From 4d77b625653e75d5976e9ebdb73232ca81eb5af2 Mon Sep 17 00:00:00 2001 From: Gabriel Stechschulte Date: Thu, 14 Sep 2023 14:23:44 +0200 Subject: [PATCH] unified explanation for cumulative and sequential models --- docs/notebooks/ordinal_regression.ipynb | 210 +++++++++++++++--------- 1 file changed, 129 insertions(+), 81 deletions(-) diff --git a/docs/notebooks/ordinal_regression.ipynb b/docs/notebooks/ordinal_regression.ipynb index 9913f843a..cb1cfed0e 100644 --- a/docs/notebooks/ordinal_regression.ipynb +++ b/docs/notebooks/ordinal_regression.ipynb @@ -2,9 +2,19 @@ "cells": [ { "cell_type": "code", - "execution_count": 85, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.configdefaults): g++ not available, if using conda: `conda install m2w64-toolchain`\n", + "WARNING (pytensor.configdefaults): g++ not detected! PyTensor will be unable to compile C-implementations and will default to Python. Performance may be severely degraded. To remove this warning, set PyTensor flags cxx to an empty string.\n", + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + } + ], "source": [ "import arviz as az\n", "import matplotlib.pyplot as plt\n", @@ -36,19 +46,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Cumulative link model\n", + "## Cumulative model\n", "\n", - "In principle, an ordered categorical response is a multinomial prediction problem. However, the constraint that the categories are *ordered* requires a different approach. Ideally, what we would like is for any predictor variable, as it increases, predictions are moved progressively (increased) through the categories in sequence. \n", + "A cumulative model assumes that the observed ordinal variable $Y$ originates from the \"categorization\" of a latent continuous variable $\\hat{Y}$. To model the categorization process, the model assumes that there are $K$ thresholds (cutpoints) $\\tau_k$ that partition $\\hat{Y}$ into $K+1$ observable, ordered categories. Additionally, if we assume $\\hat{Y}$ to have a certain distribution (e.g., Normal) with a cumulative distribution function $F$, the probability of $Y$ being equal to category $k$ is\n", "\n", - "To achieve this, a cumulative link function is used. A cumulative model assumes that the observed ordinal category $Y$ is generated from an underlying latent continuous variable $\\hat{Y}$, which is then mapped to the observed category $Y$ via a set of cutpoints $\\tau$. For example, the model assumes $K$ cutpoints $\\tau_{k}$ that partition $\\hat{Y}$ into $K+1$ observable, ordered categories.\n", + "$$Pr(Y = k) = F(\\tau_k) - F(\\tau_{k-1})$$\n", "\n", - "By linking a linear model to a cumulative probability, it is possible to guarantee the ordering of outcomes. The cumulative probability of an ordered category is the probability of that value or *any smaller value*. Building off of the rating example above, the probability of a 4 is the probability of 4, 3, 2, and 1.\n", + "where each $F(\\tau)$ is a cumulative probability. For example, suppose we have 3 categories and we are interested in the probability of $k=3$, and have thresholds $\\tau_0 = -1, \\tau_1 = 0, \\tau_2 = 1$. Additionally, if we assume $\\hat{Y}$ to be normally distributed with $\\sigma = 1$ then\n", "\n", - "The log-cumulative-odds that a response value $y_i$ is equal to or less than some possible outcome value $k$ is given by:\n", + "$$Pr(Y = 3) = \\Phi(\\tau_2) - \\Phi(\\tau_1) - \\Phi(\\tau_0)$$\n", "\n", - "$$\\text{log} \\frac{Pr(y_i \\le k)}{1 - Pr(y_i \\le k)} = \\alpha_k$$\n", + "How to set the thresholds? By default, Bambi uses a Normal distribution with a grid of evenly spaced $\\mu$'s that depends on the number of $k$ as the prior for the thresholds. Furthermore, the model specification for ordinal regression typically transforms the cumulative probabilities using the log-cumulative-odds (logit) transformation. Therefore, the learned parameters for the thresholds $\\tau$ will be logits.\n", "\n", - "where $\\alpha_k$ is the intercept of outcome $k$. Each intercept $\\alpha_k$ implies a cumulative probability for each $k$. Since the largest response value always has a cumulative probability of 1, we effectively do not need a parameter for it due to the law of total probability. For example, for $K = 5$ possible response values, we only need $K − 1 = 4$ intercepts." + "Lastly, as each $F(\\tau)$ implies a cumulative probability for each $k$, the largest response value always has a cumulative probability of 1. Thus, we effectively do not need a parameter for it due to the law of total probability. For example, for $K = 3$ response values, we only need $K − 1 = 2$ intercepts." ] }, { @@ -68,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -82,7 +92,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -92,7 +102,7 @@ "Categories (7, int64): [1 < 2 < 3 < 4 < 5 < 6 < 7]" ] }, - "execution_count": 4, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -113,14 +123,14 @@ }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/rl/y69t95y51g90tvd6gjzzs59h0000gn/T/ipykernel_32825/1548491577.py:3: RuntimeWarning: invalid value encountered in log\n", + "C:\\Users\\stechsga\\AppData\\Local\\Temp\\ipykernel_9160\\1548491577.py:3: RuntimeWarning: invalid value encountered in log\n", " logit_func = lambda x: np.log(x / (1 - x))\n" ] }, @@ -131,7 +141,7 @@ " 1.76938091, nan])" ] }, - "execution_count": 102, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -146,15 +156,17 @@ }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "/Users/gabestechschulte/Documents/repos/bambi/bambi/formula.py:111: UserWarning: The intercept is omitted in ordinal families\n", + "c:\\Users\\stechsga\\Miniconda3\\envs\\bambi\\Lib\\site-packages\\bambi\\formula.py:111: UserWarning: The intercept is omitted in ordinal families\n", " warnings.warn(\"The intercept is omitted in ordinal families\")\n", + "c:\\Users\\stechsga\\Miniconda3\\envs\\bambi\\Lib\\site-packages\\formulae\\terms\\variable.py:87: FutureWarning: is_categorical_dtype is deprecated and will be removed in a future version. Use isinstance(dtype, CategoricalDtype) instead\n", + " elif is_string_dtype(x) or is_categorical_dtype(x):\n", "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (4 chains in 4 jobs)\n", @@ -194,7 +206,7 @@ "\n", "
\n", " \n", - " 100.00% [8000/8000 00:03<00:00 Sampling 4 chains, 0 divergences]\n", + " 100.00% [8000/8000 19:14<00:00 Sampling 4 chains, 0 divergences]\n", "
\n", " " ], @@ -209,17 +221,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/Users/gabestechschulte/miniforge3/envs/bambinos/lib/python3.11/site-packages/pytensor/compile/function/types.py:970: RuntimeWarning: invalid value encountered in add\n", - " self.vm()\n", - "/Users/gabestechschulte/miniforge3/envs/bambinos/lib/python3.11/site-packages/pytensor/compile/function/types.py:970: RuntimeWarning: invalid value encountered in add\n", - " self.vm()\n", - "/Users/gabestechschulte/miniforge3/envs/bambinos/lib/python3.11/site-packages/pytensor/compile/function/types.py:970: RuntimeWarning: invalid value encountered in add\n", - " self.vm()\n", - "/Users/gabestechschulte/miniforge3/envs/bambinos/lib/python3.11/site-packages/pytensor/compile/function/types.py:970: RuntimeWarning: invalid value encountered in add\n", - " self.vm()\n", - "/Users/gabestechschulte/miniforge3/envs/bambinos/lib/python3.11/site-packages/pytensor/compile/function/types.py:970: RuntimeWarning: invalid value encountered in accumulate\n", - " self.vm()\n", - "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 3 seconds.\n" + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 1174 seconds.\n" ] } ], @@ -230,7 +232,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -270,11 +272,11 @@ " response_threshold[0]\n", " -1.923\n", " 0.030\n", - " -1.981\n", - " -1.869\n", + " -1.979\n", + " -1.868\n", " 0.0\n", " 0.0\n", - " 4206.0\n", + " 4152.0\n", " 3065.0\n", " 1.0\n", " \n", @@ -282,60 +284,60 @@ " response_threshold[1]\n", " -1.270\n", " 0.024\n", - " -1.314\n", - " -1.225\n", + " -1.315\n", + " -1.223\n", " 0.0\n", " 0.0\n", - " 5095.0\n", - " 3329.0\n", + " 5031.0\n", + " 3389.0\n", " 1.0\n", " \n", " \n", " response_threshold[2]\n", " -0.719\n", " 0.021\n", - " -0.760\n", - " -0.681\n", + " -0.758\n", + " -0.678\n", " 0.0\n", " 0.0\n", - " 5042.0\n", - " 3302.0\n", + " 5272.0\n", + " 3462.0\n", " 1.0\n", " \n", " \n", " response_threshold[3]\n", " 0.248\n", " 0.020\n", - " 0.212\n", - " 0.286\n", + " 0.208\n", + " 0.285\n", " 0.0\n", " 0.0\n", - " 4812.0\n", - " 3272.0\n", + " 4636.0\n", + " 3102.0\n", " 1.0\n", " \n", " \n", " response_threshold[4]\n", " 0.892\n", " 0.022\n", - " 0.851\n", - " 0.933\n", + " 0.852\n", + " 0.935\n", " 0.0\n", " 0.0\n", - " 4978.0\n", - " 3397.0\n", + " 4861.0\n", + " 3639.0\n", " 1.0\n", " \n", " \n", " response_threshold[5]\n", - " 1.775\n", - " 0.028\n", + " 1.774\n", + " 0.029\n", " 1.721\n", - " 1.827\n", + " 1.829\n", " 0.0\n", " 0.0\n", - " 5575.0\n", - " 3372.0\n", + " 5602.0\n", + " 3655.0\n", " 1.0\n", " \n", " \n", @@ -343,24 +345,24 @@ "" ], "text/plain": [ - " mean sd hdi_3% hdi_97% mcse_mean mcse_sd \n", - "response_threshold[0] -1.923 0.030 -1.981 -1.869 0.0 0.0 \\\n", - "response_threshold[1] -1.270 0.024 -1.314 -1.225 0.0 0.0 \n", - "response_threshold[2] -0.719 0.021 -0.760 -0.681 0.0 0.0 \n", - "response_threshold[3] 0.248 0.020 0.212 0.286 0.0 0.0 \n", - "response_threshold[4] 0.892 0.022 0.851 0.933 0.0 0.0 \n", - "response_threshold[5] 1.775 0.028 1.721 1.827 0.0 0.0 \n", + " mean sd hdi_3% hdi_97% mcse_mean mcse_sd \\\n", + "response_threshold[0] -1.923 0.030 -1.979 -1.868 0.0 0.0 \n", + "response_threshold[1] -1.270 0.024 -1.315 -1.223 0.0 0.0 \n", + "response_threshold[2] -0.719 0.021 -0.758 -0.678 0.0 0.0 \n", + "response_threshold[3] 0.248 0.020 0.208 0.285 0.0 0.0 \n", + "response_threshold[4] 0.892 0.022 0.852 0.935 0.0 0.0 \n", + "response_threshold[5] 1.774 0.029 1.721 1.829 0.0 0.0 \n", "\n", " ess_bulk ess_tail r_hat \n", - "response_threshold[0] 4206.0 3065.0 1.0 \n", - "response_threshold[1] 5095.0 3329.0 1.0 \n", - "response_threshold[2] 5042.0 3302.0 1.0 \n", - "response_threshold[3] 4812.0 3272.0 1.0 \n", - "response_threshold[4] 4978.0 3397.0 1.0 \n", - "response_threshold[5] 5575.0 3372.0 1.0 " + "response_threshold[0] 4152.0 3065.0 1.0 \n", + "response_threshold[1] 5031.0 3389.0 1.0 \n", + "response_threshold[2] 5272.0 3462.0 1.0 \n", + "response_threshold[3] 4636.0 3102.0 1.0 \n", + "response_threshold[4] 4861.0 3639.0 1.0 \n", + "response_threshold[5] 5602.0 3655.0 1.0 " ] }, - "execution_count": 6, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -380,17 +382,19 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -407,17 +411,19 @@ }, { "cell_type": "code", - "execution_count": 96, + "execution_count": 10, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -445,14 +451,17 @@ "source": [ "### Adding predictors\n", "\n", + "In the cumulative model described above, adding predictors was explicitly left out. In this section, it is described how predictors are added to ordinal cumulative models. When adding predictor variables, what we would like is for any predictor, as it increases, predictions are moved progressively (increased) through the categories in sequence. A predictor term $\\eta$ is defined as\n", + "\n", + "$$\\eta = \\beta_1 x_1 + \\beta_2 x_2 +, . . ., \\beta_n x_n + \\epsilon$$\n", "\n", - "To include predictor variables, we define the log-cumulative-odds of each response $k$ as a sum of its intercept $\\alpha_k$ and a linear model $\\phi$ where $\\phi_i = \\beta x_i$\n", + "Note how similar this looks to an ordinary linear model. However, there is no intercept term. This is because the intercept is replaced by the threshold $\\tau$. Putting the predictor term together with the thresholds and cumulative distribution function, we obtain the probability of $Y$ being equal to a category $k$ as\n", "\n", - "$$\\text{log} \\frac{Pr(y_i \\le k)}{1 - Pr(y_i \\le k)} = \\alpha_k - \\phi_i$$\n", + "$$Pr(Y = k | \\eta) = F(\\tau_k - \\eta) - F(\\tau_{k-1} - \\eta)$$\n", "\n", - "The linear model $\\phi$ is subtracted from each intercept because if we decrease the log-cumulative-odds of every outcome value $k$ below the maximum, this shifts probability mass upwards towards higher outcome values. Thus, positive $\\beta$ values correspond to increasing $x$, which is associated with an increase in the mean $y$.\n", + "The same predictor term $\\eta$ is subtracted from each threshold because if we decrease the log-cumulative-odds of every outcome value $k$ below the maximum, this shifts probability mass upwards towards higher outcome values. Thus, positive $\\beta$ values correspond to increasing $x$, which is associated with an increase in the mean response $Y$. The parameters to be estimated from the model are the thresholds $\\tau$ and the predictor terms $\\eta$ coefficients. \n", "\n", - "However, to add predictors for ordinal models in Bambi, we continue to use the familiar syntax." + "To add predictors for ordinal models in Bambi, we continue to use the familiar syntax." ] }, { @@ -807,6 +816,45 @@ "**TO DO**" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sequential Model\n", + "\n", + "For some ordinal variables, the assumption of a **single** underlying continuous variable (as in cumulative models) may not be appropriate. If the response can be understood as being the result of a sequential process, such that a higher response category is possible only after all lower categories are achieved, then a sequential model may be more appropriate than a cumulative model.\n", + "\n", + "Sequential models assume that for **every** category $k$ there is latent continuous variable $\\hat{Y_k}$ that determines the transition between categories $k$ and $k+1$. Now, a threshold $\\tau$ belongs to each latent process. If there are 3 categories, then there are 3 latent processes. If $\\hat{Y}_k$ is greater than the threshold $\\tau_k$, the sequential process continues, otherwise it stops at category $k$. As with the cumulative model, we still assume a distribution for $\\hat{Y}_k$ with a cumulative distribution function $F$.\n", + "\n", + "As an example, lets suppose we are interested in modeling the probability a boxer makes it to round 3. This implies that the particular boxer in question survived round 1 $\\hat{Y}_1 > \\tau_1$ , 2 $\\hat{Y}_2 > \\tau_2$, and 3 $\\hat{Y}_3 > \\tau_3$. This can be written as \n", + "\n", + "$$Pr(Y = 3) = (1 - Pr(\\hat{Y_1})(1 - Pr(\\hat{Y_2}))(1 - Pr(\\hat{Y_3})$$\n", + "\n", + "As in the cumulative model above, if we assume $Y$ to be normally distributed with the thresholds $\\tau_0 = -1, \\tau_1 = 0, \\tau_2 = 1$ and cumulative distribution function $\\Phi$ then\n", + "\n", + "$$Pr(Y = 3) = (1 - \\Phi(\\tau_0))(1 - \\Phi(\\tau_1))(1 - \\Phi(\\tau_2))$$\n", + "\n", + "To add predictors to this sequential model, we follow the same specification in the _Adding Predictors_ section above. Thus, the sequential model with predictor terms becomes\n", + "\n", + "$$P(Y = k) = F(\\tau_k - \\eta) * \\prod_{j=1}^{k-1}{(1 - F(\\tau_j - \\eta))}$$\n", + "\n", + "Thus, the probability that $Y$ is equal to category $k$ is equal to the probability that it did not fall in one of the former categories $1: k-1$ multiplied by the probability that the sequential process stopped at $k$ rather than continuing past it." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": null, @@ -831,7 +879,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.0" + "version": "3.11.5" }, "orig_nbformat": 4 },