Structural Equation Modelling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from semopy import Model\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from semopy import Optimizer\n",
    "from semopy.model_generator import generate_model\n",
    "from semopy.inspector import inspect\n",
    "from semopy.stats import calculate_p_values, calc_gfi, gather_statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y1</th>\n",
       "      <th>y2</th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>x3</th>\n",
       "      <th>x4</th>\n",
       "      <th>x5</th>\n",
       "      <th>x6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   y1  y2  x1  x2  x3  x4  x5  x6\n",
       "0   5   5   5   5   5   5   5   5\n",
       "1   5   5   5   5   5   5   5   5\n",
       "2   4   4   4   4   4   4   4   4\n",
       "3   4   4   4   4   4   4   4   4\n",
       "4   1   1   2   2   2   2   2   1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"file.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod = \"\"\" # Measurement Model\n",
    "          eta1 =~ x1 + x2 + x3\n",
    "          eta2 =~ x4 + x5 + x6\n",
    "          eta =~ y1 + y2\n",
    "          \n",
    "          # Structural Model\n",
    "          eta ~ eta1 + eta2\n",
    "          \n",
    "          # Residual Correlations\n",
    "          x1 ~~ x4\n",
    "          x2 ~~ x5\n",
    "          x3 ~~ x6\n",
    "      \"\"\"\n",
    "model = Model(mod)\n",
    "model.load_dataset(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resultant objective functions values are:\n",
      "MLW: 1.275, ULS: 0.192, GLS: 1.806\n"
     ]
    }
   ],
   "source": [
    "opt_mlw = Optimizer(model)\n",
    "opt_uls = Optimizer(model)\n",
    "opt_gls = Optimizer(model)\n",
    "\n",
    "# And now, we run the optimisation sequences.\n",
    "lf_mlw = opt_mlw.optimize(objective='MLW') # Although MLW is default, we still provide it here for clarity.\n",
    "lf_uls = opt_uls.optimize(objective='ULS')\n",
    "lf_gls = opt_gls.optimize(objective='GLS')\n",
    "\n",
    "print('Resultant objective functions'' values are:')\n",
    "print('MLW: {:.3f}, ULS: {:.3f}, GLS: {:.3f}'.format(lf_mlw, lf_uls, lf_gls))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ULS after Adam: 0.192\n"
     ]
    }
   ],
   "source": [
    "opt_uls_adam = Optimizer(model)\n",
    "lf_uls_adam = opt_uls_adam.optimize(objective='ULS', method='Adam', chunk_size=100, num_epochs=2000)\n",
    "print('ULS after Adam: {:.3f}'.format(lf_uls_adam))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ULS after Adam after SLSQP: 1.275\n"
     ]
    }
   ],
   "source": [
    "lf_uls_adam_slsqp = opt_uls_adam.optimize(method='SLSQP')\n",
    "print('ULS after Adam after SLSQP: {:.3f}'.format(lf_uls_adam_slsqp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lval</th>\n",
       "      <th>op</th>\n",
       "      <th>rval</th>\n",
       "      <th>Value</th>\n",
       "      <th>SE</th>\n",
       "      <th>Z-score</th>\n",
       "      <th>P-value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>eta</td>\n",
       "      <td>=~</td>\n",
       "      <td>y2</td>\n",
       "      <td>0.826376</td>\n",
       "      <td>0.128337</td>\n",
       "      <td>6.439087</td>\n",
       "      <td>1.201943e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>eta1</td>\n",
       "      <td>=~</td>\n",
       "      <td>x2</td>\n",
       "      <td>1.347495</td>\n",
       "      <td>0.293036</td>\n",
       "      <td>4.598399</td>\n",
       "      <td>4.257502e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>eta1</td>\n",
       "      <td>=~</td>\n",
       "      <td>x3</td>\n",
       "      <td>1.519331</td>\n",
       "      <td>0.307714</td>\n",
       "      <td>4.937478</td>\n",
       "      <td>7.913944e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>eta2</td>\n",
       "      <td>=~</td>\n",
       "      <td>x5</td>\n",
       "      <td>1.388807</td>\n",
       "      <td>0.724993</td>\n",
       "      <td>1.915615</td>\n",
       "      <td>5.541410e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>eta2</td>\n",
       "      <td>=~</td>\n",
       "      <td>x6</td>\n",
       "      <td>1.581242</td>\n",
       "      <td>0.895972</td>\n",
       "      <td>1.764833</td>\n",
       "      <td>7.759186e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>eta</td>\n",
       "      <td>~</td>\n",
       "      <td>eta1</td>\n",
       "      <td>2.154062</td>\n",
       "      <td>1.051181</td>\n",
       "      <td>2.049183</td>\n",
       "      <td>4.044426e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>eta</td>\n",
       "      <td>~</td>\n",
       "      <td>eta2</td>\n",
       "      <td>-0.753287</td>\n",
       "      <td>1.234108</td>\n",
       "      <td>-0.610389</td>\n",
       "      <td>5.416039e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>eta</td>\n",
       "      <td>~~</td>\n",
       "      <td>eta</td>\n",
       "      <td>0.134991</td>\n",
       "      <td>0.148400</td>\n",
       "      <td>0.909643</td>\n",
       "      <td>3.630108e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>eta1</td>\n",
       "      <td>~~</td>\n",
       "      <td>eta1</td>\n",
       "      <td>0.325119</td>\n",
       "      <td>0.141303</td>\n",
       "      <td>2.300867</td>\n",
       "      <td>2.139913e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>eta1</td>\n",
       "      <td>~~</td>\n",
       "      <td>eta2</td>\n",
       "      <td>0.293968</td>\n",
       "      <td>0.191076</td>\n",
       "      <td>1.538491</td>\n",
       "      <td>1.239285e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>eta2</td>\n",
       "      <td>~~</td>\n",
       "      <td>eta2</td>\n",
       "      <td>0.219979</td>\n",
       "      <td>0.239771</td>\n",
       "      <td>0.917452</td>\n",
       "      <td>3.589060e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>x1</td>\n",
       "      <td>~~</td>\n",
       "      <td>x1</td>\n",
       "      <td>0.181504</td>\n",
       "      <td>0.060827</td>\n",
       "      <td>2.983927</td>\n",
       "      <td>2.845751e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>x1</td>\n",
       "      <td>~~</td>\n",
       "      <td>x4</td>\n",
       "      <td>0.235331</td>\n",
       "      <td>0.134908</td>\n",
       "      <td>1.744380</td>\n",
       "      <td>8.109278e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>x2</td>\n",
       "      <td>~~</td>\n",
       "      <td>x2</td>\n",
       "      <td>0.256551</td>\n",
       "      <td>0.095594</td>\n",
       "      <td>2.683753</td>\n",
       "      <td>7.280078e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>x2</td>\n",
       "      <td>~~</td>\n",
       "      <td>x5</td>\n",
       "      <td>-0.015165</td>\n",
       "      <td>0.040654</td>\n",
       "      <td>-0.373032</td>\n",
       "      <td>7.091248e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>x3</td>\n",
       "      <td>~~</td>\n",
       "      <td>x3</td>\n",
       "      <td>0.243837</td>\n",
       "      <td>0.095914</td>\n",
       "      <td>2.542259</td>\n",
       "      <td>1.101387e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>x3</td>\n",
       "      <td>~~</td>\n",
       "      <td>x6</td>\n",
       "      <td>-0.057843</td>\n",
       "      <td>0.123697</td>\n",
       "      <td>-0.467616</td>\n",
       "      <td>6.400590e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>x4</td>\n",
       "      <td>~~</td>\n",
       "      <td>x4</td>\n",
       "      <td>1.689287</td>\n",
       "      <td>0.485288</td>\n",
       "      <td>3.480999</td>\n",
       "      <td>4.995468e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>x5</td>\n",
       "      <td>~~</td>\n",
       "      <td>x5</td>\n",
       "      <td>0.173066</td>\n",
       "      <td>0.069515</td>\n",
       "      <td>2.489604</td>\n",
       "      <td>1.278854e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>x6</td>\n",
       "      <td>~~</td>\n",
       "      <td>x6</td>\n",
       "      <td>1.128621</td>\n",
       "      <td>0.330086</td>\n",
       "      <td>3.419173</td>\n",
       "      <td>6.281189e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>y1</td>\n",
       "      <td>~~</td>\n",
       "      <td>y1</td>\n",
       "      <td>0.108134</td>\n",
       "      <td>0.060656</td>\n",
       "      <td>1.782731</td>\n",
       "      <td>7.463017e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>y2</td>\n",
       "      <td>~~</td>\n",
       "      <td>y2</td>\n",
       "      <td>0.211369</td>\n",
       "      <td>0.071600</td>\n",
       "      <td>2.952084</td>\n",
       "      <td>3.156372e-03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    lval  op  rval     Value        SE   Z-score       P-value\n",
       "6    eta  =~    y2  0.826376  0.128337  6.439087  1.201943e-10\n",
       "2   eta1  =~    x2  1.347495  0.293036  4.598399  4.257502e-06\n",
       "3   eta1  =~    x3  1.519331  0.307714  4.937478  7.913944e-07\n",
       "4   eta2  =~    x5  1.388807  0.724993  1.915615  5.541410e-02\n",
       "5   eta2  =~    x6  1.581242  0.895972  1.764833  7.759186e-02\n",
       "0    eta   ~  eta1  2.154062  1.051181  2.049183  4.044426e-02\n",
       "1    eta   ~  eta2 -0.753287  1.234108 -0.610389  5.416039e-01\n",
       "7    eta  ~~   eta  0.134991  0.148400  0.909643  3.630108e-01\n",
       "8   eta1  ~~  eta1  0.325119  0.141303  2.300867  2.139913e-02\n",
       "9   eta1  ~~  eta2  0.293968  0.191076  1.538491  1.239285e-01\n",
       "10  eta2  ~~  eta2  0.219979  0.239771  0.917452  3.589060e-01\n",
       "11    x1  ~~    x1  0.181504  0.060827  2.983927  2.845751e-03\n",
       "12    x1  ~~    x4  0.235331  0.134908  1.744380  8.109278e-02\n",
       "13    x2  ~~    x2  0.256551  0.095594  2.683753  7.280078e-03\n",
       "14    x2  ~~    x5 -0.015165  0.040654 -0.373032  7.091248e-01\n",
       "15    x3  ~~    x3  0.243837  0.095914  2.542259  1.101387e-02\n",
       "16    x3  ~~    x6 -0.057843  0.123697 -0.467616  6.400590e-01\n",
       "17    x4  ~~    x4  1.689287  0.485288  3.480999  4.995468e-04\n",
       "18    x5  ~~    x5  0.173066  0.069515  2.489604  1.278854e-02\n",
       "19    x6  ~~    x6  1.128621  0.330086  3.419173  6.281189e-04\n",
       "20    y1  ~~    y1  0.108134  0.060656  1.782731  7.463017e-02\n",
       "21    y2  ~~    y2  0.211369  0.071600  2.952084  3.156372e-03"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inspect(opt_uls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta:\n",
      "      eta      eta1      eta2\n",
      "eta   0.0  2.154062 -0.753287\n",
      "eta1  0.0  0.000000  0.000000\n",
      "eta2  0.0  0.000000  0.000000\n",
      "Lambda:\n",
      "         eta      eta1      eta2\n",
      "x1  0.000000  1.000000  0.000000\n",
      "x2  0.000000  1.347495  0.000000\n",
      "x3  0.000000  1.519331  0.000000\n",
      "x4  0.000000  0.000000  1.000000\n",
      "x5  0.000000  0.000000  1.388807\n",
      "x6  0.000000  0.000000  1.581242\n",
      "y1  1.000000  0.000000  0.000000\n",
      "y2  0.826376  0.000000  0.000000\n",
      "Psi:\n",
      "           eta      eta1      eta2\n",
      "eta   0.134991  0.000000  0.000000\n",
      "eta1  0.000000  0.325119  0.293968\n",
      "eta2  0.000000  0.293968  0.219979\n",
      "Theta:\n",
      "          x1        x2        x3        x4        x5        x6        y1  \\\n",
      "x1  0.181504  0.000000  0.000000  0.235331  0.000000  0.000000  0.000000   \n",
      "x2  0.000000  0.256551  0.000000  0.000000 -0.015165  0.000000  0.000000   \n",
      "x3  0.000000  0.000000  0.243837  0.000000  0.000000 -0.057843  0.000000   \n",
      "x4  0.235331  0.000000  0.000000  1.689287  0.000000  0.000000  0.000000   \n",
      "x5  0.000000 -0.015165  0.000000  0.000000  0.173066  0.000000  0.000000   \n",
      "x6  0.000000  0.000000 -0.057843  0.000000  0.000000  1.128621  0.000000   \n",
      "y1  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.108134   \n",
      "y2  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
      "\n",
      "          y2  \n",
      "x1  0.000000  \n",
      "x2  0.000000  \n",
      "x3  0.000000  \n",
      "x4  0.000000  \n",
      "x5  0.000000  \n",
      "x6  0.000000  \n",
      "y1  0.000000  \n",
      "y2  0.211369  \n",
      "Sigma:\n",
      "          x1        x2        x3        x4        x5        x6        y1  \\\n",
      "x1  0.506622  0.438096  0.493963  0.529300  0.408265  0.464835  0.478883   \n",
      "x2  0.438096  0.846883  0.665613  0.396121  0.534970  0.626363  0.645293   \n",
      "x3  0.493963  0.665613  0.994330  0.446635  0.620290  0.648395  0.727582   \n",
      "x4  0.529300  0.396121  0.446635  1.909266  0.305508  0.347839  0.467519   \n",
      "x5  0.408265  0.534970  0.620290  0.305508  0.597357  0.483081  0.649293   \n",
      "x6  0.464835  0.626363  0.648395  0.347839  0.483081  1.678639  0.739260   \n",
      "y1  0.478883  0.645293  0.727582  0.467519  0.649293  0.739260  0.922494   \n",
      "y2  0.395738  0.533255  0.601257  0.386346  0.536560  0.610907  0.672968   \n",
      "\n",
      "          y2  \n",
      "x1  0.395738  \n",
      "x2  0.533255  \n",
      "x3  0.601257  \n",
      "x4  0.386346  \n",
      "x5  0.536560  \n",
      "x6  0.610907  \n",
      "y1  0.672968  \n",
      "y2  0.767494  \n",
      "Cov:\n",
      "          x1        x2        x3        x4        x5        x6        y1  \\\n",
      "x1  0.506616  0.395085  0.476371  0.529301  0.425331  0.448015  0.457467   \n",
      "x2  0.395085  0.846881  0.706994  0.258979  0.534972  0.703214  0.689981   \n",
      "x3  0.476371  0.706994  0.994329  0.457467  0.623819  0.648393  0.720227   \n",
      "x4  0.529301  0.258979  0.457467  1.909263  0.287335  0.275992  0.640832   \n",
      "x5  0.425331  0.534972  0.623819  0.287335  0.597353  0.546314  0.601134   \n",
      "x6  0.448015  0.703214  0.648393  0.275992  0.546314  1.678639  0.654064   \n",
      "y1  0.457467  0.689981  0.720227  0.640832  0.601134  0.654064  0.922495   \n",
      "y2  0.493384  0.474480  0.567108  0.383743  0.531191  0.638941  0.672968   \n",
      "\n",
      "          y2  \n",
      "x1  0.493384  \n",
      "x2  0.474480  \n",
      "x3  0.567108  \n",
      "x4  0.383743  \n",
      "x5  0.531191  \n",
      "x6  0.638941  \n",
      "y1  0.672968  \n",
      "y2  0.767486  \n",
      "[('Beta',       eta      eta1      eta2\n",
      "eta   0.0  2.154062 -0.753287\n",
      "eta1  0.0  0.000000  0.000000\n",
      "eta2  0.0  0.000000  0.000000), ('Lambda',          eta      eta1      eta2\n",
      "x1  0.000000  1.000000  0.000000\n",
      "x2  0.000000  1.347495  0.000000\n",
      "x3  0.000000  1.519331  0.000000\n",
      "x4  0.000000  0.000000  1.000000\n",
      "x5  0.000000  0.000000  1.388807\n",
      "x6  0.000000  0.000000  1.581242\n",
      "y1  1.000000  0.000000  0.000000\n",
      "y2  0.826376  0.000000  0.000000), ('Psi',            eta      eta1      eta2\n",
      "eta   0.134991  0.000000  0.000000\n",
      "eta1  0.000000  0.325119  0.293968\n",
      "eta2  0.000000  0.293968  0.219979), ('Theta',           x1        x2        x3        x4        x5        x6        y1  \\\n",
      "x1  0.181504  0.000000  0.000000  0.235331  0.000000  0.000000  0.000000   \n",
      "x2  0.000000  0.256551  0.000000  0.000000 -0.015165  0.000000  0.000000   \n",
      "x3  0.000000  0.000000  0.243837  0.000000  0.000000 -0.057843  0.000000   \n",
      "x4  0.235331  0.000000  0.000000  1.689287  0.000000  0.000000  0.000000   \n",
      "x5  0.000000 -0.015165  0.000000  0.000000  0.173066  0.000000  0.000000   \n",
      "x6  0.000000  0.000000 -0.057843  0.000000  0.000000  1.128621  0.000000   \n",
      "y1  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.108134   \n",
      "y2  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
      "\n",
      "          y2  \n",
      "x1  0.000000  \n",
      "x2  0.000000  \n",
      "x3  0.000000  \n",
      "x4  0.000000  \n",
      "x5  0.000000  \n",
      "x6  0.000000  \n",
      "y1  0.000000  \n",
      "y2  0.211369  ), ('Sigma',           x1        x2        x3        x4        x5        x6        y1  \\\n",
      "x1  0.506622  0.438096  0.493963  0.529300  0.408265  0.464835  0.478883   \n",
      "x2  0.438096  0.846883  0.665613  0.396121  0.534970  0.626363  0.645293   \n",
      "x3  0.493963  0.665613  0.994330  0.446635  0.620290  0.648395  0.727582   \n",
      "x4  0.529300  0.396121  0.446635  1.909266  0.305508  0.347839  0.467519   \n",
      "x5  0.408265  0.534970  0.620290  0.305508  0.597357  0.483081  0.649293   \n",
      "x6  0.464835  0.626363  0.648395  0.347839  0.483081  1.678639  0.739260   \n",
      "y1  0.478883  0.645293  0.727582  0.467519  0.649293  0.739260  0.922494   \n",
      "y2  0.395738  0.533255  0.601257  0.386346  0.536560  0.610907  0.672968   \n",
      "\n",
      "          y2  \n",
      "x1  0.395738  \n",
      "x2  0.533255  \n",
      "x3  0.601257  \n",
      "x4  0.386346  \n",
      "x5  0.536560  \n",
      "x6  0.610907  \n",
      "y1  0.672968  \n",
      "y2  0.767494  ), ('Cov',           x1        x2        x3        x4        x5        x6        y1  \\\n",
      "x1  0.506616  0.395085  0.476371  0.529301  0.425331  0.448015  0.457467   \n",
      "x2  0.395085  0.846881  0.706994  0.258979  0.534972  0.703214  0.689981   \n",
      "x3  0.476371  0.706994  0.994329  0.457467  0.623819  0.648393  0.720227   \n",
      "x4  0.529301  0.258979  0.457467  1.909263  0.287335  0.275992  0.640832   \n",
      "x5  0.425331  0.534972  0.623819  0.287335  0.597353  0.546314  0.601134   \n",
      "x6  0.448015  0.703214  0.648393  0.275992  0.546314  1.678639  0.654064   \n",
      "y1  0.457467  0.689981  0.720227  0.640832  0.601134  0.654064  0.922495   \n",
      "y2  0.493384  0.474480  0.567108  0.383743  0.531191  0.638941  0.672968   \n",
      "\n",
      "          y2  \n",
      "x1  0.493384  \n",
      "x2  0.474480  \n",
      "x3  0.567108  \n",
      "x4  0.383743  \n",
      "x5  0.531191  \n",
      "x6  0.638941  \n",
      "y1  0.672968  \n",
      "y2  0.767486  )]\n"
     ]
    }
   ],
   "source": [
    "print(inspect(opt_uls, mode='mx'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SEMStatistics(dof=14.0, ml=-184.278031738658, fit_val=0.19176380950153094, chi2=(4.410567618535212, 0.9924460389989741), dof_baseline=28.0, chi2_baseline=384.2416372154187, rmsea=0, cfi=1.0269183368244685, gfi=0.9885213699106157, agfi=0.9770427398212314, nfi=0.9885213699106157, tli=1.0538366736489373, aic=412.556063477316, bic=437.5369362277573, params=[ParametersStatistics(value=2.1540622219691907, se=1.0511811636430433, zscore=2.049182668477316, pvalue=0.04044425616840508), ParametersStatistics(value=-0.7532866496693092, se=1.2341083393264425, zscore=-0.6103894007229796, pvalue=0.5416038877343083), ParametersStatistics(value=1.347495347915129, se=0.29303576700483924, zscore=4.59839889745704, pvalue=4.257502356441734e-06), ParametersStatistics(value=1.5193311987681783, se=0.30771403563937344, zscore=4.937477731902443, pvalue=7.913943962378767e-07), ParametersStatistics(value=1.3888066446160297, se=0.7249925160964029, zscore=1.9156151460595812, pvalue=0.055414100243476705), ParametersStatistics(value=1.581241701517513, se=0.8959724893004039, zscore=1.7648328719896507, pvalue=0.07759185824254922), ParametersStatistics(value=0.8263761265871724, se=0.12833746837817325, zscore=6.439087018185857, pvalue=1.2019429895815392e-10), ParametersStatistics(value=0.13499097284715714, se=0.14839993699709272, zscore=0.9096430603531326, pvalue=0.36301078178800505), ParametersStatistics(value=0.32511859341356897, se=0.14130262400264196, zscore=2.3008673455716524, pvalue=0.021399130368671804), ParametersStatistics(value=0.29396819073010216, se=0.19107563560819632, zscore=1.5384912356452929, pvalue=0.12392854983704504), ParametersStatistics(value=0.21997855125963156, se=0.23977124924571575, zscore=0.9174517459901198, pvalue=0.3589059676885946), ParametersStatistics(value=0.1815036940029344, se=0.060827132560970304, zscore=2.983926520258366, pvalue=0.0028457510321766577), ParametersStatistics(value=0.23533145380350842, se=0.13490833210234532, zscore=1.7443804258378561, pvalue=0.08109277589578467), ParametersStatistics(value=0.2565511814741313, se=0.09559416984258216, zscore=2.6837534328078605, pvalue=0.007280077502727522), ParametersStatistics(value=-0.015165073777272171, se=0.04065357508289294, zscore=-0.3730317381922117, pvalue=0.7091248224204996), ParametersStatistics(value=0.2438369767457991, se=0.09591352505180509, zscore=2.5422585251825005, pvalue=0.01101386756928835), ParametersStatistics(value=-0.05784277996241692, se=0.12369709480784122, zscore=-0.4676163175198729, pvalue=0.6400589937805727), ParametersStatistics(value=1.6892872393420775, se=0.4852880118254436, zscore=3.4809993203504628, pvalue=0.0004995467588473357), ParametersStatistics(value=0.17306600925004376, se=0.06951547096726793, zscore=2.48960421096829, pvalue=0.01278854209618574), ParametersStatistics(value=1.128620722934797, se=0.3300859241177407, zscore=3.4191725259051102, pvalue=0.0006281188727368381), ParametersStatistics(value=0.10813368919124043, se=0.06065621388120214, zscore=1.7827306102758456, pvalue=0.07463016598692196), ParametersStatistics(value=0.21136923343658195, se=0.07160000917998643, zscore=2.9520838873399415, pvalue=0.0031563716872222702)])\n"
     ]
    }
   ],
   "source": [
    "s = gather_statistics(opt_uls)\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLW: 0.832, ULS: 0.989, GLS: 0.531, GLS after Adam : 0.832\n"
     ]
    }
   ],
   "source": [
    "print('MLW: {:.3f}, ULS: {:.3f}, GLS: {:.3f}, GLS after Adam : {:.3f}'.format(calc_gfi(opt_mlw),\n",
    "                                                                                         calc_gfi(opt_uls),\n",
    "                                                                                         calc_gfi(opt_gls),\n",
    "                                                                                         calc_gfi(opt_uls_adam)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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