgcfuf1QJ3jZ4CqM6/BFBJ2XUAgCdnCUD5L6UMkv8BBHCWADQAumH83x5PADmvkwAYZSv/+wtgdf7niioBOGBMz6myNQAwlOaDwFmvlAAYZSv/ux8Evt3/Z7UrEoAXjOk5VbYGAIbSehpo3t7oIDCjbOV/79NAr+f/nHyvZQpAB4EfHA5lkINgGEpknOWsnzkadRooo2zlv6cA1vn3CuB6/o+b/x0EoNNA7xwOZZDT4DCUxmaGEMBtuEoAFMog+e8qgNW3IgLY5H8PAVTmXwKopOw8ALJ/O8+iHEIAN4oEwKAMkn8JwC0JgEPZewBAKRKA8l9I2T3//knW/6oUpU4AZwlAA6A3hkNpxeQdkhijGWTglf/emPCi3QVwu//P9oQhCcAPbuk0v6wMACSlGZN1SGKMZpCBV/57Y8KL9hbA9fx/3wlDEoAf3NJpflkZAEhKOybnkMQYzSADr/z3xoQX7SyA+/zvOWFIAvCDWzrNLysDAEmx1Awy8Mp/b0x40RACCCAkAC+4pdP8sjIAkBRLzSADr/z3xoQX7SuAx/wvAWgAdMRwKJaaQQZe+e+NCS/aVQCL+V8C0ADoiOFQLDWDDLzy3xsTXrSnAM4SgAYAB8OhzNqM79CzBECh7B6ZHQWwfgDkjgIA5F8CqKTsPgCQlEmb8Z58KgFQKLtHZj8BOA+A3E8AiPxLAJWU3QcAkjJnM/7LzyQACmX3yOwmAPcBkLsJAJJ/CaCSsvsAQFKmbCZwAwoJgELZPTJ7CWDz/K+9BIDJvwRQSdl9ACApUzYjAfg5HMrukdlJANsHQEoAGgD9MBzKlM1IAH4Oh7J7ZPYRwFkC0AB4pew+AJCUKZuRAPwcDmX3yOwigNv5nxKABgAHw6HM2YwOAns5HMrukdlDAPfzP0cQgA4CBzgcyu4DAEmZtBmdBurjcCi7R2YHATzO/xxCADoN1M/hUHYfAEjKrM3oQjAPh0PZPTJ8ASzO/xxDALoQzMvhUHYfAMUVvmPzhM1EKBIAg7J7ZIoFkMp/pgDcze4pAF9JABzK7gOgtCLPbJmvmRhFAmBQdo9MqQCS+ZcANAAKKLsPgMLyHzG6UmZrJkqRABiU3SNTKIB0/iUADYACyu4DoKwC54xdKZM1E6dIAAzK7pEpE0BG/uMCWJ//KQFoAHAwqA1JAI/l3appv1A1xruMwoQXcQWwfADwswSgAbD/ACgrCeCxvFs17ReqxniXUZjwIqoAzhKABsCasvsAKCsJ4LG8WzXtF6rGeJdRmPAipgCcJ8BLABoA+w+AwtJB4PvybtW0X6ga411GYcKLiAeBFw8AkwA0AC6U3QdAaek00NvybtW0X6ga411GYcKLeKeBLh8AKQFoAFwouw+A4tKFYNfl3appv1A1xruMwoQX0S4E8z0AWALQAOBgOBRLzSADr/z3xoQXFQsg/NqoALwPAJYANAA4GA7FUjPIwCv/vTHhRVwBONuQADQAOBgOxVIzyMAr/70x4UUkAfgfACwBaABwMByKpWaQgVf+e2PCizgCCDz+SwLQAOBgOBRLzSADr/z3xoQXSQD+kgA4lN0HAJJiqRlk4JX/3pjwIgnAXxIAh7L7AEBSLDWDDLzy3xsTXkQQwFkC0AAIUXYfAEiKpWaQgVf+e2PCi/oLIPIEeAlAA4CD4VAsNYMMvPLfGxNe1F0A7g3gltuQADQAOBgO5YEJXy5ZXJtNjfGTQQZe+e+NCS/qI4BbaC8f/pxDT4DPEYAv/xJA/7IyAJCUOyZyw5TS2m5qjJ8MMvDKf29MeFEXAdxDexNAYBsZAvDmXwLoX1YGAJJyw8RumVhYnk2N8ZNBBl75740JL+ohgEdorwIIbSMtAH/+JYD+ZWUAIClXTPSm6WXl29QYPxlk4JX/3pjwog4CeNT1/J/gNpICCORfAuhfVgYAkiIBKP+FlN3z31MAqxuASgAaAB7K7gMASZEAlP9Cyu757yiA9fwvAWgAeCi7DwAkRQJQ/gspu+e/nwCc+V8C0ADwUHYfAEiKDgIr/4WU3fPf7SCwO//rILAGgIey+wBAUsCngb5uY7upMX4yyMAr/70x4UXdTgN15/9yAYTzLwH0LysDAEl5YFDz/3UErDGtG84qCYBC2T3/3S4Ec+f/YgFE8i8B9C8rAwBJgWKCnyON0Qwy8Mp/b0x4UR8BrM7/DG8jttlY/iWA/mVlACApSEz4SPIYzSADr/z3xoQXdRHA5vP/wDYim43mXwLoX1YGAJLSgnGjLgHU7ReqxniXUZjwoh4C8M7/CQEU5V8C6F9WBgCS0oDZZF0CqNsvVI3xLqMw4UUdBOCf/+MCKMu/BNC/rAwAJKUesw27BFC3X6ga411GYcKLugkgZxv3bxXmXwLoX1YGAJJSjfGlXQeBq/YLVWO8yyhMeFEvAWRt4/at0vxLAP3LygBA1DWnWAEELyYY4yeDDLzy3xsTXoQQwDL/vvN/gtuICSCWfwmgf1kZAIC6JRUsgNDFBGP8ZJCBV/57Y8KLAAJY5j/w+X9gG1EBRPIvAfQvKwOgve7ZRQsgUGP8ZJCBV/57Y8KL2gWwzH9k/i8XQKAkAEpZGQDN9Qgv9CBwuMb4ySADr/z3xoQXNQtgmf/Y/F94EDhcEgClrAyA5oIIIPiBp6fG+MkgA6/898aEFyEFEJ3/C08DDZcEQCkrAyBU2XnECCCfN8hPBhl45b83JrwoJIB1HrMEEJ//Cy8EC5cEQCkrAyBQ+b+RgASQX2P8ZJCBV/57Y8KLAgJw8l8ggARp9e+qiVwCoJSVAeCvks8klwfBGDXGTwYZeOW/Nya8yC8AN/85B4ET878EoAHgoew+ALz1+K0m/9XDNlNJkQAYlN0j4xXAJv8Zp4GeX68AiOyEBKABsKXsPgC8VSaA9gvBimqMnwwy8Mp/b0x4EUAAz9ff/yUADYBiyu4DwFuFArhRxmymkiIBMCi7RwYhgOfL5z/v/hvbCQlAA2BL2X0AeEsCkAA4lN0jAxVAdCckAA2ALWX3AeCvmvl/2GbqKBIAg7J7ZNoPAj9LABJANWX3ARCoivl/3GaqKBIAg7J7ZJpPA718SwLQAKii7D4AQlU+/w/cTA1FAmBQdo9M84Vgz/c7gEoAGgDFlN0HAJJiqRlk4JX/3pjwouCtIFbfigrgdgWwBKABUEzZfQAgKZaaQQZe+e+NCS9qF8D9DhASgAZAMWX3AYCkWGoGGXjlvzcmvKhZAI87AEkAGgDFlN0HAJJiqRlk4JX/3pjwolYBLO4AJwFoABRTdh8ASIqlZpCBV/57Y8KLGgWwvAOoBKABUEzZfQAgKZaaQQZe+e+NCS9qE8DqDtASgAZAMWX3AYCkWGoGGXjlvzcmvKhJAOsnwEsAGgDFlN0HAJJiqRlk4JX/3pjwohYBXO7/dvauESKt/i0BaABwMByKpWaQgVf+e2PCixoE4N4AVALQACim7D4AkBRLzSADr/z3xoQX1QtgcwNQCUADoJiy+wBAUiw1gwy88t8bE15ULYDz5u4PEoAGQDFl9wGApFhqBhl45b83JryoVgBnCWBZEkAlZfcBgKRYagYZeOW/Nya8qFIAZwlgVRJAJWX3AYCkWGoGGXjlvzcmvKhOALfzfySAa0kAlZTdBwCSYqkZZOCV/96Y8KIqAdzP/5EAriUBVFJ2HwBIiqVmkIFX/ntjwotqBPA4/0cCuJYEUEnpjnl9sAWe4ntezP6jGUmRABiU3fNfL4BT7EVB0urfEoAGQGfA5dF2cIr3iZESgPJfStk9/w0COEkA95IAKimdMVUPd6/drASg/JdSds9/sQDODwGcJIBbSQCVlL6Y06mLAQKblQCU/1LK7vkvFcD9/M/thiUADYBiyu4DALhZCUD5L6Xsnv9CAbjzvwRwKQmgkrL7AABuVgJQ/kspu+e/TACb+V8CuJQEUEnZfQAANysBKP+llN3zXySA7fwvAVxKAqik7H4QDLhZCUD5L6Xsnv8SAdyf/3XfrARwLQmgkrL7aXAtm3W+KQEo/6WU3fNfIIDV898v+ZcArlUlgJ/+/tPTB9//iQZAz3oNqi4EK6f0F4DyP0D+8wXgPP9XF4Itq0YAf/b0Wh/8iQZAdwyHYqmZisAr/1tKf8zLZIkQgPv8L++LUjvi/Nu0AL58+uAP3r79xY+ffufPNQB6YzgUS82UB17591BmE0DiRakdcf5tWQBf//jpRy///+qjy/81AHpiOBRLzRQHXvn3UaYRwObu/74XJXfE+bdlAXz10fU3n4+ffqAB0BvDoVhqpjjwyr+PIgEU10EEcC8NAAKGQ7HUTH3glf8FRQIoroMJ4KuP7kfBvn2t6m2pVLOV8t+5TvG56bLY86Llt+43gItuPIu0+ndijaxNjVH1O/TJ0/du/9QAUJkr5b9zAQRwfQCk51USwLWqd+hLnQbHwHAolpppGy/K/5Uyw0dAiwuAwy/ybyT0Wn0EdMv/hx+450BoAHTAcCiWmqkMvPK/pkwggMcFYBLAcvmqKgXwief3Hw2ADhgOxVIzdYFX/h3KNALwv0oCuFadAP7Mm38NADyGQ7HUTFXglX+XMr4AFjeAkACWy1dVI4CvP376jnsRpAZAHwxkK6nbik7VTJLSXQDK/wwCWM3/m5dJANeqEcDHT9/9mXdB046h6jAD4BWD2EjyxtIzNZOmdBeA8j+BADx3AN2+yPdFiLT6t2kBfBLKvwYAHgPYRvrW6hM1k0HpLQDl/3l8AVwvALh87cm/BHCtmltBPN3qe86iph1D1WEGwCumfRMZD1eap5kcSmcBKP+vlLEFcL0A4PKlL/8SwLXKBfDlkwZAr262D2vEbFMCWC5vK+X/ldI//w0CWN4BWgJwl69KTwSrpPTAbHMqAZRTKNcBKP8dNrqOab0Azss7QEsA7vJVSQCVlA4YT1AlgHKKBMCg9M9/qwCcrUoAt+WrkgAqKXiML6kjHAROnUSaXWP8ZJCBV/6B5eYfJIDmg8Cbz6WSawRKAqDUYQbAKwa34cgLos0k186uMX4yyMAr/8ACCeC8uQO0L8H5Ath+LpVaI1QSAKUOMwBeMbAtx5bHmkn//ZBdY/xkkIFX/oGFEcDt/P/15zb1F4J5PpdKrBEsCYBShxkArxg4xVeRZjKOIORj2jeRQ5EAGJRBBRC5Aahnbd8X6Z2KrxEuCYBS0w6ATgeBM0oCUP5LKWMeBI7dANSztu8L/z5JABoAa8o0p4FmlASg/JdShjwNdHX/hwQq9IVvlyQADQCX0v9CmFdMD8qmJADlv5TSP//lAljM/xJAePmqJIBKipVT53UQWPn3Ufpg3FPuiwSwnP9RAtBBYA0AP8WKAHQaqPLvo4wngMX9f55xAtBpoBoAXooZASAvBINtKkaRABiU4QSwvP/PM1AAyAvBBsy/BFBJsSMAHAb3x0SMIgEwKKMJYHX/n2ekAHzr1QlgxPxLAJWUPQTQKz75zTTtAfBwQqQkAAplDwF4fhe/fePsXP3bSQC3PagK8ZD5lwAqKTsIoFt8sptp2gPkCUWRkgAolB0E4Ps0/vr1mSOA+x7UZHjM/EsAlRS+APrFJ7eZtj0YcwAo/3UUvgC85+Nc/nvmCOCxBxKABgAH8/hnx/xkNtO4B2MOAOW/jkIXgBufhQD89//JBuVO54s9kAA0ADiYxz8lgLySACiUgQRwP/9HAniWAOYeABvM45/TC2DMg2DKfx1lOAF41s4EkQQwZv4lgErK4AIoChpJAEOeBqf811HGEcDj0//VOUKpk/tDX8TWaRPAkPmXACopxFPnr/8unf/zo8Y5CDzmhTDKfx2FJIBw/m9z/tkngGROdzgIPGb+JYBKCgfjRL5s/s8OG+c00EF+MsjAK//gcgUQyX9MAOn873Aa6CA/GSezEkAlhYLZ/NJTNv/nxpR0IdgYPxlk4JV/cDkCiOU/IoCM/NcJ4L4HEoAGQGwp6E+90om8dj1T97VABl7591d1/tcC2OR4c5T3+gDgZ5YA6td4HuMnIwGgKDFM2ycl7nYkgDKKBMCg9Ml/oQCcB0BKAM8SwABvc92sHdmQBFBCkQAYlD75LxOA+wBICeBZAtj/ba6dtoFbKlxNAlD+Syl98l8jgMeC7geBG9Z4HuAnc12+KgmgksIQQP3vUmWrSQDKfymFIYBN/teLNw+A7H0aaMsazwP8ZK7LVyUBVFIoAqj/NLVoNQlA+S+lUATg5t8jgOWC1SvjeAngWhJAJYUjgLeYzaQoEoDyX0jhCMDJf74ASkASgAZAOYVxEHiEZpAYDkUCYFAYB4GfXy+e9S9ePQFeAlhQJAAKhXEa6BDNADEcigTAoDBOA40IYD3/SwALigRAoTAuBBujGRyGQ5EAGBTGhWBhATjzvwSwoEgAFIqlOROF4VAkAAYljqn9/SdTAO78LwEsKBIAhWJpzkRhOBQJgEHZUwCb+V8CWFAkAArF0pyJwnAoEgCDsqMAtvO/BLCgSAAUiqU5E4XhUCQABmU/AXjmfwlgQZEAKBRLcyYKw6FIAAzKbgK4PAD47FtPAniWAAZ5m1EYDsVSM8jAK/+B6ieA+xPgPetJAM8SwCBvMwrDoVhqBhl45T9Q3QRwvj8B3rOeBPAsAQzyNgeq9ATpoZspxnAoEgCDUieAklv0RAQQWE8CeJYABnmb/VV8ieTIzZRjOBQJgEGpEkDRTTolgKqSADiUGkz5TVIGbabuSs8xmkEGXvkPlD8e6fzHBXAeRQAHyr8EUEmpwFTcJnHMZirv9TJGM8jAK/+B8qYjI/8JAZwXDwD2rMcSwJHyLwFUUgwLoPZuj2M0gwy88h+oLgJYPwDYsx5JAIfKvwRQSbErgOr7vY/RDDLwyn+gegjAeQCwZz2OAI6VfwmgkiIBHGMAKP91FLoA3CfAe9aTAJ4lgEHeZm+VB2fEZo41AJT/Ogr7IPDiBhASQJQiAaDL97M2fBrosQaA8p+sivzDTwNd3gBIAohSJABweX/YTReC5YdnjMw4VZn/QZpBBl75D64T3lYs/yEBrG4Ap4PAUYoEgC3/j7ulG8/2QnkaIzNu1eV/kGaQgVf+gytFFkTyHxDA+gZwewvgUPmXABIV+IOvoRvP9oKJGiMzm6rK/yDNIAOv/AfXCi+I5d8vAOcGcLsL4Ej5lwASBReAZ4Phvyl7vWdrmm4FofyHCi6AaP69AnBvAAcQwLqfmtm8oobMvwSQqAYB+Of07QYDiFdM+Q7nlEOTAJT/UDUIwJdonwAW3/EJ4Oze/qFdABsBZa7XVkPmXwJIVL0AAnP6AAJwcRKA8h+qegF4Iz2EALY7kLdeYw2ZfwkgVf7JOd1NaFLfXwAbngSg/AerKv/+j/qfxxDAZg8kAA2ASHnn5mQ34Vl9830JAEqRALBVk3/fPH9dEM3/RgDXG4BuFmx4gQXxnQtvsEcNmX8JIF2+qblBANsRFXylBFBBkQDAVZH/mABi+Xfn+fv5/xJANkUCoFAaBLAdUaEXSgAVFAkAXb4/TRsEEMm/M8/77/8jAUQpEgCF0iIA/6u9mOIdy6UtiRKA8h8rtAC2G7y9bj3PB+7/o4PAUYoEQKFUHwQuwzStHSxnzyQA5T9WNQIIHgT2b/D6HZ8APAsCe6jTQJ8lgEHe5ufI5zolmLbVg7XeMwlA+Y9VlQBCp4H6NxgWwHYX2gXg5F8C0AAoplRfCFaGaVw/kyIBKP+RqhOAN//5Arid/7PdBYAAvPDeNWT+JYBKiqU5E4XhUCQAdFUKoGSm3ghgdf9PCaCAIgFQKEPNmY1/a4zVTCtFAkDXDgK4zv9vneWB3fGcQ1RSEoAGQDFlpDmz9WjDUM00UyQAdPEFcPv9P08At/xLAM8SwCBvMwqTNlwA/QAAIABJREFU86Lm841GaqadIgGgiy6A++c/WQK4518CeJYABnmbUZiM15RdceCljNMMgCIBoGsnATznCSB4zUF2SQAaAMWUceZMCWBNkQDQxRbA4/ivBFBOkQAolHHmTAlgTZEA0EUWwOL8HwmgnCIBUCjjzJkSwJoiAaCLK4DlA4AlgHKKBEChDDRn6iDwiiIBoIsqgNUDgHUQuJwiAVAoI82ZOg10SZEA0MUUwPoBwDoNtJwiAVAoQ82ZuhBsQZEA0MUXwB3j2wVdCBalIATwN//DP/y/NQCiFEtzJgrDoQAEoPyvangBpBYkSgLYDIDfPZ3+83/87zUAwhRLcyYKw6EgBKD8L4smgLME0E5BCOBv/9Xrp2r/xb8oGwNNO4aqMd5mFIZDsdRMTpCV/1XxBHB2HgAsAZRTQMcA/q//6XUM/Pf/QgPAS7E0Z6IwHArmGIDy/yiWALYPAJYAyim4g8D/7jIG/sG/sT4AfBRLcyYKw6HADgIr/9ciCcDzAGAJoJyCPAvob//d//gyBH7pH+cdEmvaMVSN8TajMByKpWZyZ3Pl/14cAfieAC8BlFPAp4H+p//lt1//FM75Nahpx1A1xtuMwnAolprJmsqV/2VRBOB9ArwEUE6B/gXwv/9396us/6HdAeCjWJozURgOBfkXgPL/UkQBODwJoJwCE8At/S/nQvynf3U6/SOzA8BHsTRnojAcCkoAyv+teAJweRJAOQUjgOunn4+zof/q9KvJc+KadgxVY7zNKAyHYqmZ5DSu/LvVXwDrJwBLAC0UyHUAf3hyD379ze/+8r+1OgB8FEtzJgrDoSCuA1D+l9VdAMEnwEsA5RSEAF6uhPyl9elvf/O7dn8D8lEszZkoDIcCEIDyv6reAnDmfwmgiYIRwD/41863/vb/SJ8K17RjqBrjbUZhOBRLzSRTrPy71VkA7vwvATRRwKeBllTTjqFqjLcZheFQLDWDDLyR/PcVwGb+lwCaKBIAhWJpzkRhOBQJAF1dBbCd/yWAJooEQKF0xCzu7j9/M0sMhyIBoKunALzz/zb/EkA2RQKgUPphls/3mr6ZFYZDkQDQ1VEAywcA31/iyb8EkE2RACiUbpjVE35nb2aN4VAkAHT1E8DqAcC3V/jyLwFkUyQACqUX5n7rgddQTt6Mg+FQJAB0dRPA+gHA1xd48y8BZFMkAApFAijHcCgSALp6CeC8fvzX9QUSQBtFAqBQJIByDIciAaCrkwDOEkAPigRAoUgA5RgORQJAVx8BnCWALhQJgELRQeByDIciAaCriwBu5/+4L9JB4EaKBECh6DTQcgyHIgGgq4cA7uf/bF6k00DbKBIAhdIRowvBmigSALo6COBx/s/2RboQrIkiAVAoluZMFIZDkQDQ1U0AgRctML5dkACiFAmAQrE0Z6IwHIoEgC4JAFJD5l8CqKRYmjNRGA5FAkAXWgBnCaAjRQKgUCzNmSgMhyIBoAssgPX5PxIAmCIBUCiW5kwUhkORANCFFcD9/p8SQBeKBEChWJozURgORQJAF1QAj/s/SwBdKBIAhWJpzkRhOBQJAF0dBBB90QLj2wUJIEqRACgUS3MmCsOhSADowgsg/qIFxrcLEkCUIgFQKJbmTBSGQ5EA0AUXQOJFC4xvFySAKEUCoFAszZkoDIciAaALJ4DV878kgC4UCYBCsTRnojAcigSALpgA1g8AlgC6UCQACsXSnInCcCgSALpQAnAeAC8BdKFIABSKpTkTheFQJAB0YQWQeNEa49sFCSBKkQAoFEtzJgrDoUgA6AIJwJn/JYA+FAmAQrE0Z6IwHIoEgC6MANz5XwLoQ5EAKBRLcyYKw6FIAOiCCOAsAXAoEgCFYmnORGE4FAkAXQgBbOd/CaAPRQKgUCzNmSgMhyIBoAsggPPyCrDQi7YlAZRTJAAKxdKcicJwKBIAutoFcF5dARZ4kackgHKKBEChWJozURgORQJAV7MA7k+Aj73IVxJAOUUCoFAszZkoDIciAaCrVQCPJ8BHXuQtCaCcIgFQKJbmTBSGQ5EA0NUogPPj+Y/hF/lLAiinSAAUiqU5E4XhUCQAdLUJ4CwBXGrI/EsAlRRLcyYKw6FIAOhqEsBZArjWkPmXACopluZMFIZDkQDQ1SKA9RPgAy8KlgRQTpEAKBTunHk69QypBKD8x6pBAPfzf9oEsMq/BBClSAAUCnXOPJ26GkACUP5jVS+Ax/k/TQJY518CiFIkAAqFOWeeTn0NIAEo/7FqFUBgG9kCcPIvAUQpOwpA1aVO99p7T1Qmqzx4lzVuAghsI7hg87p1/oNr1A4QywNLfwFUUoi/ND8GQC+K/gJQ/iNV+RfAGfQXgJt//QUQpegjIApFAijHcCgSALrqBHC7/6cEcK0h8y8BVFIkgHIMhyIBoKtKAPf7P0sA1xoy/xJAJUUHgcsxHIoEgK4aATzu/6+DwNcaMv8SQCVlwNNAqx0hASj/saoXwGNtwmmg1fmXADQAiinjXQhW/1eCBKD8x6paAIu1+18IVp9/CUADoJgy3JzZ8DnReM20UCQAdNUKYLl2460gErvz3JR/CUADoJgy2pzZcqR4uGaaKBIAuooFsHr+F0cALfmXADQAiimjzZkSwI0iAaCrVADr579LANcaMv8SQCVltDlTArhRJAB0FQrgLAF4a8j8SwCVlNHmTAngRpEA0FUmAGf+lwBuNWT+JYBKynBzpg4CXykSALqKBODO/zoIfKsh8y8BVFLGmzN1GuiFIgGgq0QAm/mfJQCdBnqlSAA965axEedMXQj2SpEA0LU6Bz+e/+38TxOALgS7UCSAjnX/LcPUnInCcCgSALqWF+HG839eXgCwWpsggOqSADQA8urxOaOpOROF4VAkAHQt7sITz/95dQHAam0JYMz8SwAFtTjTwNScicJwKBIAum4TZCr/9wcAe9aWAMbMvwRQUBJAG4ZDkQDQlSmAxwOAPWtLAGPmXwIoKAmgDcOhSADoyhPA+fH4L8/aEsCY+ZcACkoCaMNwKBIAurIEcJYAEjVk/iWAkqo5CFx9ctpLjZEZFIZDkQDQlXMQ+BwSwDX/EsCY+ZcAiqr8NND6y1NeaozMoDAcigSArozTQG/n/2yifltDAhgz/xJAWZVeCPb4namqxsgMCsOhSADoyrgQ7Hb+j5v0e/4lgDHzLwFUUvIwp2XVYCrWqaBIAMp/pJbRvf7b6eZ+/o+T8mj+JYAuFAmAQqkQQM19OstXqSgJQPmPVVIAj0//YwLYfjrkWWNdEkA5RQKgUGoEUJ6zoZppxnAoEgC6UgI4Zwpg8/GQZ411SQDlFAmAQqkSQHHQhmqmGcOhSADoSgjgnC0Ad6FnjXVJAOUUCYBCKTwIPLIAGg5SF9UYPxlk4I3kPy6Ac0QA0fyPIgDT+ZcAKillp4GOLIDa4xPFNcZPBhl4I/mPCmB9AmjgNNCRBWA7/xJArMLJCHTjPdQ1tgCqj08U15ADQPmP1DUXMQGcVyeAFuV/DAEYz78EEKlIMvzdhFaoDln/96xeTsU15ABQ/sN1y0VEAOfVCaBl+R9CANbzLwGEK5YMbzfhFWojJgGUUyQAUN2DERbA+tP/wvxLAF0oEgCootHwdRNboTJhEkA5RQLA1Onky8ZKAOvDv6X5lwC6UCQAUEEFUFkSQDlFAsBUWgDnfAH4AYsN+ksCKKdIANuq+vnaEID1g2DKf6iSAnDP/5lSANbzb0IAdT9hIwIwfhqc8h+qlADW5/9MKwDj+Z9FAPk/oy2mdlqOrVd4ELi2dCFYOeWQAtg1/14BrM//SRwEDmx/sUF/6UKwcsohBVAQrA2m/hfzyFplp4FW1xiZQWE4lCMKYN/8+wSwufo3dhpoaPOLDfqLIgDT+Z9DACUJBg4AyIVgTTVGZlAYDuWAAtg5/x4BbG//cApcCBbb+mKD/pIAyikHFEBRhJEDIEKxlBkUhkM5ngD2y/92jo4LoHHjm5IAyikSQMHa1VrYMTP4jywtDwDlP05+/Hf5ncv8/7yLAJT/OEUCCK0e2nDNLu2XGfgfM7YHgPIf22hAAO75P+6L8qpOAMp/giIBBNYPb7dil3bLTIePs0wPAOU/tlW/ADYngLovyqsqASj/KcoBBdB2EOz59leju4WiceVSdspMyz6HKYYHgPIf265XAJ4TQJ9ZAlD+k5QjCqDpNLjgNiSAG8XwALCRf+85mpUCCBz+lQCSGA7lkAIoOPITwmyDIwHcKIYHgI38n3xXaUkAN4rh/M8igPwKYDzJGUIAcbwGQDnlkALIn18DAqjLf38BKP9oigTgLV9yGrKE6iaxAzoIVk6RAHxr1+V/M7efgyeA1glA+YdTJABveX91qM8SqJtUnHUaXDlFAvCtXZd/d26/zf8oASj/eIoE4C3/347VWcJ0k/yDVhfClFMkAN/adfl35vb7/A8SgPLfgSIB+Av7t+OOAsCX5QEwS/5bBRDIf2Kz67n9Mf/vKQB8Wc7/AQUQyhP0b0dANycNgC4U6wLwxSn4cXuJABbzP0IAyn8fii0B+H6niRkAxW3v5qQB0IdiSgCZ+Q+ecFMggOX8DxCA8t+JYkoA/k818Z8Sbqq5m6z8D5IZFIZDsSSA3PwH5+h8Aazm/3YBKP+9KJYEsM1POlOYau0mL/+DZAaF4VAMCSA7/+0CuD0A2LPBGgEo/90ohgTgSRBJAM2AvPwPkhkUhkOxI4D8/DcL4H7/twfmGSaA8MvGiAwKw6FIAP0F0E7I3M8xMoPCcCgSAF4Aj/u/LSgYAURfNkZkUBgORQLoLgAAQgOgG0UC6CUAFyIBlGE4FNsCyDm5uAe2eiPxV42RGRSGQzEtgED+oQJwEU0HgeOvGiMyKAyHYkgA3hT1NwBm+1lbGCMzKAyHYkcA+flvEsC5hwCU/14USwLwpehtdwOANp+zgTEyg8JwKIYEkJ3/FgHczv8BC0D570QxJQBPit4+9z4S0PsvjEWNkRkUhkOxJABv/j0GaBCAc/+3Z5gAcmqMyKAwHIotAXg4z92naNr8P0hmUBgOxZQAtt8HC8C9/9vlu9eNSwBFGA5FAuj/Ozpr/h8kMygMhyIB4AXgvPS2bQmgCMOhSACED2lI8/8gmUFhOBQJAC6AzUuvm5YAijAcigTwTPiQxlRmUBgORQLY3vu5TQCel759625WAkhiOBQJ4KV6f0hjKjMoDIciAZw2+a8UwFkCQGI4FAngtTp/SGMqMygMhyIBXD6dab8QzHcD0BtFAijHcCgSAIViKTMoDIciAWwn5CoBrOd/CaAZw6FIABSKpcygMByKBIARgDP/SwDNGA5FAqBQLGUGheFQJACIANz5XwJoxnAoEgCFYikzKAyHIgEgBLCZ/yWAZgyHIgFQKC6mz0HnMTKDwnAoEgBOAMGXbgSg/KcxHMo8ApgrM+u9dbvpdNrpGJlBYTiUaQRQlBiyAHzz/zb/j80q/xkYDmUaAcyVGWdvnW56XXg2RmZQGA5lFgGUJYYrgPUDID176whA+c/BcCizCGCuzLh7u+6m260nxsgMCsOhTCKAwsRQBXDeCMCf/9tmlf8sDIcyiQDmysxmbyWACgyHMocASiPDFIDzBGDf3koAFRgORQJwMYCNSgAIDIciAazOzbkeog1sw7fZ8/oJwN69lQAqMByKBLChtG9UAkBgOBQJYH1uzuUYbWAbnm+dJYBOGA5FAthCmjeaEMBkBzQ2FMMDYJb8VwngjigQwLlCAMp/FoZDmUQAjMwAJeNuSKeBVmA4lDkEwDgI7P5qniOA2w1AnQX+/Os00CIMhzKLAAiZQf6V4Wxn0c3l+116GSQzKAyHMokACKeBVgjg9gT4zQJv/u8fMyn/ORgOZRoB9M8MUgDO3j666eSxK6bTdh2K4QEwS/45Anic/7l5rS//HX/3v2I6bdehGM7/oW8FARWAQ7lhuhEumD6bdSmGB8Ce+S9JDUUAi/M/E/t2F4Dyn4/hUCSAR/VL562bjo55xXTZ6oZieADsmf/eAig9CLw8+pspAOW/AMOhSACL6pZNCaACw6FIAJWngZ4lgL4YDkUCWFavaEoAFRgORQJYzPbXZOYI4CwBdMZwKBIAhSIBlGM4FAlgOduvbRBZ/Xb+jwTQDcOhSAAUig4Cl2M4FAmgRgD383/KBKD8F2A4FAmAQtFpoOUYDkUCqBDA4/yfQgEo//kYDkUCoFAemI75HyQzKAyHIgGUC2Dx6X+pAJT/bAyHIgFQKJYyg8JwKBJAsQDOLQLoWWNEBoXhUCQACsVSZlAYDkUCKBXAWQKgYDgUCYBCsZQZFIZDkQAKBXCd/33rBUsCqMBwKBIAhWIpMygMhyIBlAnAOf9HAuiG4VAkAArFUmZQGA5FAigSgHv+jwTQDcOhSAAUiqXMoDAcigRQIYDNiyQAPIZDkQAoFEuZQWE4FAlAAiikGM6/BFBJsZQZFIZDkQAkgEKK4fxLAJUUS5lBYTgUCSBfAKv7/0gAnTEcigRAoVjKDArDoUgA2QLwnQAqAXTDcCgSAIViKTMoDIciAeQK4Db/SwAcDIciAVAoljKDwnAoEkCmAO7zvwTAwXAoEgCFYikzKAyHIgHkCeAx/0sAHAyHIgFQKJYyg8JwKBJAlgAW878EwMFwKBIAhWIpMygMhyIBFAjgOfQiCQCP4VAkAArFUmZQGA5FAsgRwHL+lwA4GA5FAqBQLGUGheFQJIAMAVwvAFhtRALojOFQJIDiqnimkanMoDAcigSQFsB5JYBr/iWAzhgORQIorZqnmprKDArDoUgASQHc7wB9fckl/xJAZwyHIgEU1ulUYQBTmUFhOBQJICWAxx2gL9+95l8C6IzhUCSAsjqdagxgKjMoDIciASQEsHj+4/My/xJAZwyHIgGU1ckdAXkUS5lBYTgUCSAugHNYACd3vWBJABUYDkUCKKtTlQFMZQaF4VAkgKgAzss7QD9v8y8BdMNwKBJAvNxp/lRlAFOZQWE4FAkgJoDz6g7Qz9v8SwDdMByKBBCt7TRfZQBTmUFhOBQJICIA5wnwl+/6RoAEgMdwKBJArHzTvARgqRlk4BvzzxfA9fyfxy/6l29LABQMhyIBRMo/z0sAHAyHIgGkBOAGXQLgYDgUCSBSwXleAiBgOBQJoFQAz9uTQSWADhgORQKIVHieL5v/bWUGheFQJICAAM4RAbiXg0kAHTAcigQQqcgv+kXzv63MoDAcigTgF8D5dgFA7G9gnQbaEcOhSACxivyiXzL/28oMCsOhSABeAaznf8/2rvmXALphOBQJIFplv+iHKZYyg8JwKBKATwC3B4A5v+gHNygB4DEcigQQL8j8byszKAyHIgGEBfDs/qIf3KAEgMdwKBIAhWIpMygMhyIBBAWQw5YAumE4FAmAQrGUGRSGQ5EANgK4nv+TxZYAumE4FAmAQrGUGRSGQ5EAXAGsn/+VYEsA3TAcigRAoVjKDArDoUgAjgDOZ/fznxhbAuiG4VAkAArFUmZQGA5FAlgLwDv/SwBLiuH81wrgq4++1z4AutQYbzMKw6FYaqYy8D3yzxRANlsC6IbhUDgC+PhJAmBgOBRLzVQGvkf+iQLIZ0sA3TAcCkMAX3/8JAFQMByKpWaqAt8n/zwB5G9PAuiH4VAIAvjpD58kAA6GQ7HUTE3gO+WfIADP+T8JtgTQDcOh9BfAJ09Pv/cXEgAFw6FYaqYi8L3y318A/gPAUbYE0A3DoRAE8J0/fvvlwQWQumGEqcygMBxKfwGg8t9dAOH5PyWAvPxLAEUYDoVzEHg1AL59rcptDViXW2btvReqYQuS/5KEhV7r+f7lW+/+e53/y9ivCzLzryEyfUkAvrrdNHrv/VCNWjMIIDb/xwWQm3+NkOkLIoBbNf1pgioAJuP5kKb+akRhOBTKaaAzfAQU/vwnxj6d8vOvj4CKMBzKDh8B1Q6ALiUBlFMsNVMZ+B75ZwigdHsSQD8MhyIBNJcE0AfDoUgAgRuA5rElgG4YDkUCaC4JoA+GQ5EA4uf/JNgSQDcMh3IAATQ9tAvxNifzbyszKAyHMr8AfNErE0By/o+fBpqbfwmgCMOhzC+Atsf2Qt7m5C6YygwKw6FMLwBv+IoEkJ7/E9cBZOZfAijCcCjTCyD960ecU7nedieiFEuZQWE4lNkF4M9/hQCiu6MLwRYUw/kfTwAZH0DGOXWrlVIsZQaF4VAmF0Ag/+UCiO5N8lYQiZIAKjAcigTAKFOZQWE4FOsCSJ3/E9+eBNAPw6FwBOCtph27lQSwxHAolppBBr4x/50EkPH7vwSwohjOvwRQSbGUGRSGQzEugLz5XwJYUgznfzwBjHEQOEmxlBkUhkOZXACNB4Ez538JYEkxnP8BBTDCaaBpiqXMoDAcyuwCaDoNNOME0Pj2JIB+GA5lfgHsfyFYBsVSZlAYDmV6ATRcCJY9/0sAS4rh/A8pgKYa421GYTgUS80gA9+Y/5JJOEsA+fO/BLCkGM7/wALw/h2cjtwYbzMKw6FYagYZ+Mb8p6/GjX5rs42C+V8CWFIM539cAXjPhMgwwBhvMwrDoVhqBhn4xvxn3I8n9i13G+fgE+ADiLIFq5IAKjAcykEE4DkXIu/0oDHeZhSGQ7HUDDLwjfnPuSNn5FvONs4XAWSfbV26YFUSQAWGQzmGADxnQ2deIDDG24zCcCiWmkEGvjH/kUl4E3bPt9bbOF8EkPsuSwALiuH8SwB1ZSozKAyHYlMA54sAst9lCWBBMZx/CaCuTGUGheFQTArgLAE0UAznXwKoK1OZQWE4FIsCOEsALRTD+R9VADoIfMFwKJaaQQa+Mf+wg8C38z8lgDqK4fwPKwCdBvqK4VAsNYMMfGP+UaeBXs//eZYAKimG8z+uAHQh2LOaqaEcRAD5F4Ldzv+RAGophvM/sAAqa4y3GYXhUCw1gwx8Y/4Tk7Dz+ad/jevjvx6LJYByiuH8H0oAr78gjfE2ozAciqVmkIFvzD9aACX5lwAWFMP5P5IALh+RjvE2ozAciqVmkIFvzD9YAEX5lwAWFMP5P5AA8k4SApWpzKAwHIpFAQRPEgqWBLCgGM7/cQSQeZkAqExlBoXhUEwJ4HECaGH+JYAFxXD+JYC6MpUZFIZDsSSA+w2gJYAWiuH8SwB1ZSozKAyHYkgAjwcASAAtFMP5lwDqylRmUBgOxY4AFg+AkQBaKIbzfxwB6CBwPcVSM8jAN+a/UQDLB4DpIHALxXD+DyQAnQZaTbHUDDLwjflvE8DqAZA6DbSFYjj/RxKALgSrpVhqBhn4xvw3CWD9AGBdCNZCMZz/gwhg8afvGG8zCsOhWGoGGfjG/LcIYP0A4PL8SwALiuH8H0MAyw8/x3ibURgOxVIzyMA35r9BAPcbgF4XFudfAlhQDOd/MAHUHcRdHf4a421GYTgUS80gA9+Yf991vdfPcjaL19963AD0tlZp/iWABcVw/scSQN1pPOsT4MZ4m1EYDsVSM8jAN+Z/E/VbilMCWNwA9Lky/xLAgmI4/0MJoPJETgmglWKpGWTgG/PvJv0e44QAzhIAlmI4/yMJoPZSLgmglWKpGWTgG/PvBP10Wic5JICzBACmGM6/BFBXpjKDwnAoxxfA5fwfCQBGMZz/IwhAB4FbKZaaQQa+Mf91Alg+AHi94oUTbz/AzliwKgmgAsOhGBSATgNtpFhqBhn4xvxXCWD1AODVmldOvP0AO2PBqiSACgyHMq8Aag8CP+tCsEaKpWaQgW/Mf81B4LNPALoQrI1iOP9DCaDyNFCH07Z6LsVSZlAYDmVeAeScBrp+AryPE28/yE4uWFMkgHIMhzKzACovBFtzGtfPpFjKDArDoUwsgIwLwSSADhTD+R9MAIAa421GYTgUS80gA9+Yf8/8uZzbtwI4SwBdKIbzLwFUUixlBoXhUI4rgMcDgANrv3Li7UfYiQVrigRQjuFQJAAKxVJmUBgO5bACWDwAOLD2KyfefoSdWLCmSADlGA5FAqBQLGUGheFQDi4A/+IFJ95+hJ1YsKZIAOUYDkUCoFAsZQaF4VCOKoDlA4ADa79y4u1H2IkFa4oEUI7hUCQACsVSZlAYDuXQAti8aMuJtx9hJxasKRJAOYZDkQAoFEuZQWE4FAkgpySABcVw/iWASoqlzKAwHMohBXA9AXT7oi0n3n6EnViwpkgA5RgORQKgUF4wgMvWUpi+m79RDA+APfOfLwDPE+AHEIDyX4bhUCQACuUt5sYVKUzXrd8phgfAnvnPFsB6/h9FAMp/IYZDkQAolLfP9beuK8D03PiDYngA7Jn/XAE48/8gAlD+SzEcigRAobytv3l1CabjthcUwwNgz/xnCsCd/8cQgPJfjOFQJAAKRQOgHMOhHE0Am/lfAkBTDOdfAqikaACUYziUgwlgO/9LAGiK4fxLAJUUDYByDIdyLAGszv/0vGjLibcfYScWrCnKfzmGQ5EAKBQdBCvHcCiHEsD5+gT44Iu2nHj7EXZiwZqi/JdjOBQJgELRaXDlGA7lSAI4354AH3zRlhNvP8JOLFhTlP9yDIciAVAouhCmHMOhHEgAjwcAB1+05cTbj7ATC9YU5b8cw6FIABSKpcygMBzK4QQQfdGWE28/wk4sWFMsRQaF4VAkAArFUmZQGA5FAsgpCWBBsdSMk9n9BYD+O3KMtxmF4VAsNYMMfGP+X4O/zv/2/B8JoD/FUjNOZncXAPxI0hhvMwrDoVhqBhn4xvy/5N7J//L8n+UDgDfrSQBAiqVmnMzuLQD8uWRjvM0oDIdiqRlk4Bvz/y72bv6X5/8sHwDsrvcsAQAplppxMruzADpcTTLG24zCcCiWmkEGvjH/p9Mm/8tP/5cPAHbWe/YveOXE219vo2TBmmIpMigMhyIBMMpUZlAYDuVAAnh8x1kvsOCVE29/vY2SBWuKpcigMByKBMAoU5lBYTiU4whg8R1nvcCCV068/fU2ShasKZYig8JwKBLJGgUfAAAdg0lEQVQAo0xlBoXhUOYXgOf5j856gQWvnHj7622ULFhTLEUGheFQphKADgInMByKpWaQgW/Mf+AgsO/5j+56/gWvnHj7622ULFhTLEUGheFQ5hKATgONYzgUS80gA9+Yf/9poN7nP27WkwCAFEvNOJndXQC6ECyK4VAsNYMMfGP+vReC+Z//uF1PAsBRLDXjZHZ/AaBrjLcZheFQLDWDDHxj/j0T+fL8n+WLUustOPH2I5tNLFhTLEUGheFQJAAKxVJmUBgO5QgC2Lwotd6CE28/stnEgjXFUmRQGA5FAqBQLGUGheFQZhaA5/lfEkB/iqVmnMxKAJUUS5lBYTiU+QXgeVFivSUn3n5ks4kFa4qlyKAwHIoEQKFYygwKw6FMLIDt898lAAbFUjNOZiWASoqlzKAwHMq8AvDN/xIAgWKpGSezEkAlxVJmUBgOZVoBuCeALl8UW8/hxNuPbDaxYE2xFBkUhkORACgUS5lBYTiUWQXgn/8lAALFUjNOZiWASoqlzKAwHMrcAgi8KLKey4m3H9lsYsGaYikyKAyHIgFQKJYyg8JwKJMKIDD/SwAEiqVmnMxKAJUUS5lBYTiUOQUQmv8lAALFUjNOZiWASoqlzKAwHMqUAvBcAbZ6UWg9DyfefmSziQVriqXIoDAcigRAoVjKDArDocwogLPnCrDViwLr+Tjx9iObTSxYUyxFBoXhUCQACsVSZlAYDmVCAZwvAvCuJwH0p1hqxsmsBFBJsZQZFIZDmU8A54sA/OtJAP0plppxMisBVFIsZQaF4VBmFUBgPQmgP8VSM05mJYBKiqXMoDAcigSQUxLAgmKpGSezEkAlxVJmUBgOZTIBXC8AlgC8GA7FUjNOZiWASoqlzKAwHMpcArjdAEIC8GI4FEvNOJmVACopljKDwnAoUwngfgMgCcCL4VAsNeNkVgKopFjKDArDocwkgMcN4CQAL4ZDsdSMk1kJoJJiKTMoDIcynwAu/w6sJwH0p1hqxsmsBFBJsZQZFIZDmU4A138H1pMA+lMsNeNkVgKopFjKDArDoUwjgNX9fyQAL4ZDsdSMk1kJoJJiKTMoDIcyiwDWD4CRALwYDsVSM05mJYBKiqXMoDAcyiQCcB4AJgF4MRyKpWaczLIFcDrlBay+xnibURgOxVIzyMA35N99AKQE4MVwKJaacTJLFsDpVGqAYmOM8TajMByKpWaQga/P/+YBwKGU+/IvAYAplppxMssVwOlUaoByY4zxNqMwHIqlZpCBr87/9gHwgZB78y8BgCmWmnEySxXA6VRqgHJjDPI2ozAciqVmkIGvzf92/g/Mu/78SwBgiqVmnMyOLYByY4zyNqMwHIqlZpCBr8y/7/lf3ogH8i8BgCmWmnEyKwHUlanMoDAcyvAC8D7/SwLwYjgUS804mZUA6spUZlAYDmV0Afif/yUBeDEciqVmnMyOfRBYAuBQLDWDDHxV/v13/5cAvBgOxVIzTmYHPw20fP4f5G1GYTgUS80gA1+V/wIB6CAwh2KpGSezo18IVjz/t77NmThTmUFhOJSRBXC7/0+uAPingSr//TAcytgCKK7S+b/xbc4VjqnMoDAcysgCuJ3/ky0A9oVgyn9HDIdyMAEUVxMm+yMnU5lBYTiUgQUQef5X2QejkTWaBKD898RwKBJAfeUfdDaVGRSGQxlXALHnfw0hAOW/K4ZDkQDqSwOgK4ZDGV0AL19IAHk1RmRQGA5FAqgvDYCuGA5lWAEs7v8gAeTVGJFBYTiU4wsgHlAJoJxiqRlk4Ivyv7z/T5MArvmUAGAUS804mZ1QAImE6iBwOcVSM8jAl+T/jBLALaE6CAyjWGrGyex8AkhlVKeBllMsNYMMfEn+Ew+ALL49ik4DxVEsNeNkdjoBJP9KbcTk5d9WZlAYDmVQAaxuAFovgNMpMQLaBKD8d8RwKBIAo0xlBoXhUIYVwHPsAZCjCCCzTEUGheFQJABGmcoMCsOhjCuAwBeB74Q2IwHAKZaacTIrAdSVqcygMByKBJC3nbzXBcpUZFAYDuXgAuh8EDi3TGUGheFQji2AzgeBc8tUZFAYDuXoAuh6Gmh2mcoMCsOhHFwAXU8DzS5TkUFhOJTDC6DjhWD5ZSozKAyHcnQBdLwQLL9MRQaF4VCOL4BEgxyKpcygMBzK4QUQX0MCKKdYasbJrARQSbGUGRSGQ5EAGtbOLVORQWE4FAmAQrGUGRSGQ5EAGtbOLVORQWE4FAmAQrGUGRSGQ5EAGtbOLVORQWE4FAmAQrGUGRSGQ5EAGtbOLVORQWE4FAmAQrGUGRSGQ5EAGtbOLVORQWE4FAmAQrGUGRSGQ5EAGtbOLVORQWE4lB0FoFKpAnU6hb4IfKdog227ozJb+gugkmLplwYUhkPRXwANa+eWqcigMByKPgKiUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgORQKgUCxlBoXhUCSAhrVzy1RkUBgOZU4BnE6NiXxwMJtJUSxlBoXhUKYUQEX+JQAYxVIzTmYHEcDpBDPAGG8zCsOhWGoGGfiS/EcFUJN/CQBGsdSMk9kxBHA64QwwxtuMwnAolppBBr4k/zEBVOVfAoBRLDXjZHYIAZxOQAOM8TajMByKpWaQgS/Jf0QAdfmXAGAUS804mZUAKimWMoPCcCgSQMPauWUqMigMhyIBMMpUZlAYDkUCaFg7t0xFBoXhUCQARpnKDArDoUgADWvnlqnIoDAcyoQC0EHgIIZDsdQMMvAl+ddB4BoMh2KpGSezYwiAfxpoK85UZlAYDmVCAfBPA1X+lxRLzTiZHUQA7AvBmoVjKjMoDIcyowDYF4Ip/yuKpWaczI4iAFzlYNo/cjKVGRSGQ5lSABXVIADlf02x1IyTWZMCABx0NpUZFIZDkQDSayr/K4qlZpzM0gSA+4wnURoA5RRLzSADX51/CSATw6FYasbJLEsAwKO8idIAKKdYagYZ+Or8SwCZGA7FUjNOZkkCQJ7nmSgNgHKKpWaQga/OvwSQieFQLDXjZJYjAEDisksHwcoplppBBr46/zoInInhUCw142TWpgB0GtyaYqkZZOCr87+zAJT/NcVSM05mjQpAF8KsKJaaQQa+Ov97C0D5X1EsNeNk1qoAmimWMoPCcCgSAKFMRQaF4VBGFMBgB4ERFEuZQWE4lAEFMNhBYECZigwKw6EMKYCxTgNFUCxlBoXhUEYUwFingQLKVGRQGA5lTAE8O/nvJ4Mx3mYUhkOx1Awy8LvmXwKAUSw142R2l1tBdP1zYIy3GYXhUCw1gwz8rvmXAGAUS804md1DAH0PCIzxNqMwHIqlZpCB3zX/EgCMYqkZJ7M7CKDzKUFjvM0oDIdiqRlk4HfNvwQAo1hqxsmsBFBJsZQZFIZDkQAIZSoyKAyHIgEwylRmUBgORQIglKnIoDAcigTAKFOZQWE4FAmAUKYig8JwKMMLQAeBCzAciqVmkIHfNf8SAIxiqRknszoNtJJiKTMoDIcyvAB0Gmg+hkOx1IyT2X0eCakLwXIxHIqlZpCB3zX/EgCMYqkZJ7MmnwmMoFjKDArDoUwgAEhJADCKpWaczEoAlRRLmUFhOBQJgFCmIoPCcCgSAIViKTMoDIciARDKVGRQGA5FAqBQLGUGheFQJABCmYoMCsOhSAAUiqXMoDAcigRAKFORQWE4FAmAQrGUGRSGQ5EACGUqMigMhyIBUCiWMoPCcCgSAKFMRQaF4VAkAArFUmZQGA5FAiCUqcigMByKBEChWMoMCsOhSACEMhUZFIZDkQAoFEuZQWE4FAmAUKYig8JwKBIAhWIpMygMhyIBEMpUZFAYDkUCoFAsZQaF4VAkAEKZigwKw6FIABSKpcygMByKBEAoU5FBYTgUCYBCsZQZFIZDkQAIZSoyKAyHIgFQKJYyg8JwKBIAoUxFBoXhUCQACsVSZlAYDkUCIJSpyKAwHIoEQKFYygwKw6FIAIQyFRkUhkORACgUS5lBYTgUCYBQpiKDwnAoEgCFYikzKAyHIgEQylRkUBgORQKgUCxlBoXhUCQAQpmKDArDoUgAFIqlzKAwHIoEQChTkUFhOBQJgEKxlBkUhkORAAhlKjIoDIciAVAoljKDwnAoEgChTEUGheFQJAAKxVJmUBgORQIglKnIoDAcigRAoVjKDArDoUgAhDIVGRSGQ5EAKBRLmUFhOBQJgFCmIoPCcCgSAIViKTMoDIciARDKVGRQGA5FAqBQLGUGheFQJABCmYoMCsOhSAAUiqXMoDAcigRAKFORQWE4FAmAQrGUGRSGQ5EACGUqMigMhyIBUCiWMoPCcCgSAKFMRQaF4VAkAArFUmZQGA5FAiCUqcigMByKBEChWMoMCsOhSACEMhUZFIZDkQAoFEuZQWE4FAmAUKYig8JwKBIAhWIpMygMhyIBEMpUZFAYDkUCoFAsZQaF4VAkAEKZigwKw6FIABSKpcygMByKBEAoU5FBYTgUCYBCsZQZFIZDkQAIZSoyKAyHIgFQKJYyg8JwKBIAoUxFBoXhUCQACsVSZlAYDkUCIJSpyKAwHIoEQKFYygwKw6FIAIQyFRkUhkORACgUS5lBYTgUCYBQpiKDwnAoEgCFYikzKAyHIgEQylRkUBgORQKgUCxlBoXhUCQAQpmKDArDoUgAFIqlzKAwHIoEQChTkUFhOBQJgEKxlBkUhkORAAhlKjIoDIciAVAoljKDwnAoEgChTEUGheFQCAL4+o8+fHr6/k92HgAhDodiKTMoDIfSXwBj5F8CgFEsNeNktkYAX3309FK/8+f7DoAQh0OxlBkUhkPpLoBB8i8BwCiWmnEyWyOAj5+++5O3v/jx03d/tusACHE4FEuZQWE4lO4CGCT/EgCMYqkZJ7MVAvj5h6+/+3z10Qd/susACHE4FEuZQWE4lN4CGCX/EgCMYqkZJ7MVAvjk6XvX//9g1wEQ4nAoljKDwnAovQUwSv4lABjFUjNOZisE8PHTj17//+V1IOw1AEIcDsVSZlAYDqW3AEbJvwQAo1hqxslsuQC+/vH1T9+ff3j7EPTb1yrelko1Ww2T/xP0FG6VzZIAVKqSGib/EoCqvZoE4J4I1/SnCarG+EMLheFQLDXTOmKGyb8+AoJRLDXjxBnyF8A+AyDE4VAsZQaF4VB4Atg3/xIAjGKpGSfOEkAlxVJmUBgORQIglKnIoDAcis4ColAsZQaF4VB0FhChTEUGheFQCNcB/GD1/70GQIjDoVjKDArDofS/DmCM/EsAMIqlZpzM6krgSoqlzKAwHIquBCaUqcigMBxKdwF8/eOn74xwL5QQh0OxlBkUhkPpLYBR8i8BwCiWmnEyW3Mu8S/GuBtiiMOhWMoMCsOh9BbAKPmXAGAUS804ma26mOQXf/Qu/993f/+RADpgOBRLzdQEfsj8SwAwiqVmnMzqiWCVFEuZQWE4lP4CGCP/EgCMYqkZJ7MSQCXFUmZQGA5FAiCUqcigMByKBEChWMoMCsOhSACEMhUZFIZDkQAoFEuZQWE4FAmAUKYig8JwKBIAhWIpMygMhyIBEMpUZFAYDsWKAE4n/wgY421GYTgUS80gA6/898ZwKJaacTI7rQBOp8AIGONtRmE4FEvNIAOv/PfGcCiWmnEyO6sATqfQCBjjbUZhOBRLzSADr/z3xnAolppxMjupAE6n4AgY421GYTgUS80gA6/898ZwKJaacTIrAdSVqcygMByKBEAoU5FBYTgUCYBRpjKDwnAoEgChTEUGheFQJABGmcoMCsOhSACEMhUZFIZDMSEAHQSDUiw1gwy88t8bw6FYasbJ7KwC0GlwSIqlZpCBV/57YzgUS804mZ1WALoQBkix1Awy8Mp/bwyHYqkZJ7PzCiDI4VAsZQaF4VCMCCDI4VAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUCQACsVSZlAYDkUCYFAsRQaF4VAkAArFUmZQGA5FAmBQLEUGheFQJAAKxVJmUBgORQJgUCxFBoXhUHYUQLS+/W0ailCH6kbNEGrU/aqrQ3VjuRkJoK4O1Y2aIdSo+1VXh+rGcjMSQF0dqhs1Q6hR96uuDtWN5WYkgLo6VDdqhlCj7lddHaoby81IAHV1qG7UDKFG3a+6OlQ3lpuRAOrqUN2oGUKNul91dahuLDcjAdTVobpRM4Qadb/q6lDdWG5GAqirQ3WjZgg16n7V1aG6sdwMTwAqlUqlGqokAJVKpTJaEoBKpVIZLQlApVKpjJYEoFKpVEZLAlCpVCqjJQGoVCqV0ZIAVCqVymiRBPD1H3349PT9n3BgjPrqo+/tvQug+unvPz19cJQfzU9/+K6Zf/azvXdjU8r/sGU8/xwBfPXR00v9zp9TaIz6+OkgA+DPXn8yTx/8yd47gqhPLs18Z7ScKf/DlvX8cwTw8dN3f/L2Fz9++u54v5tV1dcfPx1kAHz59MEfvH350Rxhcvr5h6/N/HC4n43yP2qZzz9FAD//8PXt/eqjY3j29Q+tYwyAr3/89KOX/7/7FfVHe+9Le3389IOX/13jNk4p/6OW8k8RwCfXtHxy2cHZ690fWr/3F8cYAF99dM3Kx8f40bzWvalRSvkftZR/igA+vur1y2Ok5pPv/PFRWrnXkQbAzz8c7KMW5X/4Mpt/hgC+/vH1T9/hRmZ9HWwAHObTiXf1Fx8O9ue88j982c2/BFBXBxsAnxymnY+fnj744713Yl3K//BlN/9kAQz24Wx9HWsAfHmQ0+DeZe1f/tMPnz7453vvxqqU/9HLcP71F0BdHWoAfPnhB2N9aNJWPx3sMyDlf/CynH8JoK6ONAA+OczvP9f6cqwT7pX/sct0/nUWUF0dqJU/O1r+h5tolf+Ry3b+SdcB/GD1/wPUYQbA1x+Pd+eEyrpd1TOcAJT/cct6/nUlcF0dZgB8PNbHJU11u0HNaDeqUf7HLev5pwjgnZq+c6h7oRxnAHxyoJ/Ju4n26fd+9vbr4f6mV/6HLfP559wM7heHuxviQQbA9TaVTwe5t8uX11s7jnZOh/I/aCn/pOcB/OKP3u3X94/j2qMMgC+fDjUA3v5i0Ju7K/9jlvKvJ4KpVCqV0ZIAVCqVymhJACqVSmW0JACVSqUyWhKASqVSGS0JQKVSqYyWBKBSqVRGSwJQqVQqoyUBqFQqldGSAFQqlcpoSQAqlUpltCQAlUqlMloSgEqlUhktCUClUqmMlgSgUqlURksCUKlUKqMlAahUKpXRkgBUKpXKaEkAKpVKZbQkgDHrr06nX/33L//4P0+n/3LvnVGpyKX8k0oCGLT+9HT6J+/+9x9/+/TL/3bvfVGp2KX8c0oCGLT+5ndfkv+3f3gZByqVrVL+OSUBjFqvf/vqD2CV0VL+KSUBjFrvfvn55f/1pD+AVTZL+aeUBDBs/cffPp30B7DKain/jJIAxq13f//qD2CV2VL+CSUBjFsvvwL9k713QqXaqZR/QkkAw9bLGRDXk6FVKnOl/DNKAhi23v0F/D+fTv9o791QqXYp5Z9REsCo9e4P4F/9f/7w9Ev/2947olLtUMo/pSSAUetPX7L/Mgr0R7DKYCn/lJIABq2/upwB8af6I1hlsZR/TkkAY9blSvjX/+uPYJW5Uv5JJQGMWX96OwPur3QutMpeKf+kkgBUKpXKaEkAKpVKZbQkAJVKpTJaEoBKpVIZLQlApVKpjJYEoFKpVEZLAlCpVCqjJQGoVCqV0ZIAVCqVymhJACqVSmW0JACVSqUyWhKASqVSGS0JQKVSqYyWBKBSqVRGSwJQqVQqoyUBqFQqldGSAFQqlcpoSQAqlUpltCQAlUqlMloSgEqlUhmt/x8auBjUBBxttgAAAABJRU5ErkJggg==" width="768" /></p>
</div>
<div id="specification-of-a-linear-mixed-effect-model" class="slide section level2">
<h1>Specification of a Linear Mixed-Effect Model</h1>
<p>The linear mixed-effect model is more complex:</p>
<p><span class="math display">\[\boldsymbol{Y_i} = \boldsymbol{X_i\beta} + \boldsymbol{Z_ib_i} + \epsilon_i \]</span> <span class="math display">\[\boldsymbol{b_i} \sim N(\boldsymbol{0}, \boldsymbol{D})\]</span> <span class="math display">\[\epsilon_i \sim N(\boldsymbol{0}, \boldsymbol{R_i})\]</span></p>
<p>Notice the <code>i</code> subscript. Linear mixed-effect models are fit to groups of data, say repeated measures made on subjects. <span class="math inline">\(\boldsymbol{X_i}\)</span> are the predictors. <span class="math inline">\(\boldsymbol{\beta}\)</span> are the fixed effect coefficients. <span class="math inline">\(\boldsymbol{Z_i}\)</span> is a subset of the predictors. <span class="math inline">\(\boldsymbol{b_i}\)</span> are the random effect <em>predictions</em>. The <span class="math inline">\(\epsilon_i\)</span> are the random errors.</p>
<p>In contrast to a standard linear models, random errors can be correlated.</p>
</div>
<div id="random-effects-and-errors" class="slide section level2">
<h1>Random effects and errors</h1>
<p>In a standard linear model we just have to estimate one random error parameter: <span class="math inline">\(\sigma\)</span></p>
<p>In a linear mixed-effect model we have two <em>matrices</em> of error structures:<br />
- one for the random effects: <span class="math inline">\(\boldsymbol{D}\)</span><br />
- one for the random errors: <span class="math inline">\(\boldsymbol{R_i}\)</span></p>
<p><span class="math inline">\(\boldsymbol{D}\)</span> is sometimes referred to as <em>between-groups</em> variation while <span class="math inline">\(\boldsymbol{R_i}\)</span> is called <em>within-groups</em> variation</p>
<p>These matrices can take on different <em>structures</em>.</p>
</div>
<div id="what-do-we-mean-by-structures" class="slide section level2">
<h1>What do we mean by “structures”?</h1>
<p>The <span class="math inline">\(\boldsymbol{D}\)</span> and <span class="math inline">\(\boldsymbol{R_i}\)</span> matrices are known as <em>variance-covariance</em> matrices.</p>
<p>The variance is on the diagonal. The covariance is on the off-diagonal. For example, a <span class="math inline">\(\boldsymbol{D}\)</span> matrix for two random effects might be structured as follows:</p>
<p><span class="math display">\[\begin{pmatrix}
\sigma_{b1}^{2} & \sigma_{b1,b2}\\
\sigma_{b1,b2} & \sigma_{b2}^{2}
\end{pmatrix}\]</span></p>
<p>In this matrix there are three parameters to estimate: <span class="math inline">\(\sigma_{b1}^{2}\)</span>, <span class="math inline">\(\sigma_{b2}^{2}\)</span>, and <span class="math inline">\(\sigma_{b1,b2}\)</span>. This structure assumes the two random effects have covariance, ie, they vary together. <em>This is the default in R when you specify that two predictors have random effects.</em></p>
</div>
<div id="example-of-another-boldsymbold-matrix-structure" class="slide section level2">
<h1>Example of another <span class="math inline">\(\boldsymbol{D}\)</span> matrix structure</h1>
<p>We could also constrain the covariance to be 0 in a <span class="math inline">\(\boldsymbol{D}\)</span> matrix, like so:</p>
<p><span class="math display">\[\begin{pmatrix}
\sigma_{b1}^{2} & 0\\
0 & \sigma_{b2}^{2}
\end{pmatrix}\]</span></p>
<p>In this matrix there are only two parameters to estimate, <span class="math inline">\(\sigma_{b1}^{2}\)</span> and <span class="math inline">\(\sigma_{b2}^{2}\)</span>, since we assume covariance is 0.</p>
</div>
<div id="example-of-a-boldsymbolr_i-matrix-structure" class="slide section level2">
<h1>Example of a <span class="math inline">\(\boldsymbol{R_i}\)</span> matrix structure</h1>
<p>The simplest covariance matrix for the random errors is the diagonal structure:</p>
<p><span class="math display">\[\begin{pmatrix}
\sigma^{2} & 0 & \cdots & 0\\
0 & \sigma^{2} & \cdots & 0\\
\vdots & \vdots & \ddots &\vdots \\
0 & 0 & \cdots & \sigma^{2}
\end{pmatrix}\]</span></p>
<p>This says that residuals associated with observations on the same subject have equal variance and are uncorrelated. We only have one parameter to estimate. This is the same as the standard linear model. <em>This is the default in R and all that we’ll cover today.</em></p>
</div>
<div id="simple-data-for-a-linear-mixed-effect-model" class="slide section level2">
<h1>Simple data for a linear mixed-effect model</h1>
<p><img 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" width="768" /></p>
</div>
<div id="what-do-we-notice-about-the-data" class="slide section level2">
<h1>What do we notice about the data?</h1>
<ul>
<li>The different groups seem to have the same trajectory, or <em>slope</em></li>
<li>The different groups seem to have different starting points, or <em>intercepts</em></li>
<li>Each group of data appears as if it could be modeled by a straight line model</li>
</ul>
<p>If we were to imagine what kind of mathematical process gave rise to this data, we might propose a straight line model with a <em>fixed</em> slope coefficient but a <em>random</em> intercept.</p>
</div>
<div id="fitting-a-linear-mixed-effect-model-in-r" class="slide section level2">
<h1>Fitting a linear mixed-effect model in R</h1>
<p>Fit a model with a “random” intercept</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(lme4) <span class="co"># package for fitting lme</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>lme1 <span class="ot"><-</span> <span class="fu">lmer</span>(y <span class="sc">~</span> x <span class="sc">+</span> (<span class="dv">1</span> <span class="sc">|</span> g), <span class="at">data =</span> dat)</span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="fu">fixef</span>(lme1) <span class="co"># fixed effect estimates</span></span></code></pre></div>
<pre><code>## (Intercept) x
## 0.6106 1.4972</code></pre>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="fu">VarCorr</span>(lme1) <span class="co"># D and R estimates</span></span></code></pre></div>
<pre><code>## Groups Name Std.Dev.
## g (Intercept) 0.828
## Residual 0.189</code></pre>
</div>
<div id="visualizing-a-linear-mixed-effect-model" class="slide section level2">
<h1>Visualizing a linear mixed-effect model</h1>
<p><img 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" width="768" /></p>
</div>
<div id="random-slopes" class="slide section level2">
<h1>Random slopes</h1>
<p><img 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" width="768" /></p>
</div>
<div id="what-do-we-notice-about-the-data-1" class="slide section level2">
<h1>What do we notice about the data?</h1>
<ul>
<li>The different groups seem to have the same intercept</li>
<li>The different groups seem to have <em>different slopes</em></li>
<li>Each group of data appears as if it could be modeled by a straight line model</li>
</ul>
<p>If we were to imagine what kind of mathematical process gave rise to this data, we might propose a straight line model with a <em>fixed</em> intercept coefficient but a <em>random</em> slope.</p>
</div>
<div id="fit-a-lme-model-for-a-random-slope" class="slide section level2">
<h1>Fit a LME model for a random slope</h1>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>lme2 <span class="ot"><-</span> <span class="fu">lmer</span>(y <span class="sc">~</span> x <span class="sc">+</span> (<span class="sc">-</span><span class="dv">1</span> <span class="sc">+</span> x <span class="sc">|</span> g), <span class="at">data =</span> dat)</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="fu">fixef</span>(lme2) <span class="co"># fixed effect estimates</span></span></code></pre></div>
<pre><code>## (Intercept) x
## 0.4962 1.6111</code></pre>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">VarCorr</span>(lme2) <span class="co"># D and R estimates</span></span></code></pre></div>
<pre><code>## Groups Name Std.Dev.
## g x 0.820
## Residual 0.189</code></pre>
</div>
<div id="visualizing-the-fit" class="slide section level2">
<h1>Visualizing the fit</h1>
<p><img src="data:image/png;base64,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" width="768" /></p>
</div>
<div id="random-intercepts-and-slopes" class="slide section level2">
<h1>Random intercepts and slopes</h1>
<p><img 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" width="768" /></p>
</div>
<div id="fit-lme-model-for-random-intercept-and-slope" class="slide section level2">
<h1>Fit LME model for random intercept and slope</h1>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>lme3 <span class="ot"><-</span> <span class="fu">lmer</span>(y <span class="sc">~</span> x <span class="sc">+</span> (x <span class="sc">|</span> g), <span class="at">data =</span> dat)</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="fu">fixef</span>(lme3) </span></code></pre></div>
<pre><code>## (Intercept) x
## 0.6097 1.8654</code></pre>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">VarCorr</span>(lme3) </span></code></pre></div>
<pre><code>## Groups Name Std.Dev. Corr
## g (Intercept) 1.071
## x 1.018 -0.08
## Residual 0.181</code></pre>
</div>
<div id="visualizing-the-fit-1" class="slide section level2">
<h1>Visualizing the fit</h1>
<p><img src="data:image/png;base64,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" width="768" /></p>
</div>
<div id="packages-for-fitting-lme" class="slide section level2">
<h1>Packages for fitting LME</h1>
<p>The two most commonly used R packages for fitting linear mixed-effect models are <code>nlme</code> and <code>lme4</code>.</p>
<ul>
<li><p><strong><code>nlme</code></strong>: older package, comes with R, very stable; can fit linear and non-linear mixed-effect models; allows fitting of various covariance structures for random effects and residual errors.</p></li>
<li><p><strong><code>lme4</code></strong>: newer package, does not come with R; can fit linear, generalized linear, and nonlinear mixed-effect models; can also fit models with <em>crossed random effects</em>; does not currently allow fitting various covariance structures for residual errors; uses different computations than <code>nlme</code> that makes it better for larger data.</p></li>
</ul>
</div>
<div id="lme4" class="slide section level2">
<h1><code>lme4</code></h1>
<p>For today’s workshop we’ll use <code>lme4</code>.</p>
<p>The syntax is a little easier to learn than <code>nlme</code>.</p>
<p>It’s worth repeating: <code>lme4</code> does not currently provide facilities for modeling different variance-covariance structures for residuals, <span class="math inline">\(\boldsymbol{R_i}\)</span>. Residual errors are assumed to be Normally distributed with mean 0 and variance <span class="math inline">\(\sigma^2\)</span>.</p>
<p>By the way, the “4” in <code>lme4</code> refers to the technical fact that <code>lme4</code> was programmed using the S4 system in R.</p>
</div>
<div id="data-in-long-format" class="slide section level2">
<h1>Data in Long Format</h1>
<p>In R, LME data need to be in <em>long</em> format. That is, we have one record per subject per each measure of the dependent variable.</p>
<pre><code>## Reaction Days Subject
## 1 249.6 0 308
## 2 258.7 1 308
## 3 250.8 2 308
## 4 321.4 3 308
## 5 356.9 4 308
## 6 414.7 5 308</code></pre>
<p>The dependent variable is <code>Reaction</code>. Notice we have one record per subject per each measure of <code>Reaction</code>. Here, <code>Subject</code> is the random effect.</p>
</div>
<div id="fitting-a-model-with-lme4" class="slide section level2">
<h1>Fitting a model with <code>lme4</code></h1>
<p>Assuming one predictor and one level of grouping, say repeated measures on subjects.</p>
<p><strong>Random intercept</strong>:<br />
<code>lme01 <- lmer(dv ~ x1 + (1 | g), data=df)</code></p>
<p><strong>Random slope</strong>:<br />
<code>lme02 <- lmer(dv ~ x1 + (-1 + x1 | g), data=df)</code></p>
<p><strong>Correlated random slope and intercept</strong>:<br />
<code>lme03 <- lmer(dv ~ x1 + (x1 | g), data=df)</code></p>
<p><strong>Uncorrelated random slope and intercept</strong>:<br />
<code>lme04 <- lmer(dv ~ x1 + (x1 || g), data=df)</code></p>
<p>Of course we can have multiple predictors and random effects. (NOTE: the ||-syntax works only for numeric predictors)</p>
</div>
<div id="fitting-a-model-with-lme4-1" class="slide section level2">
<h1>Fitting a model with <code>lme4</code></h1>
<p>Assuming one predictor and two levels of grouping, say teachers within schools:</p>
<p><strong>Random intercept</strong>:<br />
<code>lme01 <- lmer(dv ~ x1 + (1 | sch/tch), data=df)</code><br />
<strong>Or:</strong> <code>lme01 <- lmer(dv ~ x1 + (1 | sch) + (1 | sch:tch), data=df)</code></p>
<p><strong>Random slope</strong>:<br />
<code>lme02 <- lmer(dv ~ x1 + (-1 + x1 | sch/tch), data=df)</code></p>
<p><strong>Correlated random slope and intercept</strong>:<br />
<code>lme03 <- lmer(dv ~ x1 + (x1 | sch/tch), data=df)</code></p>
<p><strong>Uncorrelated random slope and intercept</strong>:<br />
<code>lme04 <- lmer(dv ~ x1 + (x1 || sch/tch), data=df)</code></p>
<p>Again we can have multiple predictors and random effects. (NOTE: the ||-syntax works only for numeric predictors)</p>
</div>
<div id="selected-lme4-extractor-functions" class="slide section level2">
<h1>Selected <code>lme4</code> extractor functions</h1>
<p>Once we fit a model, <code>lme4</code> has several functions for extracting and viewing model information:</p>
<ul>
<li><code>summary()</code> - summary of fitted LME<br />
</li>
<li><code>fixef()</code> - estimated fixed effect coefficients, <span class="math inline">\(\beta\)</span></li>
<li><code>ranef()</code> - predicted random effects, <span class="math inline">\(\boldsymbol{b_i}\)</span></li>
<li><code>coef()</code> - coefficients for <em>each group</em>, <span class="math inline">\(\beta\)</span> and <span class="math inline">\(\beta + \boldsymbol{b_i}\)</span></li>
<li><code>VarCorr()</code> - estimated variance parameters, <span class="math inline">\(\boldsymbol{D}\)</span> and <span class="math inline">\(\boldsymbol{R_i}\)</span></li>
<li><code>resid()</code> - residuals, or estimated random errors, <span class="math inline">\(\epsilon_i\)</span></li>
</ul>
</div>
<div id="why-no-p-values-in-the-lme4-summaries" class="slide section level2">
<h1>Why no p-values in the <code>lme4</code> summaries?</h1>
<p>Recall that p-values in the coefficient summary of fitted linear models are the probability of getting a test statistic as large (or larger) if the coefficient was indeed 0.</p>
<p>Also recall that p-values are determined using null reference distributions. Under the null hypothesis, the test statistic has a known distribution.</p>
<p>In LME models, the null reference distribution is technically not known, at least not for unbalanced data. Thus the <code>lme4</code> authors elected to not output p-values based on a distribution that is not actually the distribution of the test statistic.</p>
</div>
<div id="how-do-i-know-if-a-coefficient-is-significant" class="slide section level2">
<h1>How do I know if a coefficient is “significant”?</h1>
<p>Quick, common-sense way: look at the <code>t value</code>.</p>
<p>If absolute value of <code>t value</code> is greater than 3, then the coefficient is likely significant. In other words, the coefficient estimate is more than 3 standard errors away from 0.</p>
<p>Note:<br />
<code>t value</code> = <code>Estimate</code> / <code>Std. Error</code></p>
<p>Of course ask yourself if the result is practically significant as well.</p>
</div>
<div id="how-do-i-know-if-a-coefficient-is-significant-1" class="slide section level2">
<h1>How do I know if a coefficient is “significant”?</h1>
<p>Another way is to compute 95% confidence intervals using the <code>confint()</code> function. If the interval contains 0, it is not significant. Further, confidence intervals give an indication of coefficient size and variability.</p>
<p>Say your fitted model object is <code>lme1</code>. Two ways to compute confidence intervals are as follows:</p>
<p><code>confint(lme1)</code></p>
<blockquote>
<p>computes a likelihood profile and finds the appropriate cutoffs based on the likelihood ratio test</p>
</blockquote>
<p><code>confint(lme1, method="boot")</code></p>
<blockquote>
<p>parametric bootstrapping (B = 500) with confidence intervals computed from the bootstrap distribution</p>
</blockquote>
</div>
<div id="but-i-want-p-values" class="slide section level2">
<h1>But I want p-values!</h1>
<p>The <code>lmerTest</code> package provides the kind of p-values SAS provides (based on Satterthwaite’s approximations). Just load it, run <code>lmer</code> as usual and call <code>summary</code> on the object.</p>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(lmerTest)</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>m <span class="ot"><-</span> <span class="fu">lmer</span>(dv <span class="sc">~</span> x1 <span class="sc">+</span> (x1 <span class="sc">|</span> g), <span class="at">data=</span>df)</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a><span class="fu">summary</span>(m)</span></code></pre></div>
<p>A column of p-values is included in the summary output. Again, they’re <em>approximate</em>.</p>
</div>
<div id="diagnostic-plots" class="slide section level2">
<h1>Diagnostic plots</h1>
<p>Once we fit a LME, we should assess our assumptions:</p>
<ol style="list-style-type: decimal">
<li><p>within-group errors (ie, residuals) are normally distributed, centered at 0 and have constant variance</p></li>
<li><p>random effects are normally distributed, centered at 0 and have constant variance</p></li>
</ol>
<p><code>lme4</code> provides a <code>plot()</code> method to help graphically check the variance assumptions of residuals. Say you have a fitted model object named <code>lme1</code>. The basic syntax is as follows:</p>
<p><code>plot(lme1, form=)</code></p>
<p>Where the <code>form=</code> argument is an optional formula specifying the desired type of plot.</p>
</div>
<div id="examples-of-the-form-argument" class="slide section level2">
<h1>Examples of the <code>form=</code> argument</h1>
<p>Say we fit the following LME:<br />
<code>lme1 <- lmer(y ~ x + (x | id), data=df)</code></p>
<p><strong>standardized residuals vs fitted values</strong>:<br />
<code>plot(lme1)</code></p>
<p><strong>standardized residuals versus fitted values by x</strong>:<br />
<code>plot(lme1, form = resid(.) ~ fitted(.) | x)</code></p>
<p><strong>box-plots of residuals by id</strong>:<br />
<code>plot(lme1, form = id ~ resid(.))</code></p>
</div>
<div id="diagnostic-plots-continued" class="slide section level2">
<h1>Diagnostic plots continued</h1>
<p><strong>To check constant variance of random effects</strong>:<br />
<code>plot(ranef(lme1))</code><br />
<em>Note: if only one random effect was fit, this produces a qq plot.</em></p>
<p><strong>To assess normality of residuals</strong>:<br />
<code>qqnorm(resid(lme1))</code></p>
<p><strong>To assess normality of random effects</strong>:<br />
<code>lattice::qqmath(ranef(lme1))</code></p>
</div>
<div id="two-other-plots-of-interest" class="slide section level2">
<h1>Two other plots of interest</h1>
<p><strong>plot predicted random effects for each level of a grouping factor</strong><br />
<code>lattice::dotplot(ranef(lme1))</code></p>
<p>Also known as a caterpillar plot. Good for checking if there are levels of a grouping factor with extremely large or small predicted random effects.</p>
<p><strong>To assess model fit</strong><br />
<code>plot(lme1, y ~ fitted(.) | id, abline = c(0,1))</code></p>
<p>Points lying on a diagonal line can provide indication of a good model fit.</p>
</div>
<div id="making-predictions-using-model" class="slide section level2">
<h1>Making predictions using model</h1>
<p>The predict function allows you to make predictions with and without random effects.</p>
<p><strong>with random effects</strong><br />
<code>predict(lme1)</code></p>
<p><strong>without random effects; also known as marginal predictions</strong><br />
<code>predict(lme1, re.form=NA)</code></p>
<p>From the lme4 documentation for predict: “<em>There is no option for computing standard errors of predictions because it is difficult to define an efficient method that incorporates uncertainty in the variance parameters.</em>”</p>
</div>
<div id="bootstrap-predictions" class="slide section level2">
<h1>Bootstrap predictions</h1>
<p>Bootstrapping allows us to resample our data (with replacement), fit the same model, and make predictions.</p>
<p>If we bootstrap 1000 times, this means resample our data 1000 times, each time fitting a model and making predictions.</p>
<p>When done, we’ll have 1000 predictions, which we can use to estimate a confidence interval.</p>
<p>The <code>bootMer</code> function in <code>lme4</code> automates some of this for us.</p>
</div>
<div id="using-the-bootmer-function" class="slide section level2">
<h1>Using the <code>bootMer</code> function</h1>
<p>Let’s say we fit the following <code>lme4</code> model and want to make marginal predictions for thiouracil at week 5 with a confidence interval.</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>lmm1 <span class="ot"><-</span> <span class="fu">lmer</span>(wt <span class="sc">~</span> treat <span class="sc">+</span> weeks <span class="sc">+</span> (<span class="dv">1</span> <span class="sc">|</span> subject), </span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a> <span class="at">data=</span>ratdrink)</span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a>nd <span class="ot"><-</span> <span class="fu">data.frame</span>(<span class="at">treat=</span><span class="st">"thiouracil"</span>, <span class="at">weeks=</span><span class="dv">5</span>)</span></code></pre></div>
<p>The following will perform 1000 bootstrap predictions and return a percentile CI.</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>b.out <span class="ot"><-</span> <span class="fu">bootMer</span>(<span class="at">x =</span> lmm1, </span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a> <span class="at">FUN =</span> <span class="cf">function</span>(x)<span class="fu">predict</span>(x, <span class="at">newdata=</span>nd, </span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a> <span class="at">re.form=</span><span class="cn">NA</span>), </span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a> <span class="at">nsim =</span> <span class="dv">1000</span>, <span class="at">.progress =</span> <span class="st">"txt"</span>)</span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a><span class="fu">quantile</span>(b.out<span class="sc">$</span>t, <span class="at">probs =</span> <span class="fu">c</span>(<span class="fl">0.025</span>, <span class="fl">0.975</span>))</span></code></pre></div>
</div>
<div id="reml-vs.-ml" class="slide section level2">
<h1>REML vs. ML</h1>
<p>If you look closely at the summary output for a model fit with <code>lme4</code>, you’ll see the message: <code>Linear mixed model fit by REML</code>.</p>
<p>REML stands for Restricted Maximum-Likelihood. It provides unbiased estimates for the variance parameters.</p>
<p>By setting <code>REML=FALSE</code> in the <code>lmer()</code> function, we can estimate parameters using ML, Maximum Likelihood. But the variance estimates will be biased downwards.</p>
<p>The choice of ML vs REML affects model comparisons.</p>
</div>
<div id="model-comparisons" class="slide section level2">
<h1>Model Comparisons</h1>
<p>We often compare models to see if a smaller model fits as well as a larger model.</p>
<p>We can compare models either by hypothesis testing or by selection criteria (such as AIC or BIC).</p>
<p>When it comes to hypothesis testing, the choice of ML vs REML estimation is important:</p>
<blockquote>
<p>To compare two models fit by REML, each must have the same fixed effects.</p>
</blockquote>
<blockquote>
<p>To compare two models fit by ML, one must be nested within the other.</p>
</blockquote>
<p>The function to compare models is <code>anova()</code>. Its default behavior is to refit the models with ML before comparing. Specify <code>refit=FALSE</code> to suppress refitting.</p>
</div>
<div id="comparing-nested-models" class="slide section level2">
<h1>Comparing nested models</h1>
<p>Say we fit two models:<br />
<code>lme1 <- lmer(y ~ x + z + x:z + (1 | g), data=df)</code><br />
<code>lme2 <- lmer(y ~ x + z + (1 | g), data=df)</code></p>
<p>The following refits the models with ML and compares them via Likelihood Ratio hypothesis test:<br />
<code>anova(lme1, lme2)</code></p>
<p>Notice that <code>lme2</code> is nested in <code>lme1</code>. That is, <code>lme2</code> is a special case of <code>lme1</code> with interaction coefficient(s) for <code>x:z</code> equal to 0.</p>
<p>The null hypothesis states the models are equal. Rejecting the null means we prefer the larger model.</p>
</div>
<div id="model-comparison-with-aic" class="slide section level2">
<h1>Model comparison with AIC</h1>
<p>AIC (Akaike Information Criterion) is a criterion-based approach to model building. It is a measure of “goodness” we try to optimize. We want to minimize AIC.</p>
<p>To see AIC:<br />
<code>AIC(lme1)</code></p>
<p>Among several models, the one with lower AIC is usually preferred. This approach requires <em>no hypothesis testing</em>, involves no p-values, and doesn’t care whether you used REML or ML.</p>
<p>Is it better than hypothesis testing? That’s up to you. Whatever you do, expect to do some experimentation and iteration to find better models. Also expect to use a great deal of subjective judgment.</p>
</div>
<div id="comparing-models-with-different-random-effects" class="slide section level2">
<h1>Comparing models with different random effects</h1>
<p>Random effect parameters are measures of variances. Variance is greater than or equal to 0.</p>
<p>When testing whether or not to include a random effect in a model, we’re testing that its variance is 0. In that case our hypothesis test involves values lying on the boundary of the parameter space.</p>
<p>The result is that the standard hypothesis test (ie, a likelihood ratio test) is <em>conservative</em>. The p-value is too high.</p>
<p>If you have a small p-value (say < 0.001), that’s not a problem.</p>
<p>If you have a p-value close to significance, (say about 0.10) you may want to consider calculating a corrected p-value using a <em>mixture of chi-square distributions</em>.</p>
</div>
<div id="a-mixture-of-chi-square-distributions" class="slide section level2">
<h1>A mixture of chi-square distributions</h1>
<p>A likelihood ratio test (LRT) statistic has a chi-square distribution with degrees of freedom equal to the difference in parameters between two models.</p>
<p>Let’s say our LRT is on 2 degrees of freedom. The null distribution of this test statistic is NOT a chi-square with 2 degrees of freedom since our null value (variance = 0) is on the boundary of the parameter space.</p>
<p>It’s been suggested that a 50:50 mixture, <span class="math inline">\(0.5\chi_{df}^{2} + 0.5\chi_{df-1}^{2}\)</span>, can serve as a reference null distribution for computing the p-value. But this is still only an approximation.</p>
</div>
<div id="references" class="slide section level2">
<h1>References</h1>
<p>Faraway, J. (2006). <em>Extending the Linear Model with R</em>. Chapman and Hall/CRC.</p>
<p>Fox, J. & Weisberg, S. (2015). <em>Mixed-Effects Models in R: an appendix to An R Companion to Applied Regression</em>.</p>
<p>Galecki, A. and Burzykowski T. (2013). <em>Linear Mixed-Effect Models Using R</em>. Springer.</p>
<p>Pinheiro, J. & Bates, D. (2000). <em>Mixed-Effects Models in S and S-PLUS</em>. Springer.</p>
<p>West, B., Welch, K., & Galecki, A. (2015) <em>Linear Mixed Models</em>. Chapman and Hall/CRC.</p>
<p>GLMM FAQ:<br />
<a href="http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html" class="uri">http://bbolker.github.io/mixedmodels-misc/glmmFAQ.html</a></p>
</div>
<div id="thanks-for-coming-today" class="slide section level2">
<h1>Thanks for coming today!</h1>
<p>For help and advice with statistics, contact us to set up an appointment: <a href="mailto:[email protected]" class="email">[email protected]</a></p>
<p>Sign up for more workshops or see past workshops: <a href="http://data.library.virginia.edu/training/" class="uri">http://data.library.virginia.edu/training/</a></p>
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