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MRPyMC3-Multilevel Regression and Poststratification with PyMC3
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"title: MRPyMC3: Multilevel Regression and Poststratification with PyMC3\n",
"tags: PyMC3, Bayesian Statistics\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A few weeks ago, [YouGov](https://today.yougov.com/) correctly [predicted](https://yougov.co.uk/uk-general-election-2017/#/uk-elections-charts-anchor) a hung parliament as a result of the 2017 UK general election, to the astonishment of many commentators. YouGov's predictions were [based](https://yougov.co.uk/news/2017/05/31/how-yougov-model-2017-general-election-works/) on a technique called multilevel regression with poststratification, or MRP for short (Andrew Gelman playfully refers to it as [Mister P](http://andrewgelman.com/2009/05/09/the_next_suprem/)).\n",
"\n",
"I was impressed with YouGov's prediction and decided to work through an MRP example to improve my understanding of this technique. Since all of the applications of MRP I have found online involve `R`'s [`lme4`](https://cran.r-project.org/web/packages/lme4/index.html) package or [Stan](http://mc-stan.org/), I also thought this was a good opportunity to illustrate MRP in Python with PyMC3. This post is essentially a port of [Jonathan Kastellec](http://www.princeton.edu/~jkastell/)'s excellent [MRP primer](http://www.princeton.edu/~jkastell/mrp_primer.html) to Python and PyMC3. I am very grateful for his clear exposition of MRP and willingness to share a relevant data set.\n",
"\n",
"MRP was developed to estimate American state-level opinions from national polls. This sort of estimation is crucial to understanding American politics at the national level, as many of the important political positions of the federal government are impacted by state-level elections:\n",
"\n",
"* the president is chosen by the Electoral College, which (with a few exceptions) votes according to state-level vote totals,\n",
"* senators are chosen by state-level elections,\n",
"* many political and all judicial (notably Supreme Court) appointees require Senate approval, and therefore are subject to indirect state-level elections.\n",
"\n",
"Of course, as YouGov demonstrates, MRP is more widely applicable than estimation of state-level opinion.\n",
"\n",
"In this post, we will follow Kastellec's example of estimating state-level opinion about gay marriage in 2005/2006 using a combination of three national polls. We begin by loading a data set that consists of repsonses to the three national polls."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"#%config InlineBackend.figure_format = 'retina'"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import os\n",
"import us"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import matplotlib as mpl\n",
"from matplotlib import pyplot as plt\n",
"from matplotlib.colors import Normalize, rgb2hex\n",
"from matplotlib.patches import Polygon\n",
"from matplotlib.ticker import FuncFormatter\n",
"from mpl_toolkits.basemap import Basemap\n",
"import numpy as np\n",
"import pandas as pd\n",
"import pymc3 as pm\n",
"import scipy as sp\n",
"import seaborn as sns\n",
"from theano import shared"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%%bash\n",
"if [ ! -e ./st99_d00.dbf ];\n",
"then\n",
" wget -q https://github.com/matplotlib/basemap/raw/master/examples/st99_d00.dbf\n",
" wget -q https://github.com/matplotlib/basemap/raw/master/examples/st99_d00.shp\n",
" wget -q https://github.com/matplotlib/basemap/raw/master/examples/st99_d00.shx\n",
"fi"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"SEED = 4260026 # from random.org, for reproducibility\n",
"\n",
"np.random.seed(SEED)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We load only the columns which we will use in the analysis and transform categorical variables to be zero-indexed."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def to_zero_indexed(col):\n",
" return lambda df: (df[col] - 1).astype(np.int64)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"DATA_PREFIX = 'http://www.princeton.edu/~jkastell/MRP_primer/'\n",
"\n",
"survey_df = (pd.read_stata(os.path.join(DATA_PREFIX, 'gay_marriage_megapoll.dta'),\n",
" columns=['race_wbh', 'age_cat', 'edu_cat', 'female',\n",
" 'state_initnum', 'state', 'region_cat', 'region', 'statename',\n",
" 'poll', 'yes_of_all'])\n",
" .dropna(subset=['race_wbh', 'age_cat', 'edu_cat', 'state_initnum'])\n",
" .assign(state_initnum=to_zero_indexed('state_initnum'),\n",
" race_wbh=to_zero_indexed('race_wbh'),\n",
" edu_cat=to_zero_indexed('edu_cat'),\n",
" age_cat=to_zero_indexed('age_cat'),\n",
" region_cat=to_zero_indexed('region_cat')))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>race_wbh</th>\n",
" <th>age_cat</th>\n",
" <th>edu_cat</th>\n",
" <th>female</th>\n",
" <th>state_initnum</th>\n",
" <th>state</th>\n",
" <th>region_cat</th>\n",
" <th>region</th>\n",
" <th>statename</th>\n",
" <th>poll</th>\n",
" <th>yes_of_all</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0</td>\n",
" <td>2</td>\n",
" <td>2</td>\n",
" <td>1</td>\n",
" <td>22</td>\n",
" <td>MI</td>\n",
" <td>1</td>\n",
" <td>midwest</td>\n",
" <td>michigan</td>\n",
" <td>Gall2005Aug22</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0</td>\n",
" <td>2</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>10</td>\n",
" <td>GA</td>\n",
" <td>2</td>\n",
" <td>south</td>\n",
" <td>georgia</td>\n",
" <td>Gall2005Aug22</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>2</td>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>34</td>\n",
" <td>NY</td>\n",
" <td>0</td>\n",
" <td>northeast</td>\n",
" <td>new york</td>\n",
" <td>Gall2005Aug22</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" <td>3</td>\n",
" <td>1</td>\n",
" <td>30</td>\n",
" <td>NH</td>\n",
" <td>0</td>\n",
" <td>northeast</td>\n",
" <td>new hampshire</td>\n",
" <td>Gall2005Aug22</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" <td>2</td>\n",
" <td>1</td>\n",
" <td>14</td>\n",
" <td>IL</td>\n",
" <td>1</td>\n",
" <td>midwest</td>\n",
" <td>illinois</td>\n",
" <td>Gall2005Aug22</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" race_wbh age_cat edu_cat female state_initnum state region_cat \\\n",
"0 0 2 2 1 22 MI 1 \n",
"1 0 2 3 0 10 GA 2 \n",
"2 2 0 3 0 34 NY 0 \n",
"3 0 3 3 1 30 NH 0 \n",
"5 0 3 2 1 14 IL 1 \n",
"\n",
" region statename poll yes_of_all \n",
"0 midwest michigan Gall2005Aug22 0 \n",
"1 south georgia Gall2005Aug22 0 \n",
"2 northeast new york Gall2005Aug22 1 \n",
"3 northeast new hampshire Gall2005Aug22 1 \n",
"5 midwest illinois Gall2005Aug22 0 "
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"survey_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These three surveys collected data from roughly 6,300 respondents during 2005 and 2006."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"6341"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"survey_df.shape[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the number of respondents varies widely between states."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def state_plot(state_data, cmap, norm, cbar=True, default=None, ax=None):\n",
" if ax is None:\n",
" fig, ax = plt.subplots(figsize=(8, 6))\n",
" else:\n",
" fig = plt.gcf()\n",
"\n",
" m = Basemap(llcrnrlon=-121, llcrnrlat=20,\n",
" urcrnrlon=-62, urcrnrlat=51,\n",
" projection='lcc',\n",
" lat_1=32, lat_2=45, lon_0=-95)\n",
" m.readshapefile('st99_d00', name='states', drawbounds=True)\n",
"\n",
" for state_info, state_seg in zip(m.states_info, m.states):\n",
" if state_info['NAME'] == 'Alaska':\n",
" state_seg = list(map(lambda xy: (0.35 * xy[0] + 1100000, 0.35 * xy[1] - 1300000), state_seg))\n",
" elif state_info['NAME'] == 'Hawaii' and float(state_info['AREA']) > 0.005:\n",
" state_seg = list(map(lambda xy: (xy[0] + 5100000, xy[1] - 1400000), state_seg))\n",
"\n",
" try:\n",
" state_datum = state_data.loc[us.states.lookup(state_info['NAME']).abbr] \n",
" except KeyError:\n",
" state_datum = default\n",
" \n",
" if state_datum is not None:\n",
" color = rgb2hex(cmap(norm(state_datum))) \n",
"\n",
" poly = Polygon(state_seg, facecolor=color, edgecolor='#000000')\n",
" ax.add_patch(poly)\n",
" \n",
" if cbar:\n",
" cbar_ax = fig.add_axes([0.925, 0.25, 0.04, 0.5])\n",
" mpl.colorbar.ColorbarBase(cbar_ax, cmap=cmap, norm=norm)\n",
" else:\n",
" cbar_ax = None\n",
" \n",
" return fig, ax, cbar_ax"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"state_counts = survey_df.groupby('state').size()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
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gwD5oNBImJibUrFkHH5+25Mlja7A4BUEQhJzjq0sUAgMvU7Bg6mYYPHz4kOvXr1GmTBls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uVl167v4OIyBHv3HmhWJJCO4/P5rH21ZvDgwdi1axeAxp4kNTU1iI2NbfpQOmrUKFy7dg0JCQlw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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5222bbd6a0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax, cbar_ax = state_plot(state_counts,\n",
" mpl.cm.binary,\n",
" Normalize(0, state_counts.max()),\n",
" default=None)\n",
"\n",
"ax.set_title(\"Number of poll respondents\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notably, there are no respondents from some less populous states, such as Alaska and Hawaii.\n",
"\n",
"Faced with this data set, it is inuitively appealing to estimate state-level opinion by the observed proportion of that state's respondents that supported gay marriage. This approach is known as disaggregation."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"disagg_p = (survey_df.groupby('state')\n",
" .yes_of_all\n",
" .mean())"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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bmoQCoHfv3jRv3pxevXrx008/cfDgQc6cOcOuXbs4cOAA0dHRqsJVAH///TcHDhxIk1AA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Al8KlehmKeXQZ5ArwcGktPNPcvHzUrEEgkqtX6a32WW+g0bITWTERsbi52d3UfbY+PiKFCjOs45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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f52224450f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p_norm = Normalize(0., 0.6)\n",
"p_cmap = sns.diverging_palette(220, 10, as_cmap=True)\n",
"\n",
"fig, ax, cbar_ax = state_plot(disagg_p, p_cmap, p_norm)\n",
"\n",
"p_formatter = FuncFormatter(lambda prop, _: '{:.1%}'.format(p_norm.inverse(prop)))\n",
"cbar_ax.yaxis.set_major_formatter(p_formatter);\n",
"\n",
"ax.set_title(\"Disaggregation estimate of\\nsupport for gay marriage in 2005\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The simplicity of disaggregation is appealing, but it suffers from a number of drawbacks. Obviously, it cannot estimate the state-level support for gay marriage in states with no respondents, such as Alaska and Hawaii. Similarly, for small/low population states with some respondents, the sample size may be too small to produce reliable estimates of opinion. This problem is exacerbated by the fact that for many issues, opinion is quite correlated with demographic factors such as age, race, education, gender, etc. Many more states will not have sufficient sample size for each combination of these factors for the disaggregate estimate to be representative of that state's demographic compositon."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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A8eyG9tGjRyVJUVFRtmUWi4XQBgDAyeyG9rUh7j97bRsAABQOu98eP3bsmPr2\n7avAwEBJUmhoqA4cOODwwgAAQF52Q/u1117TG2+8IW9vb0lSjx499Oabbzq8MAAAkJfd0LZarXkm\nVqldu/YN05MCAADHK1Bonz171nY9e8uWLQWaghQAABQuu13mSZMmadSoUfrll1/UsmVL1axZU7Nm\nzXJGbQAA4Dp2Q7tBgwYKDw9XQkKC3NzcVK5cOWfUBQAA/sBuaJ88eVLz5s3TyZMnZbFYVL9+fY0Z\nM0Z16tRxRn0AAOD/2Q3tiRMnKigoSOPGjZMk7dmzRy+88ILWrl3r8OIAAMDv7IZ22bJl1b9/f9vr\nunXr2p7UBQAAnCffb4/n5uYqNzdXvr6+2rBhgy5duqTLly8rMjJSrVq1cmaNAABAt+hpN2rUSBaL\n5aa3d1mtVo0cOdKhhQEAgLzyDe1jx445sw4AAGCH3WvaMTExioiIUGpqap5e95gxYxxaGAAAyMvu\njGhPPfWUjh49qqysLGVnZ9v+AwAAzmW3p12xYkUeEAIAQDFgN7S7deumr776Si1atJCrq6ttefXq\n1R1aGAAAyMtuaB8/flzh4eGqWLGibZnFYtHmzZsdWRcAAPgDu6F94MAB7d69W25ubs6oBwAA5MPu\nF9GaNGmijIwMZ9QCAABuoUC3fPn5+alu3bp5rmkvX77coYUBAIC87IY2M58BAFA82A3tnJwcZ9QB\nAADssBvaCxYssP07KytLJ0+eVMuWLeXr6+vQwgAAQF52Q3vp0qV5XsfHx+udd95xWEEAAODm7H57\n/I+8vLz0888/O6IWAABwC3Z72i+88IIsFovt9fnz5+Xi8j9nPQAA+Ivshna7du1s/7ZYLCpXrpza\nt2/v0KIAAMCN7Ib2o48+6ow6AACAHfmGtp+fX55hccMwZLFYlJmZqbi4OB09etQpBQIAgKvyDe1N\nmzbdsCwyMlLvvPOO+vXr59CiAADAjewOj0vS6dOnNWPGDJUqVUoffvih7rrrLkfXBQAA/uCWoZ2W\nlqbQ0FBt2bJFL7zwgjp27OisugAAwB/ke+/W119/rb59+6pChQr64osvCGwAAIpYvj3t559/Xvfc\nc4+2bdum//znP7bl176Q9umnnzqlQAAAcFW+ob1x40Zn1gEAAOzIN7Rr1KjhzDoAAIAdzEcKAIBJ\nENoAAJgEoQ0AgEkQ2gAAmAShDQCASRDaAACYBKENAIBJENoAAJgEoQ0AgEkQ2gAAmAShDQCASRDa\nAACYBKEqHHSgAAAMYUlEQVQNAIBJENoAAJgEoQ0AgEkQ2gAAmAShDQCASRDaAACYBKENAIBJENoA\nAJgEoQ0AgEkQ2gAAmAShDQCASRDaAACYBKENAIBJENoAAJgEoQ0AgEkQ2gAAmAShDQCASRDaAACY\nBKENAIBJENoAAJgEoQ0AgEkQ2gAAmITVmTvbtWuXnn32WdWrV0+SVL9+fb300kvOLAEAANNyamhL\nUuvWrTV37lxn7xYAANNjeBwAAJNwek/75MmTGjlypJKTkzVmzBi1b98+33U9Pd1ltbo6sTpz8/Yu\nX9QlAA7FOY7CZrZzyqmhfc8992jMmDEKDAzU2bNnFRISog0bNsjNze2m6ycmpjmzPFPz9i6v2NjU\noi4DcCjOcRS24nhO3eoPCacOj1etWlU9evSQxWJRrVq1VLlyZcXExDizBAAATMupof3VV19p0aJF\nkqTY2FjFx8eratWqziwBAADTcurwuJ+fn55//nlt3LhRWVlZmjZtWr5D4wAAIC+nhna5cuW0cOFC\nZ+4SAIDbBrd8AQBgEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgDAGAS\nhDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2\nAAAmQWgDAGAShDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKENgAA\nJkFoAwBgEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgDAGAShDYAACZB\naAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgD\nAGAShDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKENgAAJkFoAwBg\nEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKENgAAJkFoAwBgEoQ2AAAmQWgDAGAShDYAACZBaAMAYBKE\nNgAAJmF19g7feOMNHThwQBaLRVOmTFGzZs2cXQIAAKbk1ND+73//q19//VWrVq3SqVOnNGXKFK1a\ntcqZJQAAYFpOHR7fsWOHunbtKkmqW7eukpOTdenSJWeWAACAaTk1tOPi4uTp6Wl7XalSJcXGxjqz\nBAAATMvp17SvZxjGLd/39i7vpEpuD3xe5hT+Tu+iLiEfxbUu2FM8z6niWJP5OLWnXaVKFcXFxdle\nX7x4Ud7e3s4sAQAA03JqaLdv314RERGSpCNHjqhKlSoqV66cM0sAAMC0nDo83rJlSzVu3FiDBg2S\nxWLRK6+84szdAwBgahbD3oVlAABQLDAjGgAAJkFoAwBgEoR2MdSrVy+dOXPG9rpHjx7asmWL7fXo\n0aM1cOBAnThxIs92R48e1dy5cyVJGzduVGZmpnMKhimcO3dOLVq0UHBwsIKDgzVw4EBFRUVp8uTJ\n+ve///0/teXn56fLly87qFIUJ+fOnVPfvn3zLJs3b54WLFigl19+2WH73bp1q1asWOGw9s2qSO/T\nxs21adNGu3fvVq1atZSQkKD09HTt3r1bHTt2lCQdOHBAVatWvWG7hg0bqmHDhpKkxYsXq23btnJz\nc3Nq7SjeateuraVLl0qSdu/erffff5/bLvGneHh4aNSoUQ5rv0OHDg5r28zoaRdDbdq0UVRUlCRp\n7969euSRR7R//35J0qlTp1SzZk25u7vru+++09ChQ9W7d29FR0dr165dGjdunNatW6f9+/frqaee\nUmZmppYvX65BgwYpKChIH3/8cVEeGoqRuLg4ValSxfb60qVLevrppxUcHKzHHntMBw8elCRt375d\n/fr104ABA7R48eI8bZw/f159+/bVxYsXnVk6iolrPfAPP/xQjz32mAYOHKiFCxdKujoaM3fuXAUF\nBWno0KFKSUnJ9xzr1q2bwsLCNHjwYD322GO6dOmSPv/8c82aNUuSFBYWpv79+2vAgAHauXNn0Rxs\nMUFoF0OtWrXSnj17JElRUVFq166dcnJydOXKFe3evVtt2rSRJHl5eWnJkiXq0KGDNmzYYNu+T58+\n8vb2VlhYmGJiYrR+/XqtXLlSy5cv14YNGxQdHV0kx4Wi98svvyg4OFgDBgzQzJkz9eSTT9rei42N\n1WOPPaalS5dqwoQJCgsLk2EYevXVVxUWFqaVK1dqx44dunLliiQpIyNDEydO1IwZM/KEP24/186b\na/998cUXed7/+OOPtXLlSn322Wfy8PCwLa9bt65WrFihhg0b6osvvrjpOSZJOTk5qlu3rpYvX66a\nNWvmCebTp08rIiJCq1ev1ltvvaXw8HDnHHQxxfB4MVSxYkW5u7srJiZGBw4c0Pjx49WsWTPt379f\nUVFR6tevn/bu3SsfHx9JUtWqVZWUlHTTtg4dOqRff/1VISEhkqTLly/rt99+U/Xq1Z12PCg+rh8e\nP3XqlMaPH68GDRpIkipXrqwFCxZo0aJFyszMlLu7uxISElS6dGlVqlRJkvTBBx/Y2po2bZr8/PzU\nqFEj5x8InOr680a6ek37ev7+/ho2bJh69uypRx55xLbc19dXktS8eXPt3LlTffv2veEcu+aBBx6Q\nJFWrVk2pqam25T/++KPuv/9+ubi46O6779brr7/ukGM0C3raxVSbNm20bds2WSwWlSlTRj4+Ptq3\nb58OHTqkFi1aSJJcXV1t6+d3u32pUqXUqVMnLV26VEuXLlV4eLhatWrllGNA8Va3bl2VLl3adh4t\nWbJEVatW1cqVKzVt2jRJkouLi3Jzc2+6fdWqVfXll1/yhUfo1Vdf1bRp0xQbG6vg4GBlZ2dL+v33\nkmEYslgsNz3Hrsnv95mrq2u+52BJRGgXU23atNGqVavUvHlzSZKPj482b94sb29vlSlTxu72FotF\nOTk5aty4sXbt2qX09HQZhqEZM2bYhjdRsiUlJSk2Ntb2CzYxMVG1atWSJEVGRiorK0uenp7KyclR\nTEyMDMPQ008/rZSUFEnS+PHj5efnp9DQ0CI7BhS91NRUzZ8/X3Xr1tWYMWNUoUIF2yOXr303Z//+\n/br33ntveo7Z07hxY+3du1fZ2dmKi4vT6NGjHXcwJkBoF1OtWrXSkSNHbEPgXl5eSkpKsl3Ptqd1\n69YKCgpSmTJlFBISosGDB2vAgAEFDn3cnq6/NjlixAi99NJLKlWqlCSpd+/e+uSTTzR8+HA1a9ZM\nsbGxWrt2rV555RWNGzdOgwYNkq+vb55rliNHjtTWrVt1+PDhojokFLHy5csrMTFR/fv3V0hIiO6/\n/35VrFhR0tVnTAwdOlTHjx9X79698z3HbqVmzZrq3bu3hgwZotGjRys4ONgZh1VsMY0pAKDQ+fn5\nKTw8XGXLli3qUm4r9LQBADAJetoAAJgEPW0AAEyC0AYAwCQIbQAATIIZ0YAS4ty5cwoICLBNziNJ\n2dnZmjBhAhPuACZBaAMlSKVKlfJMR3ny5Ek98cQTttn3ABRvhDZQgt17773KyMhQdHS0Zs6cqaSk\nJF2+fFkBAQEaMWKEJGnBggXauHGjXFxcbJNcREdH69VXX1V6errS0tI0YcIEtWvXroiPBrj9EdpA\nCbZx40ZVqlRJubm56tKli/r06aPMzEz5+voqKChIx44d0+bNm7V69Wrl5uZq7NixeuSRRzRt2jQN\nHz5cbdu2VWxsrAYOHKgNGzbIauVXCuBI/B8GlCAJCQm2aSCjo6NVvXp1LVy4UF5eXtqzZ48+++wz\nlSpVShkZGUpKStKBAwfk4+MjV1dXubq62p6VvGvXLl2+fNk277jValV8fLyqVq1aZMcGlASENlCC\nXH9NOyIiQkuXLtU999yjhQsXKjMzUytXrpTFYrHNcW+xWG76BDk3NzfNmzfP9shOAM7BLV9ACeXv\n7y8PDw8tW7ZM8fHxqlu3riwWizZu3KgrV64oMzNTLVq00I4dO5SVlaWsrCwFBwfr4sWL8vHx0Xff\nfSfpau+9pD/jGHAWpjEFSohz584pKChIW7dutS2LiYlRv3799MEHH+j555+Xt7e3unTpop9++kk/\n/vijPv/8c4WGhmrLli0yDEM9e/bU0KFDdfbsWb388svKyMhQZmamnnnmGXXp0qUIjw4oGQhtAABM\nguFxAABMgtAGAMAkCG0AAEyC0AYAwCQIbQAATILQBgDAJAhtAABMgtAGAMAk/g8Qb4Wmkl9NNgAA\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f5217dc2e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = (survey_df.groupby(['state', 'female', 'race_wbh'])\n",
" .size()\n",
" .unstack(level=['female', 'race_wbh'])\n",
" .isnull()\n",
" .sum()\n",
" .unstack(level='female')\n",
" .rename(index={0: 'White', 1: 'Black', 2: 'Hispanic'},\n",
" columns={0: 'Male', 1: 'Female'})\n",
" .rename_axis('Race', axis=0)\n",
" .rename_axis('Gender', axis=1)\n",
" .plot(kind='bar', rot=0, figsize=(8, 6)))\n",
"\n",
"ax.set_yticks(np.arange(0, 21, 5));\n",
"ax.set_ylabel(\"Number of states\");\n",
"\n",
"ax.set_title(\"States with no respondents\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plot above illustrates this phenomenon; a number of states have no nonwhite male or female respondents. Even more states will have very few such respondents. This lack of data renders the disaggregation estimates suspect. For further discussion and references on disaggregation (as well as an empirical comparison of disaggregation and MRP), consult Lax and Phillip's [_How Should We Estimate Public Opinion in the States?_](http://www.columbia.edu/~jrl2124/Lax%20Phillips%20-%20Estimating%20State%20Public%20Opinion.pdf).\n",
"\n",
"MRP lessens the impact of this per-state respondent sparsity by first building a [multilevel model](https://en.wikipedia.org/wiki/Multilevel_model) of the relationship between respondents' states and demographic characteristics to opinion, and subsequently using the predictions of this multilevel model along with census data about the demographic composition of each state to predict state-level opinion. Intuitively, the multilevel model employed by MRP is a principled statistical method for estimating, for example, how much men in Pennsylvania share opinions with men in other states versus how much they share opinions with women in Pennsylvania. This partial pooling at both the state- and demographic-levels helps MRP impute the opinions of groups present in states that were not surveyed.\n",
"\n",
"The rest of this post is focused primarily on the execution of MRP in Python with PyMC3. For more detail on the theory and accuracy of MRP, consult the following (very incomplete) list of MRP resources:\n",
"\n",
"* the [MRP primer](http://www.princeton.edu/~jkastell/MRP_primer/mrp_primer.pdf) from which our example is taken,\n",
"* Park, Gelman, and Bafumi's [_Bayesian Multilevel Estimation with Poststratification: State-Level Estimates from National Polls_](https://pdfs.semanticscholar.org/2008/bee9f8c2d7e41ac9c5c54489f41989a0d7ba.pdf), which assesses the accuracy of MRP in predicting the state-level results of the 1998 and 1992 US presidential elections,\n",
"* Section 14.1 of Gelman and Hill's [_Data Analysis Using Regression and Multilevel/Hierarchical Models_](http://www.stat.columbia.edu/~gelman/arm/), which gives an expanded discussion of the example from the previous paper,\n",
"* Lax and Phillips' [_How Should We Estimate Public Opinion in The States?_](http://www.columbia.edu/~jrl2124/Lax%20Phillips%20-%20Estimating%20State%20Public%20Opinion.pdf), which is also mentioned above,\n",
"* Gelman's blog post [Mister P: What’s its secret sauce?](http://andrewgelman.com/2013/10/09/mister-p-whats-its-secret-sauce/), which is an extended discussion of several asssesments of MRP's accuracy ([1](https://academic.oup.com/pan/article-abstract/21/4/449/1544117/How-Does-Multilevel-Regression-and?redirectedFrom=fulltext), [2](http://www.columbia.edu/~jrl2124/mrp2.pdf)).\n",
"\n",
"Following the MRP primer, our multilevel opinion model will include factors for state, race, gender, education, age, and poll. In order to accelerate inference, we count the number of unique combinations of these factors, along with how many respondents with each combination supported gay marriage."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"uniq_survey_df = (survey_df.groupby(['race_wbh', 'female', 'edu_cat', 'age_cat',\n",
" 'region_cat', 'state_initnum', 'poll'])\n",
" .yes_of_all\n",
" .agg({\n",
" 'yes_of_all': 'sum',\n",
" 'n': 'size'\n",
" })\n",
" .reset_index())"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>race_wbh</th>\n",
" <th>female</th>\n",
" <th>edu_cat</th>\n",
" <th>age_cat</th>\n",
" <th>region_cat</th>\n",
" <th>state_initnum</th>\n",
" <th>poll</th>\n",
" <th>yes_of_all</th>\n",
" <th>n</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>6</td>\n",
" <td>Pew 2004Dec01</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>30</td>\n",
" <td>Gall2005Aug22</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>34</td>\n",
" <td>ABC 2004Jan15</td>\n",
" <td>1</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>38</td>\n",
" <td>Pew 2004Dec01</td>\n",
" <td>1</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>12</td>\n",
" <td>ABC 2004Jan15</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" race_wbh female edu_cat age_cat region_cat state_initnum \\\n",
"0 0 0 0 0 0 6 \n",
"1 0 0 0 0 0 30 \n",
"2 0 0 0 0 0 34 \n",
"3 0 0 0 0 0 38 \n",
"4 0 0 0 0 1 12 \n",
"\n",
" poll yes_of_all n \n",
"0 Pew 2004Dec01 0 1 \n",
"1 Gall2005Aug22 0 1 \n",
"2 ABC 2004Jan15 1 1 \n",
"3 Pew 2004Dec01 1 1 \n",
"4 ABC 2004Jan15 0 1 "
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uniq_survey_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This reduction adds negligible mathematical complexity (several Bernoulli distributions are combined into a single binomial distribution), but reduces the number of rows in the data set by nearly half."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.5824002523261316"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"uniq_survey_df.shape[0] / survey_df.shape[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will refer to each unique combination of state and demographic characteristics as a cell. Let $n_i$ denote the number of respondents in cell $i$, $y_i$ the number of those respondents that supported gay marriage, and $p_i$ the probability that a member of the general population of cell $i$ supports gay marriage. We build a Bayesian multilevel logistic regression model of opinion as follows.\n",
"\n",
"$$\\begin{align*}\n",
"\\eta_i\n",
" & = \\beta_0 + \\alpha^{\\textrm{gender : race}}_{j(i)} + \\alpha^{\\textrm{age}}_{k(i)} + \\alpha^{\\textrm{edu}}_{l(i)} + \\alpha^{\\textrm{age : edu}}_{k(i),\\ l(i)} + \\alpha^{\\textrm{state}}_{s(i)} + \\alpha^{\\textrm{poll}}_{m(i)} \\\\\n",
"\\log \\left(\\frac{p_i}{1 - p_i}\\right)\n",
" & = \\eta_i \\\\\n",
"y_i\n",
" & \\sim \\textrm{Bernoulli}(n_i, p_i)\n",
"\\end{align*}$$\n",
"\n",
"Here each subscript indexed by $i$ is the categorical level of that characteristic for respondents in cell $i$. The prior for the intercept is $\\beta_0 \\sim N(0, 5^2)$. The prior for the effects of the interaction of gender and age is $\\alpha^{\\textrm{gender : race}}_j \\sim N\\left(0, \\sigma_{\\textrm{gender : race}}^2\\right),$ with $\\sigma_{\\textrm{gender : race}} \\sim \\textrm{HalfCauchy}(5)$. The priors on $\\alpha^{\\textrm{age}}_k,$ $\\alpha^{\\textrm{edu}}_l,$ $\\alpha^{\\textrm{age : edu}}_{k,\\ l},$ and $\\alpha^{\\textrm{poll}}_m$ are defined similarly. The prior on the state term, $\\alpha^{\\textrm{state}}_s$, includes state-level predictors for region of the country, religiosity, and support for John Kerry in the 2004 presidential election.\n",
"\n",
"$$\\begin{align*}\n",
"\\alpha^{\\textrm{state}}_s\n",
" & \\sim N\\left(\\alpha^{\\textrm{region}}_s + \\beta^{\\textrm{relig}} x^{\\textrm{relig}}_s + \\beta^{\\textrm{kerry}} x^{\\textrm{kerry}}_s, \\sigma^2_{\\textrm{state}}\\right)\n",
"\\end{align*}$$\n",
"\n",
"Here $x^{\\textrm{relig}}_s$ is the log odds of the proportion of the state's residents that are evangelical Christian or Mormon, and $x^{\\textrm{kerry}}_s$ is the log odds of the proportion of the state's voters that voted for John Kerry in 2004. The priors on $\\alpha^{\\textrm{region}}_s$, $\\beta^{\\textrm{relig}}$, $\\beta^{\\textrm{kerry}}$ are the same as those on the analagous terms in the definition of $\\eta$.\n",
"\n",
"First we encode the respondent information."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def encode_gender_race(female, race_wbh):\n",
" return (3 * female + race_wbh).values\n",
"\n",
"def encode_age_edu(age, edu):\n",
" return (4 * age + edu).values"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"gender_race = encode_gender_race(uniq_survey_df.female, uniq_survey_df.race_wbh)\n",
"n_gender_race = np.unique(gender_race).size\n",
"\n",
"age = uniq_survey_df.age_cat.values\n",
"n_age = np.unique(age).size\n",
"\n",
"edu = uniq_survey_df.edu_cat.values\n",
"n_edu = np.unique(edu).size\n",
"\n",
"age_edu = encode_age_edu(uniq_survey_df.age_cat, uniq_survey_df.edu_cat)\n",
"n_age_edu = np.unique(age_edu).size\n",
"\n",
"poll, poll_map = uniq_survey_df.poll.factorize()\n",
"n_poll = poll_map.size\n",
"\n",
"region = uniq_survey_df.region_cat.values\n",
"n_region = np.unique(region).size\n",
"\n",
"state = uniq_survey_df.state_initnum.values\n",
"n_state = 51\n",
"\n",
"n = uniq_survey_df.n.values\n",
"yes_of_all = uniq_survey_df.yes_of_all.values"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we load the state-level data and encode $x^{\\textrm{relig}}$ and $x^{\\textrm{kerry}}$."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"STATE_URL = 'http://www.princeton.edu/~jkastell/MRP_primer/state_level_update.dta'\n",
"\n",
"state_df = (pd.read_stata(STATE_URL,\n",
" columns=['sstate_initnum', 'sstate',\n",
" 'p_evang', 'p_mormon', 'kerry_04'])\n",
" .rename(columns={'sstate_initnum': 'state_initnum', 'sstate': 'state'})\n",
" .assign(state_initnum=to_zero_indexed('state_initnum'),\n",
" p_relig=lambda df: df.p_evang + df.p_mormon))"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>state_initnum</th>\n",
" <th>state</th>\n",
" <th>p_evang</th>\n",
" <th>p_mormon</th>\n",
" <th>kerry_04</th>\n",
" <th>p_relig</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>12.440000</td>\n",
" <td>3.003126</td>\n",
" <td>35.500000</td>\n",
" <td>15.443126</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1</td>\n",
" <td>AL</td>\n",
" <td>40.549999</td>\n",
" <td>0.458273</td>\n",
" <td>36.799999</td>\n",
" <td>41.008274</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>2</td>\n",
" <td>AR</td>\n",
" <td>43.070000</td>\n",
" <td>0.560113</td>\n",
" <td>44.599998</td>\n",
" <td>43.630112</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>3</td>\n",
" <td>AZ</td>\n",
" <td>9.410000</td>\n",
" <td>4.878735</td>\n",
" <td>44.400002</td>\n",
" <td>14.288734</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>4</td>\n",
" <td>CA</td>\n",
" <td>7.160000</td>\n",
" <td>1.557627</td>\n",
" <td>54.299999</td>\n",
" <td>8.717627</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" state_initnum state p_evang p_mormon kerry_04 p_relig\n",
"0 0 AK 12.440000 3.003126 35.500000 15.443126\n",
"1 1 AL 40.549999 0.458273 36.799999 41.008274\n",
"2 2 AR 43.070000 0.560113 44.599998 43.630112\n",
"3 3 AZ 9.410000 4.878735 44.400002 14.288734\n",
"4 4 CA 7.160000 1.557627 54.299999 8.717627"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"state_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"state_kerry = sp.special.logit(state_df.kerry_04.values / 100.)\n",
"state_relig = sp.special.logit(state_df.p_relig.values / 100.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The state-level data doesn't contain region information, so we load census data in order to build a mapping between state and region."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"CENSUS_URL = 'http://www.princeton.edu/~jkastell/MRP_primer/poststratification%202000.dta'\n",
"\n",
"census_df = (pd.read_stata(CENSUS_URL)\n",
" .rename(columns=lambda s: s.lstrip('c_').lower())\n",
" .assign(race_wbh=to_zero_indexed('race_wbh'),\n",
" edu_cat=to_zero_indexed('edu_cat'),\n",
" age_cat=to_zero_indexed('age_cat')))"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>race_wbh</th>\n",
" <th>age_cat</th>\n",
" <th>edu_cat</th>\n",
" <th>female</th>\n",
" <th>state</th>\n",
" <th>freq</th>\n",
" <th>freq_state</th>\n",
" <th>percent_state</th>\n",
" <th>region</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>467</td>\n",
" <td>21222.0</td>\n",
" <td>0.022005</td>\n",
" <td>west</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>377</td>\n",
" <td>21222.0</td>\n",
" <td>0.017765</td>\n",
" <td>west</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0</td>\n",
" <td>2</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>419</td>\n",
" <td>21222.0</td>\n",
" <td>0.019744</td>\n",
" <td>west</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>343</td>\n",
" <td>21222.0</td>\n",
" <td>0.016162</td>\n",
" <td>west</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>958</td>\n",
" <td>21222.0</td>\n",
" <td>0.045142</td>\n",
" <td>west</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" race_wbh age_cat edu_cat female state freq freq_state percent_state \\\n",
"0 0 0 0 0 AK 467 21222.0 0.022005 \n",
"1 0 1 0 0 AK 377 21222.0 0.017765 \n",
"2 0 2 0 0 AK 419 21222.0 0.019744 \n",
"3 0 3 0 0 AK 343 21222.0 0.016162 \n",
"4 0 0 1 0 AK 958 21222.0 0.045142 \n",
"\n",
" region \n",
"0 west \n",
"1 west \n",
"2 west \n",
"3 west \n",
"4 west "
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"census_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"state_df = (pd.merge(\n",
" pd.merge((survey_df.groupby('region')\n",
" .region_cat\n",
" .first()\n",
" .reset_index()),\n",
" (census_df[['state', 'region']].drop_duplicates()),\n",
" on='region')[['state', 'region_cat']],\n",
" state_df, on='state')\n",
" .set_index('state_initnum')\n",
" .sort_index())"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>state</th>\n",
" <th>region_cat</th>\n",
" <th>p_evang</th>\n",
" <th>p_mormon</th>\n",
" <th>kerry_04</th>\n",
" <th>p_relig</th>\n",
" </tr>\n",
" <tr>\n",
" <th>state_initnum</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>AK</td>\n",
" <td>3</td>\n",
" <td>12.440000</td>\n",
" <td>3.003126</td>\n",
" <td>35.500000</td>\n",
" <td>15.443126</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>AL</td>\n",
" <td>2</td>\n",
" <td>40.549999</td>\n",
" <td>0.458273</td>\n",
" <td>36.799999</td>\n",
" <td>41.008274</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>AR</td>\n",
" <td>2</td>\n",
" <td>43.070000</td>\n",
" <td>0.560113</td>\n",
" <td>44.599998</td>\n",
" <td>43.630112</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>AZ</td>\n",
" <td>3</td>\n",
" <td>9.410000</td>\n",
" <td>4.878735</td>\n",
" <td>44.400002</td>\n",
" <td>14.288734</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>CA</td>\n",
" <td>3</td>\n",
" <td>7.160000</td>\n",
" <td>1.557627</td>\n",
" <td>54.299999</td>\n",
" <td>8.717627</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" state region_cat p_evang p_mormon kerry_04 p_relig\n",
"state_initnum \n",
"0 AK 3 12.440000 3.003126 35.500000 15.443126\n",
"1 AL 2 40.549999 0.458273 36.799999 41.008274\n",
"2 AR 2 43.070000 0.560113 44.599998 43.630112\n",
"3 AZ 3 9.410000 4.878735 44.400002 14.288734\n",
"4 CA 3 7.160000 1.557627 54.299999 8.717627"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"state_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"state_region = state_df.region_cat.values"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we are ready to specify the model with PyMC3. First, we wrap the predictors in `theano.shared` so that we can eventually replace the survey respondent's predictors with census predictors for posterior prediction (the poststratification step of MRP)."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"gender_race_ = shared(gender_race)\n",
"age_ = shared(age)\n",
"edu_ = shared(edu)\n",
"age_edu_ = shared(age_edu)\n",
"poll_ = shared(poll)\n",
"state_ = shared(state)\n",
"use_poll_ = shared(1)\n",
"n_ = shared(n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We specify the model for $\\alpha^{\\textrm{state}}$."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def hierarchical_normal(name, shape, μ=0.):\n",
" Δ = pm.Normal('Δ_{}'.format(name), 0., 1., shape=shape)\n",
" σ = pm.HalfCauchy('σ_{}'.format(name), 5.)\n",
" \n",
" return pm.Deterministic(name, μ + Δ * σ)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with pm.Model() as model:\n",
" α_region = hierarchical_normal('region', n_region)\n",
" β_relig = pm.Normal('relig', 0., 5.)\n",
" β_kerry = pm.Normal('kerry', 0., 5.)\n",
" μ_state = α_region[state_region] + β_relig * state_relig + β_kerry * state_kerry\n",
" α_state = hierarchical_normal('state', n_state, μ=μ_state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Throughout, we use a [non-centered parametrization](http://twiecki.github.io/blog/2017/02/08/bayesian-hierchical-non-centered/) for our hierarchical normal priors for more efficient sampling. We now specify the rest of $\\eta_i$."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with model:\n",
" β0 = pm.Normal('β0', 0., 5.,\n",
" testval=sp.special.logit(survey_df.yes_of_all.mean()))\n",
" α_gender_race = hierarchical_normal('gender_race', n_gender_race)\n",
" α_age = hierarchical_normal('age', n_age)\n",
" α_edu = hierarchical_normal('edu', n_edu)\n",
" α_age_edu = hierarchical_normal('age_edu', n_age_edu)\n",
" α_poll = hierarchical_normal('poll', n_poll)\n",
" \n",
" η = β0 \\\n",
" + α_gender_race[gender_race_] \\\n",
" + α_age[age_] \\\n",
" + α_edu[edu_] \\\n",
" + α_age_edu[age_edu_] \\\n",
" + α_state[state_] \\\n",
" + use_poll_ * α_poll[poll_]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here the `theano.shared` variable `use_poll_` will allow us to ignore poll effects when we do posterior predictive sampling with census data.\n",
"\n",
"Finally, we specify the likelihood and sample from the model using NUTS."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"with model:\n",
" p = pm.math.sigmoid(η)\n",
" obs = pm.Binomial('obs', n_, p, observed=yes_of_all)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using ADVI...\n",
"Average Loss = 2,800: 19%|█▉ | 37824/200000 [00:44<03:05, 876.09it/s] \n",
"Convergence archived at 37900\n",
"Interrupted at 37,900 [18%]: Average Loss = 3,804.3\n",
"100%|██████████| 1500/1500 [08:29<00:00, 3.77it/s]\n"
]
}
],
"source": [
"NUTS_KWARGS = {\n",
" 'target_accept': 0.99\n",
"} \n",
"\n",
"with model:\n",
" trace = pm.sample(draws=1000, random_seed=SEED,\n",
" nuts_kwargs=NUTS_KWARGS, njobs=3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The marginal energy and energy transition distributions are fairly close, showing no obvious problem with NUTS."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
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H++//IV/+8jcoK9vIrbf++7zTSyYnJzhw4DUeeeSPBINBnn76Kf76r99z2u93cr9bRVH4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\n9A6u6BQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f522204e1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.energyplot(trace);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Gelman-Rubin statistics for all parameters are quite close to one, indicating convergence."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0088100577623547"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"max(np.max(score) for score in pm.gelman_rubin(trace).values())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are now ready for the post-stratification step of MRP. First we combine the census and state-level data."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ps_df = pd.merge(census_df,\n",
" state_df[['state', 'region_cat']].reset_index(),\n",
" on='state')"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>race_wbh</th>\n",
" <th>age_cat</th>\n",
" <th>edu_cat</th>\n",
" <th>female</th>\n",
" <th>state</th>\n",
" <th>freq</th>\n",
" <th>freq_state</th>\n",
" <th>percent_state</th>\n",
" <th>region</th>\n",
" <th>state_initnum</th>\n",
" <th>region_cat</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>467</td>\n",
" <td>21222.0</td>\n",
" <td>0.022005</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>377</td>\n",
" <td>21222.0</td>\n",
" <td>0.017765</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0</td>\n",
" <td>2</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>419</td>\n",
" <td>21222.0</td>\n",
" <td>0.019744</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>343</td>\n",
" <td>21222.0</td>\n",
" <td>0.016162</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>958</td>\n",
" <td>21222.0</td>\n",
" <td>0.045142</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" race_wbh age_cat edu_cat female state freq freq_state percent_state \\\n",
"0 0 0 0 0 AK 467 21222.0 0.022005 \n",
"1 0 1 0 0 AK 377 21222.0 0.017765 \n",
"2 0 2 0 0 AK 419 21222.0 0.019744 \n",
"3 0 3 0 0 AK 343 21222.0 0.016162 \n",
"4 0 0 1 0 AK 958 21222.0 0.045142 \n",
"\n",
" region state_initnum region_cat \n",
"0 west 0 3 \n",
"1 west 0 3 \n",
"2 west 0 3 \n",
"3 west 0 3 \n",
"4 west 0 3 "
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ps_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we encode this combined data as before."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ps_gender_race = encode_gender_race(ps_df.female, ps_df.race_wbh)\n",
"ps_age = ps_df.age_cat.values\n",
"ps_edu = ps_df.edu_cat.values\n",
"ps_age_edu = encode_age_edu(ps_df.age_cat, ps_df.edu_cat)\n",
"ps_region = ps_df.region_cat.values\n",
"ps_state = ps_df.state_initnum.values\n",
"ps_n = ps_df.freq.values.astype(np.int64)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now set the values of the `theano.shared` variables in our PyMC3 model to the poststratification data and sample from the posterior predictive distribution."
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"gender_race_.set_value(ps_gender_race)\n",
"age_.set_value(ps_age)\n",
"edu_.set_value(ps_edu)\n",
"age_edu_.set_value(ps_age_edu)\n",
"poll_.set_value(np.zeros_like(ps_gender_race))\n",
"state_.set_value(ps_state)\n",
"use_poll_.set_value(0)\n",
"n_.set_value(ps_n)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 1000/1000 [00:01<00:00, 568.29it/s]\n"
]
}
],
"source": [
"with model:\n",
" pp_trace = pm.sample_ppc(trace, random_seed=SEED)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"PP_COLS = ['pp_yes_of_all_{}'.format(i) for i in range(pp_trace['obs'].shape[0])]\n",
"\n",
"pp_df = pd.merge(ps_df,\n",
" pd.DataFrame(pp_trace['obs'].T, columns=PP_COLS),\n",
" left_index=True, right_index=True)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>race_wbh</th>\n",
" <th>age_cat</th>\n",
" <th>edu_cat</th>\n",
" <th>female</th>\n",
" <th>state</th>\n",
" <th>freq</th>\n",
" <th>freq_state</th>\n",
" <th>percent_state</th>\n",
" <th>region</th>\n",
" <th>state_initnum</th>\n",
" <th>...</th>\n",
" <th>pp_yes_of_all_990</th>\n",
" <th>pp_yes_of_all_991</th>\n",
" <th>pp_yes_of_all_992</th>\n",
" <th>pp_yes_of_all_993</th>\n",
" <th>pp_yes_of_all_994</th>\n",
" <th>pp_yes_of_all_995</th>\n",
" <th>pp_yes_of_all_996</th>\n",
" <th>pp_yes_of_all_997</th>\n",
" <th>pp_yes_of_all_998</th>\n",
" <th>pp_yes_of_all_999</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>467</td>\n",
" <td>21222.0</td>\n",
" <td>0.022005</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>205</td>\n",
" <td>151</td>\n",
" <td>144</td>\n",
" <td>185</td>\n",
" <td>137</td>\n",
" <td>122</td>\n",
" <td>145</td>\n",
" <td>139</td>\n",
" <td>171</td>\n",
" <td>186</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>377</td>\n",
" <td>21222.0</td>\n",
" <td>0.017765</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>86</td>\n",
" <td>71</td>\n",
" <td>83</td>\n",
" <td>95</td>\n",
" <td>84</td>\n",
" <td>96</td>\n",
" <td>66</td>\n",
" <td>79</td>\n",
" <td>64</td>\n",
" <td>121</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0</td>\n",
" <td>2</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>419</td>\n",
" <td>21222.0</td>\n",
" <td>0.019744</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>94</td>\n",
" <td>77</td>\n",
" <td>45</td>\n",
" <td>86</td>\n",
" <td>80</td>\n",
" <td>61</td>\n",
" <td>47</td>\n",
" <td>54</td>\n",
" <td>50</td>\n",
" <td>65</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>343</td>\n",
" <td>21222.0</td>\n",
" <td>0.016162</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>69</td>\n",
" <td>38</td>\n",
" <td>33</td>\n",
" <td>40</td>\n",
" <td>39</td>\n",
" <td>18</td>\n",
" <td>32</td>\n",
" <td>35</td>\n",
" <td>32</td>\n",
" <td>39</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>AK</td>\n",
" <td>958</td>\n",
" <td>21222.0</td>\n",
" <td>0.045142</td>\n",
" <td>west</td>\n",
" <td>0</td>\n",
" <td>...</td>\n",
" <td>430</td>\n",
" <td>287</td>\n",
" <td>342</td>\n",
" <td>430</td>\n",
" <td>342</td>\n",
" <td>348</td>\n",
" <td>307</td>\n",
" <td>382</td>\n",
" <td>312</td>\n",
" <td>450</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 1011 columns</p>\n",
"</div>"
],
"text/plain": [
" race_wbh age_cat edu_cat female state freq freq_state percent_state \\\n",
"0 0 0 0 0 AK 467 21222.0 0.022005 \n",
"1 0 1 0 0 AK 377 21222.0 0.017765 \n",
"2 0 2 0 0 AK 419 21222.0 0.019744 \n",
"3 0 3 0 0 AK 343 21222.0 0.016162 \n",
"4 0 0 1 0 AK 958 21222.0 0.045142 \n",
"\n",
" region state_initnum ... pp_yes_of_all_990 \\\n",
"0 west 0 ... 205 \n",
"1 west 0 ... 86 \n",
"2 west 0 ... 94 \n",
"3 west 0 ... 69 \n",
"4 west 0 ... 430 \n",
"\n",
" pp_yes_of_all_991 pp_yes_of_all_992 pp_yes_of_all_993 pp_yes_of_all_994 \\\n",
"0 151 144 185 137 \n",
"1 71 83 95 84 \n",
"2 77 45 86 80 \n",
"3 38 33 40 39 \n",
"4 287 342 430 342 \n",
"\n",
" pp_yes_of_all_995 pp_yes_of_all_996 pp_yes_of_all_997 pp_yes_of_all_998 \\\n",
"0 122 145 139 171 \n",
"1 96 66 79 64 \n",
"2 61 47 54 50 \n",
"3 18 32 35 32 \n",
"4 348 307 382 312 \n",
"\n",
" pp_yes_of_all_999 \n",
"0 186 \n",
"1 121 \n",
"2 65 \n",
"3 39 \n",
"4 450 \n",
"\n",
"[5 rows x 1011 columns]"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pp_df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We complete the poststratification step by taking a weighted sum across the demographic cells within each state, to produce posterior predictive samples from the state-level opinion distribution."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"ps_prob = (pp_df.groupby('state')\n",
" .apply(lambda df: df[PP_COLS].sum(axis=0) / df.freq.sum()))"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>pp_yes_of_all_0</th>\n",
" <th>pp_yes_of_all_1</th>\n",
" <th>pp_yes_of_all_2</th>\n",
" <th>pp_yes_of_all_3</th>\n",
" <th>pp_yes_of_all_4</th>\n",
" <th>pp_yes_of_all_5</th>\n",
" <th>pp_yes_of_all_6</th>\n",
" <th>pp_yes_of_all_7</th>\n",
" <th>pp_yes_of_all_8</th>\n",
" <th>pp_yes_of_all_9</th>\n",
" <th>...</th>\n",
" <th>pp_yes_of_all_990</th>\n",
" <th>pp_yes_of_all_991</th>\n",
" <th>pp_yes_of_all_992</th>\n",
" <th>pp_yes_of_all_993</th>\n",
" <th>pp_yes_of_all_994</th>\n",
" <th>pp_yes_of_all_995</th>\n",
" <th>pp_yes_of_all_996</th>\n",
" <th>pp_yes_of_all_997</th>\n",
" <th>pp_yes_of_all_998</th>\n",
" <th>pp_yes_of_all_999</th>\n",
" </tr>\n",
" <tr>\n",
" <th>state</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>AK</th>\n",
" <td>0.306380</td>\n",
" <td>0.390585</td>\n",
" <td>0.361229</td>\n",
" <td>0.275893</td>\n",
" <td>0.374140</td>\n",
" <td>0.410847</td>\n",
" <td>0.362360</td>\n",
" <td>0.389172</td>\n",
" <td>0.372491</td>\n",
" <td>0.302281</td>\n",
" <td>...</td>\n",
" <td>0.411413</td>\n",
" <td>0.290312</td>\n",
" <td>0.297521</td>\n",
" <td>0.387287</td>\n",
" <td>0.365988</td>\n",
" <td>0.328386</td>\n",
" <td>0.316982</td>\n",
" <td>0.357035</td>\n",
" <td>0.280417</td>\n",
" <td>0.373433</td>\n",
" </tr>\n",
" <tr>\n",
" <th>AL</th>\n",
" <td>0.174168</td>\n",
" <td>0.199505</td>\n",
" <td>0.203892</td>\n",
" <td>0.155924</td>\n",
" <td>0.214749</td>\n",
" <td>0.190090</td>\n",
" <td>0.204509</td>\n",
" <td>0.203507</td>\n",
" <td>0.188764</td>\n",
" <td>0.147419</td>\n",
" <td>...</td>\n",
" <td>0.217865</td>\n",
" <td>0.145274</td>\n",
" <td>0.153651</td>\n",
" <td>0.220120</td>\n",
" <td>0.185526</td>\n",
" <td>0.187560</td>\n",
" <td>0.101283</td>\n",
" <td>0.175781</td>\n",
" <td>0.117774</td>\n",
" <td>0.218250</td>\n",
" </tr>\n",
" <tr>\n",
" <th>AR</th>\n",
" <td>0.142486</td>\n",
" <td>0.207379</td>\n",
" <td>0.219824</td>\n",
" <td>0.221326</td>\n",
" <td>0.229756</td>\n",
" <td>0.204580</td>\n",
" <td>0.221235</td>\n",
" <td>0.239279</td>\n",
" <td>0.193739</td>\n",
" <td>0.198919</td>\n",
" <td>...</td>\n",
" <td>0.210138</td>\n",
" <td>0.164843</td>\n",
" <td>0.146860</td>\n",
" <td>0.238502</td>\n",
" <td>0.185973</td>\n",
" <td>0.245931</td>\n",
" <td>0.114837</td>\n",
" <td>0.189018</td>\n",
" <td>0.164965</td>\n",
" <td>0.232096</td>\n",
" </tr>\n",
" <tr>\n",
" <th>AZ</th>\n",
" <td>0.353140</td>\n",
" <td>0.395125</td>\n",
" <td>0.388163</td>\n",
" <td>0.361972</td>\n",
" <td>0.394620</td>\n",
" <td>0.378743</td>\n",
" <td>0.387904</td>\n",
" <td>0.375209</td>\n",
" <td>0.385323</td>\n",
" <td>0.443167</td>\n",
" <td>...</td>\n",
" <td>0.390827</td>\n",
" <td>0.318305</td>\n",
" <td>0.340562</td>\n",
" <td>0.411255</td>\n",
" <td>0.376126</td>\n",
" <td>0.455857</td>\n",
" <td>0.318835</td>\n",
" <td>0.387193</td>\n",
" <td>0.329390</td>\n",
" <td>0.405663</td>\n",
" </tr>\n",
" <tr>\n",
" <th>CA</th>\n",
" <td>0.384078</td>\n",
" <td>0.463444</td>\n",
" <td>0.463495</td>\n",
" <td>0.405385</td>\n",
" <td>0.468195</td>\n",
" <td>0.475593</td>\n",
" <td>0.463783</td>\n",
" <td>0.474011</td>\n",
" <td>0.429405</td>\n",
" <td>0.431427</td>\n",
" <td>...</td>\n",
" <td>0.468451</td>\n",
" <td>0.384701</td>\n",
" <td>0.374767</td>\n",
" <td>0.486855</td>\n",
" <td>0.434450</td>\n",
" <td>0.475072</td>\n",
" <td>0.378866</td>\n",
" <td>0.471518</td>\n",
" <td>0.378529</td>\n",
" <td>0.496080</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 1000 columns</p>\n",
"</div>"
],
"text/plain": [
" pp_yes_of_all_0 pp_yes_of_all_1 pp_yes_of_all_2 pp_yes_of_all_3 \\\n",
"state \n",
"AK 0.306380 0.390585 0.361229 0.275893 \n",
"AL 0.174168 0.199505 0.203892 0.155924 \n",
"AR 0.142486 0.207379 0.219824 0.221326 \n",
"AZ 0.353140 0.395125 0.388163 0.361972 \n",
"CA 0.384078 0.463444 0.463495 0.405385 \n",
"\n",
" pp_yes_of_all_4 pp_yes_of_all_5 pp_yes_of_all_6 pp_yes_of_all_7 \\\n",
"state \n",
"AK 0.374140 0.410847 0.362360 0.389172 \n",
"AL 0.214749 0.190090 0.204509 0.203507 \n",
"AR 0.229756 0.204580 0.221235 0.239279 \n",
"AZ 0.394620 0.378743 0.387904 0.375209 \n",
"CA 0.468195 0.475593 0.463783 0.474011 \n",
"\n",
" pp_yes_of_all_8 pp_yes_of_all_9 ... pp_yes_of_all_990 \\\n",
"state ... \n",
"AK 0.372491 0.302281 ... 0.411413 \n",
"AL 0.188764 0.147419 ... 0.217865 \n",
"AR 0.193739 0.198919 ... 0.210138 \n",
"AZ 0.385323 0.443167 ... 0.390827 \n",
"CA 0.429405 0.431427 ... 0.468451 \n",
"\n",
" pp_yes_of_all_991 pp_yes_of_all_992 pp_yes_of_all_993 \\\n",
"state \n",
"AK 0.290312 0.297521 0.387287 \n",
"AL 0.145274 0.153651 0.220120 \n",
"AR 0.164843 0.146860 0.238502 \n",
"AZ 0.318305 0.340562 0.411255 \n",
"CA 0.384701 0.374767 0.486855 \n",
"\n",
" pp_yes_of_all_994 pp_yes_of_all_995 pp_yes_of_all_996 \\\n",
"state \n",
"AK 0.365988 0.328386 0.316982 \n",
"AL 0.185526 0.187560 0.101283 \n",
"AR 0.185973 0.245931 0.114837 \n",
"AZ 0.376126 0.455857 0.318835 \n",
"CA 0.434450 0.475072 0.378866 \n",
"\n",
" pp_yes_of_all_997 pp_yes_of_all_998 pp_yes_of_all_999 \n",
"state \n",
"AK 0.357035 0.280417 0.373433 \n",
"AL 0.175781 0.117774 0.218250 \n",
"AR 0.189018 0.164965 0.232096 \n",
"AZ 0.387193 0.329390 0.405663 \n",
"CA 0.471518 0.378529 0.496080 \n",
"\n",
"[5 rows x 1000 columns]"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ps_prob.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The simplest summary of state-level opinion is the posterior expected mean, shown below."
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": true,
"scrolled": false
},
"outputs": [],
"source": [
"ps_mean = ps_prob.mean(axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"state\n",
"AK 0.365962\n",
"AL 0.189076\n",
"AR 0.201302\n",
"AZ 0.395071\n",
"CA 0.459842\n",
"dtype: float64"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ps_mean.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following choropleth maps show the disaggregation and MRP estimates of support for gay marriage by state."
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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RcRBK8kVEREREREQchJJ8EREREREREQehJF9ERERERETEQSjJFxEREREREXEQ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\nvXxo0b6jbvBJpnNyMmE0Ghj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37MSrkC9tOnTOtGMDXLt6lYJeXpjyUHcluaVyzVps2ryR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\nULUqKSkp3L55g+XLluHh5c2ggdm97pcsW4Fvxcr07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GIxWpEInUhEjEqJwrcMqLMo5ehI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\nGspHj8jKVKJWZfEoS0VKejo6vR6tRo1Oq0WvN2DIyf57XDOcW26