11-group_level_predictors.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Bayesian Multilevel Modelling using PyStan\n",
    "\n",
    "This is a tutorial, following through Chris Fonnesbeck's [primer on using PyStan with Bayesian Multilevel Modelling](http://mc-stan.org/documentation/case-studies/radon.html).\n",
    "\n",
    "# 11. Partial Pooling - Group-Level Predictors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lpritc/Development/GitHub/Teaching/Teaching-Stan-Hierarchical-Modelling/venv-Teaching-Stan-Hierarchical/lib/python3.5/site-packages/Cython/Distutils/old_build_ext.py:30: UserWarning: Cython.Distutils.old_build_ext does not properly handle dependencies and is deprecated.\n",
      "  \"Cython.Distutils.old_build_ext does not properly handle dependencies \"\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pystan\n",
    "import seaborn as sns\n",
    "\n",
    "import clean_data\n",
    "\n",
    "sns.set_context('notebook')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Group-Level Predictors\n",
    "\n",
    "One of the strengths of multilevel modelling is that ability to handle predictors that are defined at multiple levels *simultaneously*. For instance, we previously (notebook `08-partial_pooling_varying_intercept.ipynb`) defined the *varying intercept* model to capture county-level variation in prevailing radon concentration:\n",
    "\n",
    "$$y_i = \\alpha_{j[i]} + \\beta x_i + \\epsilon_i$$\n",
    "\n",
    "Instead of using a simple *random effect* to describe variation in the expected radon value for each county (as we do here: the parameter $\\alpha_{j[i]}$ is drawn from a random distribution), we can specify *another regression model* that has a county-level radon concentration as its covariate, dependent on the county-level uranium measurement $u_j$ - such as:\n",
    "\n",
    "$$\\alpha_j = \\gamma_0 + \\gamma_1 u_j + \\zeta_j$$\n",
    "\n",
    "Where\n",
    "\n",
    "* $\\alpha_j$: county-level prevailing radon concentration\n",
    "* $u_j$: the prevailing uranium concentration at county level\n",
    "* $\\gamma_0$: intercept of a linear model relating uranium level to radon level in a county\n",
    "* $\\gamma_1$: slope of a linear model relating uranium level to radon level in a county\n",
    "* $\\zeta_j$: irreducible noise in this relationship, where\n",
    "\n",
    "$$\\zeta_j \\sim N(0, \\sigma_{\\alpha}^2)$$\n",
    "\n",
    "In this new model, we are incorporating a house-level predictor (floor at which measurement is taken), and a county-level predictor (county uranium level)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Collinearity\n",
    "\n",
    "The new model has [indicator (dummy) variables](https://en.wikipedia.org/wiki/Dummy_variable_(statistics)) for each county - $\\gamma_0, \\gamma_1$ - as well as a county-level covariate $u_j$. In classical regression, this would result in [*(multi)collinearity*](https://en.wikipedia.org/wiki/Multicollinearity): the estimates of the collinear coefficients could vary drastically and still deliver the same fit for the model. In a multilevel model such as this, the partial pooling of coefficients towards expected values of the group-level model avoids this tendency.\n",
    "\n",
    "Group-level predictors also help to reduce the group-level variation $\\sigma_{\\alpha}$, which implies that group-level estimates induce a stronger pooling effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specifying the model\n",
    "\n",
    "We define the model in `stan`, as usual specifying `data`, `parameters`, `transformed parameters` and `model` blocks. The model is built up as follows.\n",
    "\n",
    "Our observed log(radon) measurements ($y$) approximate an intermediate transformed parameter $\\hat{y}$, which is normally distributed with variance $\\sigma_y^2$ (we leave the estimation of $\\sigma_y^2$ to `Stan`'s defaults - this is not encouraged by `Stan`'s authors, as the defaults may change between versions!).\n",
    "\n",
    "$$y \\sim N(\\hat{y}, \\sigma_y^2)$$\n",
    "\n",
    "The transformed variable $\\hat{y}$ is a linear function of $x_i$, the floor at which radon is measured. The parameters are $m_i$, the prevailing log(radon) measurement within the county $i$ ($i=1,\\ldots,N$) in which each household is found, and the effect due to which floor is used for measurement, $\\beta_2$.\n",
    "\n",
    "$$\\hat{y_i} = m_i + \\beta_2 x_i$$\n",
    "\n",
    "The transformed variable $m_i$ is a linear function of $u_i$, the uranium level in the county. The parameters are the intercept $\\alpha_{j[i]}$, drawn from a Normal distribution with mean $\\mu_{\\alpha}$ and variance $\\sigma_{\\alpha}^2$, and the effect due to uranium level, $\\beta_1$ (we again leave estimation of $\\sigma_{\\alpha}^2$ to `Stan`'s defaults). The mean $\\mu_{\\alpha}$ is Normally distributed with mean 0 and unit variance.\n",
    "\n",
    "$$m_i = \\alpha_{j[i]} + \\beta_1 u_i$$\n",
    "$$\\alpha_{j[i]} \\sim N(\\mu_{\\alpha}, \\sigma_{\\alpha}^2)$$\n",
    "$$\\mu_{\\alpha} \\sim N(0, 1)$$\n",
    "\n",
    "The values of $\\beta_1$ and $\\beta_2$ are Normally distributed with mean $0$ and variance $1$. \n",
    "\n",
    "$$\\beta_1 \\sim N(0, 1)$$\n",
    "$$\\beta_2 \\sim N(0, 1)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In `data`:\n",
    "* `J` is the number of counties (`int`)\n",
    "* `N` is the number of samples (`int`)\n",
    "* `county` is a list of `N` values from 1-85, specifying the county index each measurement\n",
    "* `u` is a `vector` of uranium levels, in each county\n",
    "* `x` is a `vector` of indices for which floor the radon measurements were taken at each household\n",
    "* `y` is a `vector` of log(radon) measurements, one per household/sample.\n",
    "\n",
    "We define parameters:\n",
    "\n",
    "* `a` (`vector`, one value per county), representing $\\alpha_j[i]$, the county-level intercept for the relationship of county radon level to county uranium level.\n",
    "* `mu_a`, a `real` corresponding to $\\mu_{\\alpha}$, the mean radon level underlying the distribution from which the county levels are drawn.\n",
    "* `sigma_a` is $\\sigma_{\\alpha}$, the standard deviation of the radon level distribution underlying the county levels: variability of county means about the average.\n",
    "* `b` (`vector`, two values), representing: $\\beta_1$, the slope of the relationship between county-level uranium and radon level; and $\\beta_2$, the slope of the relationship between floor measurement and radon level.\n",
    "* `sigma_y` is $\\sigma_y$, the standard deviation of the measurement/sampling error: residual error of the observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hierarchical_intercept = \"\"\"\n",
    "data {\n",
    "  int<lower=0> J; \n",
    "  int<lower=0> N; \n",
    "  int<lower=1,upper=J> county[N];\n",
    "  vector[N] u;\n",
    "  vector[N] x;\n",
    "  vector[N] y;\n",
    "} \n",
    "parameters {\n",
    "  vector[J] a;\n",
    "  vector[2] b;\n",
    "  real mu_a;\n",
    "  real<lower=0,upper=100> sigma_a;\n",
    "  real<lower=0,upper=100> sigma_y;\n",
    "} \n",
    "transformed parameters {\n",
    "  vector[N] y_hat;\n",
    "  vector[N] m;\n",
    "\n",
    "  for (i in 1:N) {\n",
    "    m[i] <- a[county[i]] + u[i] * b[1];\n",
    "    y_hat[i] <- m[i] + x[i] * b[2];\n",
    "  }\n",
    "}\n",
    "model {\n",
    "  mu_a ~ normal(0, 1);\n",
    "  a ~ normal(mu_a, sigma_a);\n",
    "  b ~ normal(0, 1);\n",
    "  y ~ normal(y_hat, sigma_y);\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting the model\n",
    "\n",
    "Again, we map Python variables to those in the model, and run the fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_09c24493b150e61b5f7babd2ed515f09 NOW.\n"
     ]
    }
   ],
   "source": [
    "n_county = clean_data.srrs_mn.groupby('county')['idnum'].count()  # number of samples from each county\n",
    "\n",
    "hierarchical_intercept_data = {'N': len(clean_data.log_radon),\n",
    "                               'J': len(n_county),\n",
    "                               'county': clean_data.county+1, # Stan counts starting at 1\n",
    "                               'u': clean_data.u,\n",
    "                               'x': clean_data.floor_measure,\n",
    "                               'y': clean_data.log_radon}\n",
    "\n",
    "hierarchical_intercept_fit = pystan.stan(model_code=hierarchical_intercept,\n",
    "                                         data=hierarchical_intercept_data, \n",
    "                                         iter=1000, chains=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then extract mean estimates for each parameter (and standard deviation for estimate of county-level radon):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g0 = hierarchical_intercept_fit['mu_a'].mean()\n",
    "g1 = hierarchical_intercept_fit['b'][:, 0].mean()\n",
    "m_means = hierarchical_intercept_fit['m'].mean(axis=0)\n",
    "m_se = hierarchical_intercept_fit['m'].std(axis=0)\n",
    "m_county = hierarchical_intercept_fit['a'].mean(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting the model output\n",
    "\n",
    "We can visualise the county-level estimate of radon level as a function of uranium level in the county (i.e. $m_i = \\alpha_{j[i]} + \\beta_1 u_i$) with a scatterplot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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1vU3KewtMbVqvXj3Wrl1L165dWbNmDUWLFk2RTwdEnoSSXZEkypYtG6GhoTb7zeNivby8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c9b8438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(clean_data.u, m_means)\n",
    "xvals = np.linspace(-1, 0.8)\n",
    "plt.plot(xvals, g0 + g1 * xvals, 'k--')  # fitted relationship\n",
    "for ui, m, se in zip(clean_data.u, m_means, m_se):  # std errors of fitted value\n",
    "    plt.plot([ui, ui], [m - se, m + se], 'b-',\n",
    "             linewidth=0.2, alpha=0.2)\n",
    "\n",
    "# presentation\n",
    "plt.xlim(-1, 0.8)\n",
    "plt.title(\"log(radon) as a function of uranium, by county\")\n",
    "plt.xlabel(\"uranium\")\n",
    "plt.ylabel(\"log(radon)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The black dashed line indictes the inferred relationship between uranium level and prevailing radon level in the county. The intensity of the vertical line indicates sample size in that county.\n",
    "\n",
    "These standard errors are narrower than for the partial-pooling models that do not contain a county-level covariate for uranium, implying that we may have improved the accuracy of our estimates of prevailing log(radon) level by county."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}