docs/notebooks/negative_binomial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Negative Binomial Regression (Students absence example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative binomial distribution review"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I always experience some kind of confusion when looking at the negative binomial distribution after a while of not working with it. There are so many different definitions that I usually need to read everything more than once. The definition I've first learned, and the one I like the most, says as follows: The negative binomial distribution is the distribution of a random variable that is defined as the number of independent Bernoulli trials until the k-th \"success\". In short, we repeat a Bernoulli experiment until we observe k  successes and record the number of trials it required.\n",
    "\n",
    "$$\n",
    "Y \\sim \\text{NB}(k, p)\n",
    "$$\n",
    "\n",
    "where $0 \\le p \\le 1$ is the probability of success in each Bernoulli trial, $k > 0$, usually integer, and $y \\in \\{k, k + 1, \\cdots\\}$\n",
    "\n",
    "The probability mass function (pmf) is \n",
    "\n",
    "$$\n",
    "p(y | k, p)= \\binom{y - 1}{y-k}(1 -p)^{y - k}p^k\n",
    "$$\n",
    "\n",
    "If you, like me, find it hard to remember whether $y$ starts at $0$, $1$, or $k$, try to think twice about the definition of the variable. But how? First, recall we aim to have $k$ successes. And success is one of the two possible outcomes of a trial, so the number of trials can never be smaller than the number of successes. Thus, we can be confident to say that $y \\ge k$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But this is not the only way of defining the negative binomial distribution, there are plenty of options! One of the most interesting, and the one you see in [PyMC3](https://docs.pymc.io/api/distributions/discrete.html#pymc3.distributions.discrete.NegativeBinomial), the library we use in Bambi for the backend, is as a continuous mixture. The negative binomial distribution describes a Poisson random variable whose rate is also a random variable (not a fixed constant!) following a gamma distribution. Or in other words, conditional on a gamma-distributed variable $\\mu$, the variable $Y$ has a Poisson distribution with mean $\\mu$.\n",
    "\n",
    "Under this alternative definition, the pmf is\n",
    "\n",
    "$$\n",
    "\\displaystyle p(y | k, \\alpha) = \\binom{y + \\alpha - 1}{y} \\left(\\frac{\\alpha}{\\mu + \\alpha}\\right)^\\alpha\\left(\\frac{\\mu}{\\mu + \\alpha}\\right)^y\n",
    "$$\n",
    "\n",
    "where $\\mu$ is the parameter of the Poisson distribution (the mean, and variance too!) and $\\alpha$ is the rate parameter of the gamma."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "import bambi as bmb\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.stats import nbinom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter(action='ignore', category=FutureWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In SciPy, the definition of the negative binomial distribution differs a little from the one in our introduction. They define $Y$ = Number of failures until k successes and then $y$ starts at 0. In the following plot, we have  the probability of observing $y$ failures before we see $k=3$ successes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.arange(0, 30)\n",
    "k = 3\n",
    "p1 = 0.5\n",
    "p2 = 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n",
    "\n",
    "ax[0].bar(y, nbinom.pmf(y, k, p1))\n",
    "ax[0].set_xticks(np.linspace(0, 30, num=11))\n",
    "ax[0].set_title(f\"k = {k}, p = {p1}\")\n",
    "\n",
    "ax[1].bar(y, nbinom.pmf(y, k, p2))\n",
    "ax[1].set_xticks(np.linspace(0, 30, num=11))\n",
    "ax[1].set_title(f\"k = {k}, p = {p2}\")\n",
    "\n",
    "fig.suptitle(\"Y = Number of failures until k successes\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, when $p=0.5$, the probability of seeing $y=0$ failures before 3 successes (or in other words, the probability of having 3 successes out of 3 trials) is 0.125, and the probability of seeing $y=3$ failures before 3 successes is 0.156."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.12499999999999997\n",
      "0.15624999999999992\n"
     ]
    }
   ],
   "source": [
    "print(nbinom.pmf(y, k, p1)[0])\n",
    "print(nbinom.pmf(y, k, p1)[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if one wants to show this probability mass function as if we are following the first definition of negative binomial distribution we introduced, we just need to shift the whole thing to the right by adding $k$ to the $y$ values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n",
    "\n",
    "ax[0].bar(y + k, nbinom.pmf(y, k, p1))\n",
    "ax[0].set_xticks(np.linspace(3, 30, num=10))\n",
    "ax[0].set_title(f\"k = {k}, p = {p1}\")\n",
    "\n",
    "ax[1].bar(y + k, nbinom.pmf(y, k, p2))\n",
    "ax[1].set_xticks(np.linspace(3, 30, num=10))\n",
    "ax[1].set_title(f\"k = {k}, p = {p2}\")\n",
    "\n",
    "fig.suptitle(\"Y = Number of trials until k successes\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative binomial in GLM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The negative binomial distribution belongs to the exponential family, and the canonical link function is \n",
    "\n",
    "$$\n",
    "g(\\mu_i) = \\log\\left(\\frac{\\mu_i}{k + \\mu_i}\\right) = \\log\\left(\\frac{k}{\\mu_i} + 1\\right)\n",
    "$$\n",
    "\n",
    "but it is difficult to interpret. The log link is usually preferred because of the analogy with Poisson model, and it also tends to give better results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and explore Students data\n",
    "\n",
    "This example is based on this [UCLA example](https://stats.idre.ucla.edu/r/dae/negative-binomial-regression/).\n",
    "\n",
    "School administrators study the attendance behavior of high school juniors at two schools.  Predictors of the **number of days of absence** include the **type of program** in which the student is enrolled and a **standardized test in math**. We have attendance data on 314 high school juniors.\n",
    "\n",
    "The variables of insterest in the dataset are\n",
    "\n",
    "* daysabs: The number of days of absence. It is our response variable.\n",
    "* progr: The type of program. Can be one of 'General', 'Academic', or 'Vocational'.\n",
    "* math: Score in a standardized math test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_stata(\"https://stats.idre.ucla.edu/stat/stata/dae/nb_data.dta\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\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>id</th>\n",
       "      <th>gender</th>\n",
       "      <th>math</th>\n",
       "      <th>daysabs</th>\n",
       "      <th>prog</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001.0</td>\n",
       "      <td>male</td>\n",
       "      <td>63.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1002.0</td>\n",
       "      <td>male</td>\n",
       "      <td>27.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1003.0</td>\n",
       "      <td>female</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1004.0</td>\n",
       "      <td>female</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1005.0</td>\n",
       "      <td>female</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       id  gender  math  daysabs  prog\n",
       "0  1001.0    male  63.0      4.0   2.0\n",
       "1  1002.0    male  27.0      4.0   2.0\n",
       "2  1003.0  female  20.0      2.0   2.0\n",
       "3  1004.0  female  16.0      3.0   2.0\n",
       "4  1005.0  female   2.0      3.0   2.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We assign categories to the values 1, 2, and 3 of our `\"prog\"` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\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>id</th>\n",
       "      <th>gender</th>\n",
       "      <th>math</th>\n",
       "      <th>daysabs</th>\n",
       "      <th>prog</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001.0</td>\n",
       "      <td>male</td>\n",
       "      <td>63.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1002.0</td>\n",
       "      <td>male</td>\n",
       "      <td>27.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1003.0</td>\n",
       "      <td>female</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1004.0</td>\n",
       "      <td>female</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1005.0</td>\n",
       "      <td>female</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       id  gender  math  daysabs      prog\n",
       "0  1001.0    male  63.0      4.0  Academic\n",
       "1  1002.0    male  27.0      4.0  Academic\n",
       "2  1003.0  female  20.0      2.0  Academic\n",
       "3  1004.0  female  16.0      3.0  Academic\n",
       "4  1005.0  female   2.0      3.0  Academic"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[\"prog\"] = data[\"prog\"].map({1: \"General\", 2: \"Academic\", 3: \"Vocational\"})\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Academic program is the most popular program (167/314) and General is the least popular one (40/314)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "prog\n",
       "Academic      167\n",
       "Vocational    107\n",
       "General        40\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[\"prog\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's explore the distributions of math score and days of absence for each of the three programs listed above. The vertical lines indicate the mean values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(3, 2, figsize=(8, 6), sharex=\"col\")\n",
    "programs = list(data[\"prog\"].unique())\n",
    "programs.sort()\n",
    "\n",
    "for idx, program in enumerate(programs):\n",
    "    # Histogram\n",
    "    ax[idx, 0].hist(data[data[\"prog\"] == program][\"math\"], edgecolor='black', alpha=0.9)\n",
    "    ax[idx, 0].axvline(data[data[\"prog\"] == program][\"math\"].mean(), color=\"C1\")\n",
    "    \n",
    "    # Barplot\n",
    "    days = data[data[\"prog\"] == program][\"daysabs\"]\n",
    "    days_mean = days.mean()\n",
    "    days_counts = days.value_counts()\n",
    "    values = list(days_counts.index)\n",
    "    count = days_counts.values\n",
    "    ax[idx, 1].bar(values, count, edgecolor='black', alpha=0.9)\n",
    "    ax[idx, 1].axvline(days_mean, color=\"C1\")\n",
    "    \n",
    "    # Titles\n",
    "    ax[idx, 0].set_title(program)\n",
    "    ax[idx, 1].set_title(program)\n",
    "\n",
    "plt.setp(ax[-1, 0], xlabel=\"Math score\")\n",
    "plt.setp(ax[-1, 1], xlabel=\"Days of absence\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first impression we have is that the distribution of math scores is not equal for any of the programs. It looks right-skewed for students under the Academic program, left-skewed for students under the Vocational program, and roughly uniform for students in the General program (although there's a drop in the highest values). Clearly those in the Vocational program has the highest mean for the math score.\n",
    " \n",
    "On the other hand, the distribution of the days of absence is right-skewed in all cases. Students in the General program present the highest absence mean while the Vocational group is the one who misses fewer classes on average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Models\n",
    "\n",
    "We are interested in measuring the association between the type of the program and the math score with the days of absence. It's also of interest to see if the association between math score and days of absence is different in each type of program. \n",
    "\n",
    "In order to answer our questions, we are going to fit and compare two models. The first model uses the type of the program and the math score as predictors. The second model also includes the interaction between these two variables. The score in the math test is going to be standardized in both cases to make things easier for the sampler and save some seconds. A good idea to follow along is to run these models without scaling `math` and comparing how long it took to fit.\n",
    "\n",
    "We are going to use a negative binomial likelihood to model the days of absence. But let's stop here and think why we use this likelihood. Earlier, we said that the negative binomial distributon arises when our variable represents the number of trials until we got $k$ successes. However, the number of trials is fixed, i.e. the number of school days in a given year is not a random variable. So if we stick to the definition, we could think of the two alternative views for this problem\n",
    "\n",
    "* Each of the $n$ days is a trial, and we record whether the student is absent ($y=1$) or not ($y=0$). This corresponds to a binary regression setting, where we could think of logistic regression or something alike. A problem here is that we have the sum of $y$ for a student, but not the $n$.\n",
    "* The whole school year represents the space where events occur and we count how many absences we see in that space for each student. This gives us a Poisson regression setting (count of an event in a given space or time).\n",
    "\n",
    "We also know that when $n$ is large and $p$ is small, the Binomial distribution can be approximated with a Poisson distribution with $\\lambda = n * p$. We don't know exactly $n$ in this scenario, but we know it is around 180, and we do know that $p$ is small because you can't skip classes all the time. So both modeling approaches should give similar results.\n",
    "\n",
    "But then, why negative binomial? Can't we just use a Poisson likelihood?\n",
    "\n",
    "Yes, we can. However, using a Poisson likelihood implies that the mean is equal to the variance, and that is usually an unrealistic assumption. If it turns out the variance is either substantially smaller or greater than the mean, the Poisson regression model results in a poor fit. Alternatively, if we use a negative binomial likelihood, the variance is not forced to be equal to the mean, and there's more flexibility to handle a given dataset, and consequently, the fit tends to better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model 1 \n",
    "\n",
    "$$\n",
    "\\log(\\mathbb{E}[Y_i]) = \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i\n",
    "$$\n",
    "\n",
    "### Model 2\n",
    "\n",
    "$$\n",
    "\\log(\\mathbb{E}[Y_i]) = \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i\n",
    "            + \\beta_5 \\text{General}_i \\cdot \\text{Math\\_std}_i + \\beta_6 \\text{Vocational}_i \\cdot \\text{Math\\_std}_i\n",
    "$$\n",
    "\n",
    "In both cases we have the following dummy variables\n",
    "\n",
    "\n",
    "$$\\text{Academic}_i = \n",
    "\\left\\{ \n",
    "    \\begin{array}{ll}\n",
    "        1 & \\textrm{if student is under Academic program} \\\\\n",
    "        0 & \\textrm{other case} \n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "$$\\text{General}_i = \n",
    "\\left\\{ \n",
    "    \\begin{array}{ll}\n",
    "        1 & \\textrm{if student is under General program} \\\\\n",
    "        0 & \\textrm{other case} \n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "$$\\text{Vocational}_i = \n",
    "\\left\\{ \n",
    "    \\begin{array}{ll}\n",
    "        1 & \\textrm{if student is under Vocational program} \\\\\n",
    "        0 & \\textrm{other case} \n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "and $Y$ represents the days of absence.\n",
    "\n",
    "So, for example, the first model for a student under the Vocational program reduces to\n",
    "$$\n",
    "\\log(\\mathbb{E}[Y_i]) = \\beta_3 + \\beta_4 \\text{Math\\_std}_i\n",
    "$$\n",
    "\n",
    "And one last thing to note is we've decided not to inclide an intercept term, that's why you don't see any $\\beta_0$ above. This choice allows us to represent the effect of each program directly with $\\beta_1$, $\\beta_2$, and $\\beta_3$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model fit\n",
    "\n",
    "It's very easy to fit these models with Bambi. We just pass a formula describing the terms in the model and Bambi will know how to handle each of them correctly. The `0` on the right hand side of `~` simply means we don't want to have the intercept term that is added by default. `scale(math)` tells Bambi we want to use standardize `math` before being included in the model. By default, Bambi uses a log link for negative binomial GLMs. We'll stick to this default here.\n",
    "\n",
    "### Model 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [alpha, prog, scale(math)]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "da92930f19f1410eadcc61e357d9669b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 3 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
     ]
    }
   ],
   "source": [
    "model_additive = bmb.Model(\"daysabs ~ 0 + prog + scale(math)\", data, family=\"negativebinomial\")\n",
    "idata_additive = model_additive.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model 2\n",
    "\n",
    "For this second model we just add `prog:scale(math)` to indicate the interaction. A shorthand would be to use `y ~ 0 + prog*scale(math)`, which uses the **full interaction** operator. In other words, it just means we want to include the interaction between `prog` and `scale(math)` as well as their main effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [alpha, prog, scale(math), prog:scale(math)]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "94d81704090d476cadec4f42e8ceb1f0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 3 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
     ]
    }
   ],
   "source": [
    "model_interaction = bmb.Model(\"daysabs ~ 0 + prog + scale(math) + prog:scale(math)\", data, family=\"negativebinomial\")\n",
    "idata_interaction = model_interaction.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explore models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first thing we do is calling `az.summary()`. Here we pass the `InferenceData` object the `.fit()` returned. This prints information about the marginal posteriors for each parameter in the model as well as convergence diagnostics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.019</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.842</td>\n",
       "      <td>1.234</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2575.0</td>\n",
       "      <td>1621.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Academic]</th>\n",
       "      <td>1.889</td>\n",
       "      <td>0.088</td>\n",
       "      <td>1.719</td>\n",
       "      <td>2.045</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2702.0</td>\n",
       "      <td>1253.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[General]</th>\n",
       "      <td>2.337</td>\n",
       "      <td>0.165</td>\n",
       "      <td>2.028</td>\n",
       "      <td>2.643</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>2429.0</td>\n",
       "      <td>1531.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Vocational]</th>\n",
       "      <td>1.047</td>\n",
       "      <td>0.117</td>\n",
       "      <td>0.818</td>\n",
       "      <td>1.254</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>2346.0</td>\n",
       "      <td>1468.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scale(math)</th>\n",
       "      <td>-0.151</td>\n",
       "      <td>0.064</td>\n",
       "      <td>-0.270</td>\n",
       "      <td>-0.031</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2970.0</td>\n",
       "      <td>1670.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha             1.019  0.105   0.842    1.234      0.002    0.001    2575.0   \n",
       "prog[Academic]    1.889  0.088   1.719    2.045      0.002    0.001    2702.0   \n",
       "prog[General]     2.337  0.165   2.028    2.643      0.003    0.002    2429.0   \n",
       "prog[Vocational]  1.047  0.117   0.818    1.254      0.002    0.002    2346.0   \n",
       "scale(math)      -0.151  0.064  -0.270   -0.031      0.001    0.001    2970.0   \n",
       "\n",
       "                  ess_tail  r_hat  \n",
       "alpha               1621.0    1.0  \n",
       "prog[Academic]      1253.0    1.0  \n",
       "prog[General]       1531.0    1.0  \n",
       "prog[Vocational]    1468.0    1.0  \n",
       "scale(math)         1670.0    1.0  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_additive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.016</td>\n",
       "      <td>0.104</td>\n",
       "      <td>0.812</td>\n",
       "      <td>1.205</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>2366.0</td>\n",
       "      <td>1715.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Academic]</th>\n",
       "      <td>1.875</td>\n",
       "      <td>0.085</td>\n",
       "      <td>1.713</td>\n",
       "      <td>2.032</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2641.0</td>\n",
       "      <td>1545.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[General]</th>\n",
       "      <td>2.341</td>\n",
       "      <td>0.172</td>\n",
       "      <td>2.021</td>\n",
       "      <td>2.654</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2072.0</td>\n",
       "      <td>1124.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Vocational]</th>\n",
       "      <td>0.994</td>\n",
       "      <td>0.124</td>\n",
       "      <td>0.774</td>\n",
       "      <td>1.241</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1962.0</td>\n",
       "      <td>1661.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog:scale(math)[General]</th>\n",
       "      <td>0.012</td>\n",
       "      <td>0.170</td>\n",
       "      <td>-0.322</td>\n",
       "      <td>0.312</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1949.0</td>\n",
       "      <td>1664.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog:scale(math)[Vocational]</th>\n",
       "      <td>0.193</td>\n",
       "      <td>0.164</td>\n",
       "      <td>-0.123</td>\n",
       "      <td>0.490</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1830.0</td>\n",
       "      <td>1593.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scale(math)</th>\n",
       "      <td>-0.195</td>\n",
       "      <td>0.081</td>\n",
       "      <td>-0.335</td>\n",
       "      <td>-0.036</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1737.0</td>\n",
       "      <td>1545.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                               mean     sd  hdi_3%  hdi_97%  mcse_mean  \\\n",
       "alpha                         1.016  0.104   0.812    1.205      0.002   \n",
       "prog[Academic]                1.875  0.085   1.713    2.032      0.002   \n",
       "prog[General]                 2.341  0.172   2.021    2.654      0.004   \n",
       "prog[Vocational]              0.994  0.124   0.774    1.241      0.003   \n",
       "prog:scale(math)[General]     0.012  0.170  -0.322    0.312      0.004   \n",
       "prog:scale(math)[Vocational]  0.193  0.164  -0.123    0.490      0.004   \n",
       "scale(math)                  -0.195  0.081  -0.335   -0.036      0.002   \n",
       "\n",
       "                              mcse_sd  ess_bulk  ess_tail  r_hat  \n",
       "alpha                           0.002    2366.0    1715.0    1.0  \n",
       "prog[Academic]                  0.001    2641.0    1545.0    1.0  \n",
       "prog[General]                   0.003    2072.0    1124.0    1.0  \n",
       "prog[Vocational]                0.002    1962.0    1661.0    1.0  \n",
       "prog:scale(math)[General]       0.003    1949.0    1664.0    1.0  \n",
       "prog:scale(math)[Vocational]    0.003    1830.0    1593.0    1.0  \n",
       "scale(math)                     0.001    1737.0    1545.0    1.0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_interaction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The information in the two tables above can be visualized in a more concise manner using a forest plot. ArviZ provides us with `plot_forest()`. There we simply pass a list containing the `InferenceData` objects of the models we want to compare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(\n",
    "    [idata_additive, idata_interaction],\n",
    "    model_names=[\"Additive\", \"Interaction\"],\n",
    "    var_names=[\"prog\", \"scale(math)\"],\n",
    "    combined=True,\n",
    "    figsize=(8, 4)\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the first things one can note when seeing this plot is the similarity between the marginal posteriors. Maybe one can conclude that the variability of the marginal posterior of `scale(math)` is slightly lower in the model that considers the interaction, but the difference is not significant. \n",
    "\n",
    "We can also make conclusions about the association between the program and the math score with the days of absence. First, we see the posterior for the Vocational group is to the left of the posterior for the two other programs, meaning it is associated with fewer absences (as we have seen when first exploring our data). There also seems to be a difference between General and Academic, where we may conclude the students in the General group tend to miss more classes.\n",
    "\n",
    "In addition, the marginal posterior for `math` shows negative values in both cases. This means that students with higher math scores tend to miss fewer classes. Below, we see a forest plot with the posteriors for the coefficients of the interaction effects. Both of them overlap with 0, which means the data does not give much evidence to support there is an interaction effect between program and math score (i.e., the association between math and days of absence is similar for all the programs)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(idata_interaction, var_names=[\"prog:scale(math)\"], combined=True, figsize=(8, 4))\n",
    "plt.axvline(0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot predicted mean response\n",
    "\n",
    "We finish this example showing how we can get predictions for new data and plot the mean response for each program together with confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "math_score = np.arange(1, 100)\n",
    "\n",
    "# This function takes a model and an InferenceData object.\n",
    "# It returns of length 3 with predictions for each type of program.\n",
    "def predict(model, idata):\n",
    "    predictions = []\n",
    "    for program in programs:\n",
    "        new_data = pd.DataFrame({\"math\": math_score, \"prog\": [program] * len(math_score)})\n",
    "        new_idata = model.predict(\n",
    "            idata, \n",
    "            data=new_data,\n",
    "            inplace=False\n",
    "        )\n",
    "        prediction = new_idata.posterior[\"mu\"]\n",
    "        predictions.append(prediction)\n",
    "    \n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction_additive = predict(model_additive, idata_additive)\n",
    "prediction_interaction = predict(model_interaction, idata_interaction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu_additive = [prediction.mean((\"chain\", \"draw\")) for prediction in prediction_additive]\n",
    "mu_interaction = [prediction.mean((\"chain\", \"draw\")) for prediction in prediction_interaction]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, sharex=True, sharey=True, figsize = (10, 4))\n",
    "\n",
    "for idx, program in enumerate(programs):\n",
    "    ax[0].plot(math_score, mu_additive[idx], label=f\"{program}\", color=f\"C{idx}\", lw=2)\n",
    "    az.plot_hdi(math_score, prediction_additive[idx], color=f\"C{idx}\", ax=ax[0])\n",
    "\n",
    "    ax[1].plot(math_score, mu_interaction[idx], label=f\"{program}\", color=f\"C{idx}\", lw=2)\n",
    "    az.plot_hdi(math_score, prediction_interaction[idx], color=f\"C{idx}\", ax=ax[1])\n",
    "\n",
    "ax[0].set_title(\"Additive\");\n",
    "ax[1].set_title(\"Interaction\");\n",
    "ax[0].set_xlabel(\"Math score\")\n",
    "ax[1].set_xlabel(\"Math score\")\n",
    "ax[0].set_ylim(0, 25)\n",
    "ax[0].legend(loc=\"upper right\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see in this plot, the interval for the mean response for the Vocational program does not overlap with the interval for the other two groups, representing the group of students who miss fewer classes. On the right panel we can also see that including interaction terms does not change the slopes significantly because the posterior distributions of these coefficients have a substantial overlap with 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you've made it to the end of this notebook and you're still curious about what else you can do with these two models, you're invited to use `az.compare()` to compare the fit of the two models. What do you expect before seeing the plot? Why? Is there anything else you could do to improve the fit of the model?\n",
    "\n",
    "Also, if you're still curious about what this model would have looked like with the Poisson likelihood, you just need to replace `family=\"negativebinomial\"` with `family=\"poisson\"` and then you're ready to compare results!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sat May 25 2024\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.11.9\n",
      "IPython version      : 8.24.0\n",
      "\n",
      "pandas    : 2.2.2\n",
      "numpy     : 1.26.4\n",
      "arviz     : 0.18.0\n",
      "matplotlib: 3.8.4\n",
      "bambi     : 0.13.1.dev37+g2a54df76.d20240525\n",
      "\n",
      "Watermark: 2.4.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.9"
  },
  "vscode": {
   "interpreter": {
    "hash": "1008626715a3728f1d66c057190bde332dc65ea99517a942c5f170959679b77d"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}