{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A Primer on Bayesian Multilevel Modeling using PyStan\n", "\n", "*Author*: Chris Fonnesbeck \n", "*License*: Apache, Version 2.0 (code); CC-BY 3.0 (text)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hierarchical or multilevel modeling is a generalization of regression modeling.\n", "\n", "*Multilevel models* are regression models in which the constituent model parameters are given **probability models**. This implies that model parameters are allowed to **vary by group**.\n", "\n", "Observational units are often naturally **clustered**. Clustering induces dependence between observations, despite random sampling of clusters and random sampling within clusters.\n", "\n", "A *hierarchical model* is a particular multilevel model where parameters are nested within one another.\n", "\n", "Some multilevel structures are not hierarchical. \n", "\n", "* e.g. \"country\" and \"year\" are not nested, but may represent separate, but overlapping, clusters of parameters\n", "\n", "We will motivate this topic using an environmental epidemiology example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Radon contamination (Gelman and Hill 2006)\n", "\n", "Radon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n", "\n", "![radon](http://www.fix-your-radon.com/images/how_radon_enters.jpg)\n", "\n", "The EPA did a study of radon levels in 80,000 houses. Two important predictors:\n", "\n", "* measurement in basement or first floor (radon higher in basements)\n", "* county uranium level (positive correlation with radon levels)\n", "\n", "We will focus on modeling radon levels in Minnesota.\n", "\n", "The hierarchy in this example is households within county. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data organization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we import the data from a local file, and extract Minnesota's data." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set_context('notebook')\n", "\n", "# Import radon data\n", "srrs2 = pd.read_csv('../data/srrs2.dat')\n", "srrs2.columns = srrs2.columns.map(str.strip)\n", "srrs_mn = srrs2.assign(fips=srrs2.stfips*1000 + srrs2.cntyfips)[srrs2.state=='MN']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, obtain the county-level predictor, uranium, by combining two variables." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "cty = pd.read_csv('../data/cty.dat')\n", "cty_mn = cty[cty.st=='MN'].copy()\n", "cty_mn[ 'fips'] = 1000*cty_mn.stfips + cty_mn.ctfips" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use the `merge` method to combine home- and county-level information in a single DataFrame." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "srrs_mn = srrs_mn.merge(cty_mn[['fips', 'Uppm']], on='fips')\n", "srrs_mn = srrs_mn.drop_duplicates(subset='idnum')\n", "u = np.log(srrs_mn.Uppm)\n", "\n", "n = len(srrs_mn)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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idnumstatestate2stfipszipregiontypebldgfloorroombasement...stopdtactivitypcterradjwtdupflagzipflagcntyfipscountyfipsUppm
05081MNMN27557355113N...122882.29.71146.499190101AITKIN270010.502054
15082MNMN27557485104Y...120882.214.5471.366223001AITKIN270010.502054
25083MNMN27557485104Y...211882.99.6433.316718001AITKIN270010.502054
35084MNMN27564695104Y...1231871.024.3461.623670001AITKIN270010.502054
45085MNMN27550113104Y...130883.113.8433.316718003ANOKA270030.428565
\n", "

5 rows × 27 columns

\n", "
" ], "text/plain": [ " idnum state state2 stfips zip region typebldg floor room basement \\\n", "0 5081 MN MN 27 55735 5 1 1 3 N \n", "1 5082 MN MN 27 55748 5 1 0 4 Y \n", "2 5083 MN MN 27 55748 5 1 0 4 Y \n", "3 5084 MN MN 27 56469 5 1 0 4 Y \n", "4 5085 MN MN 27 55011 3 1 0 4 Y \n", "\n", " ... stopdt activity pcterr adjwt dupflag zipflag cntyfips \\\n", "0 ... 12288 2.2 9.7 1146.499190 1 0 1 \n", "1 ... 12088 2.2 14.5 471.366223 0 0 1 \n", "2 ... 21188 2.9 9.6 433.316718 0 0 1 \n", "3 ... 123187 1.0 24.3 461.623670 0 0 1 \n", "4 ... 13088 3.1 13.8 433.316718 0 0 3 \n", "\n", " county fips Uppm \n", "0 AITKIN 27001 0.502054 \n", "1 AITKIN 27001 0.502054 \n", "2 AITKIN 27001 0.502054 \n", "3 AITKIN 27001 0.502054 \n", "4 ANOKA 27003 0.428565 \n", "\n", "[5 rows x 27 columns]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "srrs_mn.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also need a lookup table (`dict`) for each unique county, for indexing." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "srrs_mn.county = srrs_mn.county.str.strip()\n", "mn_counties = srrs_mn.county.unique()\n", "counties = len(mn_counties)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, create local copies of variables." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "county_lookup = dict(zip(mn_counties, range(len(mn_counties))))\n", "county = srrs_mn['county_code'] = srrs_mn.county.replace(county_lookup).values\n", "radon = srrs_mn.activity\n", "srrs_mn['log_radon'] = log_radon = np.log(radon + 0.1).values\n", "floor_measure = srrs_mn.floor.values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Distribution of radon levels in MN (log scale):" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "srrs_mn.activity.apply(lambda x: np.log(x+0.1)).hist(bins=25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conventional approaches\n", "\n", "The two conventional alternatives to modeling radon exposure represent the two extremes of the bias-variance tradeoff:\n", "\n", "***Complete pooling***: \n", "\n", "Treat all counties the same, and estimate a single radon level.\n", "\n", "$$y_i = \\alpha + \\beta x_i + \\epsilon_i$$\n", "\n", "***No pooling***:\n", "\n", "Model radon in each county independently.\n", "\n", "$$y_i = \\alpha_{j[i]} + \\beta x_i + \\epsilon_i$$\n", "\n", "where $j = 1,\\ldots,85$\n", "\n", "The errors $\\epsilon_i$ may represent measurement error, temporal within-house variation, or variation among houses." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To specify this model in Stan, we begin by constructing the `data` block, which includes vectors of log-radon measurements (`y`) and floor measurement covariates (`x`), as well as the number of samples (`N`)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pooled_data = \"\"\"\n", "data {\n", " int N; \n", " vector[N] x;\n", " vector[N] y;\n", "}\n", "\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we initialize our parameters, which in this case are the linear model coefficients and the normal scale parameter. Notice that `sigma` is constrained to be positive." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pooled_parameters = \"\"\"\n", "parameters {\n", " vector[2] beta;\n", " real sigma;\n", "} \n", "\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we model the log-radon measurements as a normal sample with a mean that is a function of the floor measurement." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pooled_model = \"\"\"\n", "model {\n", " y ~ normal(beta[1] + beta[2] * x, sigma);\n", "}\n", "\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then pass the code, data, and parameters to the `stan` function. The sampling requires specifying how many iterations we want, and how many parallel chains to sample. Here, we will sample 2 chains of length 1000." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pystan\n", "\n", "pooled_data_dict = {'N': len(log_radon),\n", " 'x': floor_measure,\n", " 'y': log_radon}\n", "\n", "pooled_fit = pystan.stan(model_code=pooled_data + pooled_parameters + pooled_model, \n", " data=pooled_data_dict, iter=1000, chains=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sample can be extracted for plotting and summarization." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pooled_sample = pooled_fit.extract(permuted=True)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "b0, m0 = pooled_sample['beta'].T.mean(1)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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7CktyAt51orhU5Q0Es6+slfSkos85Vkv6UExlA17xkZjK9gaC2VcMxe8u9X/2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\nI47Qli1bVF1drcbGRq1evVr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(srrs_mn.floor, np.log(srrs_mn.activity+0.1))\n", "xvals = np.linspace(-0.2, 1.2)\n", "plt.plot(xvals, m0*xvals+b0, 'r--')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At the other end of the extreme, we can fit separate (independent) means for each county. The only things that are shared in this model are the coefficient for the basement measurement effect, and the standard deviation of the error." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "unpooled_model = \"\"\"data {\n", " int N; \n", " int county[N];\n", " vector[N] x;\n", " vector[N] y;\n", "} \n", "parameters {\n", " vector[85] a;\n", " real beta;\n", " real sigma;\n", "} \n", "transformed parameters {\n", " vector[N] y_hat;\n", "\n", " for (i in 1:N)\n", " y_hat[i] <- beta * x[i] + a[county[i]];\n", "}\n", "model {\n", " y ~ normal(y_hat, sigma);\n", "}\"\"\"" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "unpooled_data = {'N': len(log_radon),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'x': floor_measure,\n", " 'y': log_radon}\n", "\n", "unpooled_fit = pystan.stan(model_code=unpooled_model, data=unpooled_data, iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "unpooled_estimates = pd.Series(unpooled_fit['a'].mean(0), index=mn_counties)\n", "unpooled_se = pd.Series(unpooled_fit['a'].std(0), index=mn_counties)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the ordered estimates to identify counties with high radon levels:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "order = unpooled_estimates.sort_values().index\n", "\n", "plt.scatter(range(len(unpooled_estimates)), unpooled_estimates[order])\n", "for i, m, se in zip(range(len(unpooled_estimates)), unpooled_estimates[order], unpooled_se[order]):\n", " plt.plot([i,i], [m-se, m+se], 'b-')\n", "plt.xlim(-1,86); plt.ylim(-1,4)\n", "plt.ylabel('Radon estimate');plt.xlabel('Ordered county');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are visual comparisons between the pooled and unpooled estimates for a subset of counties representing a range of sample sizes." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LmTdvHiqVCi8vL2bNmiUPidBoNCxbtowFCxYwZswY1Go1KpWKhx56qEKOS03lu/zfZW3+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\ntKKZ14q9G2fHZ3ozi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_counties = ('LAC QUI PARLE', 'AITKIN', 'KOOCHICHING', \n", " 'DOUGLAS', 'CLAY', 'STEARNS', 'RAMSEY', 'ST LOUIS')\n", "\n", "fig, axes = plt.subplots(2, 4, figsize=(12, 6), sharey=True, sharex=True)\n", "axes = axes.ravel()\n", "m = unpooled_fit['beta'].mean(0)\n", "for i,c in enumerate(sample_counties):\n", " y = srrs_mn.log_radon[srrs_mn.county==c]\n", " x = srrs_mn.floor[srrs_mn.county==c]\n", " axes[i].scatter(x + np.random.randn(len(x))*0.01, y, alpha=0.4)\n", " \n", " # No pooling model\n", " b = unpooled_estimates[c]\n", " \n", " # Plot both models and data\n", " xvals = np.linspace(-0.2, 1.2)\n", " axes[i].plot(xvals, m*xvals+b)\n", " axes[i].plot(xvals, m0*xvals+b0, 'r--')\n", " axes[i].set_xticks([0,1])\n", " axes[i].set_xticklabels(['basement', 'floor'])\n", " axes[i].set_ylim(-1, 3)\n", " axes[i].set_title(c)\n", " if not i%2:\n", " axes[i].set_ylabel('log radon level')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Neither of these models are satisfactory:\n", "\n", "* if we are trying to identify high-radon counties, pooling is useless\n", "* we do not trust extreme unpooled estimates produced by models using few observations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multilevel and hierarchical models\n", "\n", "When we pool our data, we imply that they are sampled from the same model. This ignores any variation among sampling units (other than sampling variance):\n", "\n", "![pooled](http://f.cl.ly/items/0R1W063h1h0W2M2C0S3M/Screen%20Shot%202013-10-10%20at%208.22.21%20AM.png)\n", "\n", "When we analyze data unpooled, we imply that they are sampled independently from separate models. At the opposite extreme from the pooled case, this approach claims that differences between sampling units are to large to combine them:\n", "\n", "![unpooled](http://f.cl.ly/items/38020n2t2Y2b1p3t0B0e/Screen%20Shot%202013-10-10%20at%208.23.36%20AM.png)\n", "\n", "In a hierarchical model, parameters are viewed as a sample from a population distribution of parameters. Thus, we view them as being neither entirely different or exactly the same. This is ***parital pooling***.\n", "\n", "![hierarchical](http://f.cl.ly/items/1B3U223i002y3V2W3r0W/Screen%20Shot%202013-10-10%20at%208.25.05%20AM.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use PyStan to easily specify multilevel models, and fit them using Hamiltonian Monte Carlo." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Partial pooling model\n", "\n", "The simplest partial pooling model for the household radon dataset is one which simply estimates radon levels, without any predictors at any level. A partial pooling model represents a compromise between the pooled and unpooled extremes, approximately a weighted average (based on sample size) of the unpooled county estimates and the pooled estimates.\n", "\n", "$$\\hat{\\alpha} \\approx \\frac{(n_j/\\sigma_y^2)\\bar{y}_j + (1/\\sigma_{\\alpha}^2)\\bar{y}}{(n_j/\\sigma_y^2) + (1/\\sigma_{\\alpha}^2)}$$\n", "\n", "- Estimates for counties with smaller sample sizes will shrink towards the state-wide average.\n", "- Estimates for counties with larger sample sizes will be closer to the unpooled county estimates." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "partial_pooling = \"\"\"\n", "data {\n", " int N; \n", " int county[N];\n", " vector[N] y;\n", "} \n", "parameters {\n", " vector[85] a;\n", " real mu_a;\n", " real sigma_a;\n", " real sigma_y;\n", "} \n", "transformed parameters {\n", " vector[N] y_hat;\n", " for (i in 1:N)\n", " y_hat[i] <- a[county[i]];\n", "}\n", "model {\n", " mu_a ~ normal(0, 1);\n", " a ~ normal (10 * mu_a, sigma_a);\n", "\n", " y ~ normal(y_hat, sigma_y);\n", "}\"\"\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice now we have two standard deviations, one describing the residual error of the observations, and another the variability of the county means around the average." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "partial_pool_data = {'N': len(log_radon),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'y': log_radon}\n", "\n", "partial_pool_fit = pystan.stan(model_code=partial_pooling, data=partial_pool_data, iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OVCBhWVK5LFmWEXrvl+7u5eW0AQCrmaYRWJ+aVmeaRmh9k+oJuKJGnyikCTM5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\niCAnhSzLqUBWLjv/wighHbc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_trace = partial_pool_fit['a']\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(14,6), sharex=True, sharey=True)\n", "samples, counties = sample_trace.shape\n", "jitter = np.random.normal(scale=0.1, size=counties)\n", "\n", "n_county = srrs_mn.groupby('county')['idnum'].count()\n", "unpooled_means = srrs_mn.groupby('county')['log_radon'].mean()\n", "unpooled_sd = srrs_mn.groupby('county')['log_radon'].std()\n", "unpooled = pd.DataFrame({'n':n_county, 'm':unpooled_means, 'sd':unpooled_sd})\n", "unpooled['se'] = unpooled.sd/np.sqrt(unpooled.n)\n", "\n", "axes[0].plot(unpooled.n + jitter, unpooled.m, 'b.')\n", "for j, row in zip(jitter, unpooled.iterrows()):\n", " name, dat = row\n", " axes[0].plot([dat.n+j,dat.n+j], [dat.m-dat.se, dat.m+dat.se], 'b-')\n", "axes[0].set_xscale('log')\n", "axes[0].hlines(sample_trace.mean(), 0.9, 100, linestyles='--')\n", "\n", " \n", "samples, counties = sample_trace.shape\n", "means = sample_trace.mean(axis=0)\n", "sd = sample_trace.std(axis=0)\n", "axes[1].scatter(n_county.values + jitter, means)\n", "axes[1].set_xscale('log')\n", "axes[1].set_xlim(1,100)\n", "axes[1].set_ylim(0, 3)\n", "axes[1].hlines(sample_trace.mean(), 0.9, 100, linestyles='--')\n", "for j,n,m,s in zip(jitter, n_county.values, means, sd):\n", " axes[1].plot([n+j]*2, [m-s, m+s], 'b-')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the difference between the unpooled and partially-pooled estimates, particularly at smaller sample sizes. The former are both more extreme and more imprecise." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Varying intercept model\n", "\n", "This model allows intercepts to vary across county, according to a random effect.\n", "\n", "$$y_i = \\alpha_{j[i]} + \\beta x_{i} + \\epsilon_i$$\n", "\n", "where\n", "\n", "$$\\epsilon_i \\sim N(0, \\sigma_y^2)$$\n", "\n", "and the intercept random effect:\n", "\n", "$$\\alpha_{j[i]} \\sim N(\\mu_{\\alpha}, \\sigma_{\\alpha}^2)$$\n", "\n", "As with the the “no-pooling” model, we set a separate intercept for each county, but rather than fitting separate least squares regression models for each county, multilevel modeling **shares strength** among counties, allowing for more reasonable inference in counties with little data." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "varying_intercept = \"\"\"\n", "data {\n", " int J; \n", " int N; \n", " int county[N];\n", " vector[N] x;\n", " vector[N] y;\n", "} \n", "parameters {\n", " vector[J] a;\n", " real b;\n", " real mu_a;\n", " real sigma_a;\n", " real sigma_y;\n", "} \n", "transformed parameters {\n", "\n", " vector[N] y_hat;\n", "\n", " for (i in 1:N)\n", " y_hat[i] <- a[county[i]] + x[i] * b;\n", "}\n", "model {\n", " sigma_a ~ uniform(0, 100);\n", " a ~ normal (mu_a, sigma_a);\n", "\n", " b ~ normal (0, 1);\n", "\n", " sigma_y ~ uniform(0, 100);\n", " y ~ normal(y_hat, sigma_y);\n", "}\n", "\"\"\"" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ "varying_intercept_data = {'N': len(log_radon),\n", " 'J': len(n_county),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'x': floor_measure,\n", " 'y': log_radon}\n", "\n", "varying_intercept_fit = pystan.stan(model_code=varying_intercept, data=varying_intercept_data, iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a_sample = pd.DataFrame(varying_intercept_fit['a'])" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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GPij3TLhNpEwdLe6FMOP5tdHjdYLCaobs4vtMz+1gTFBWJOVr8NXpWd3MGvof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\nAse64+PS1tamgQMHOpbNxNatW7V27Vr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "sns.set(style=\"ticks\", palette=\"muted\", color_codes=True)\n", "\n", "# Plot the orbital period with horizontal boxes\n", "plt.figure(figsize=(16, 6))\n", "sns.boxplot(data=a_sample, whis=np.inf, color=\"c\")" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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naIwvhDxWj0hlgmtZvXo18vPzMWjQICxZsgR//PEHXn/9dTz77LNm20mlUojF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kAAAg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\n0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "varying_intercept_fit.plot(pars=['sigma_a', 'b']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimate for the `floor` coefficient is approximately -0.66, which can be interpreted as houses without basements having about half ($\\exp(-0.66) = 0.52$) the radon levels of those with basements, after accounting for county." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-0.66292666591258154" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "varying_intercept_fit['b'].mean()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bU5wIHHUjMA6UXeo0/SDFcDKLtednmJff1U4TvtovA4Fn2don/RiRQuBhLJCmEmDASSQw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "bp = varying_intercept_fit['a'].mean(axis=0)\n", "mp = varying_intercept_fit['b'].mean()\n", "for bi in bp:\n", " plt.plot(xvals, mp*xvals + bi, 'bo-', alpha=0.4)\n", "plt.xlim(-0.1,1.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is easy to show that the partial pooling model provides more objectively reasonable estimates than either the pooled or unpooled models, at least for counties with small sample sizes." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1grVJ9aAx2F66dClevXqFkSNHYvTo0di5cyeysrL00TeigYuLC9auXcvaSUlJ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GRU/3nz5hklYG7atAkTJ05ky7/88gvatWtntOJleXD4fMPjeF9fuPbrZ/I1DMMg9fvvoZPLDWss\nNG7MDjuR+vtT8F1BDg4OeP21Tvj9VBry1Hpo8uUQC3hQ6/kmF7YpGiiOGTPGaKhFfHw8mhRZHGnT\npk1wdXVln5zVRDw7O8jatIGsTZsSX6NMTkbqhg0ADEmXhcNO7Jo1Q45ci+TMNGjyYcjzqFPy0BVz\nKnPSQ4lEgh07dkChUEAul2PLli3stFiEmIuoYUO4jxwJ+3btwOTnI+fsWaRt3ozMPXusXbUa4cWv\nfTcoOG44fTnZ2lWqMRy7doXroEGQ+vtDk5qK53FxeLxuHRS3bsHf3xcOTi/Gyw4b8Q46F3mcP3fu\nXGRnZ7PlAwcOWGVhr+rW7xcmQd+99wj/396dR1VZ7f8Dfx/OxDkchlQccQJFnA3nn1OIplddXlNU\nzMTS282+we2qq6xbea0ky7GC61e9KzOqlaa37KurYeV4y0QMJXMCFVFR04OZcDicef/+QB45gCJy\nRni/1nItN2d4Ng8fNp/zPHt/tk3VAprQ5g0ybsPCwpxKSr777rtSfAghsHr1aqfka9OmTdDr9a45\nuMOBFjNnIiwuDqrwcBhPnkTR9u24uGrVXdcz0P25ek2PZs3bIOShcDRp3h7yAAcU6tD7it/Kyfcb\nb7yBxytVndm9e7dTvKxevbpRTvFVtWiBFjNnIrhfPwiHAyVZWbj2ySe4/p//4OLlq7BAByh1sECH\ni5ev1v6GblDrR9UVK1bgzTffxNKlSyGTyTBkyBAsX77cE32jRkzZtCmajBkjLbq0/PZbecH88PAa\nn19y5AhMBQXQREdDExXlt4soPKUh1tr2FdrOnaG9ffXJYbXCVFAAY24utF26YLBa7XRHYe4Tk1H8\nzTcwa7VQd+qEV199FV1ub5dsMpmQkpKCn2/PEQeAb7/9FqNGjbrvMnIPytfG/YpF0eayUmhUBkRG\nlNewbuhxW7V82MaNG6Wr2mVlZXjrrbcwZcoU6fF///vfmDVrltMizfslk8sROniwtNulzWBA2Zkz\nsBYV1TzVz2DA9W3bpHrfXHR5d03DdMg89jOu/yFgMRsQFqaBzdoKt0ostb+4isq7U27atMnpsf/8\n5z+YNGmS1F6yZAmeeuqpem3I5Q+UDz2EJqNHS4surdeuSZXR2l4XOHf1Gsz2AKjlDrRt3QKGY8fK\npwLe3mPBE/lCrSN2mzZtsG7dOqevmUwNfIQjnyKTyaBu1Qrqe9xav5WZiZKsrPLG7W1mtdHRCBs+\nHOq77GjVmGkDgVsVt+TtAQgOuAmz2b9vyfuiAKXSKflWAE7zBYXNhhtffw1xe/v4ToGBuHTqVPnK\n++HDsWbNGunK1aVLl7Bo0SIcvV1f2WKxIDMzE8OHD3d5v31t3K+8KNoou/OBuzGV/ZTJZOjevbvU\nViqV2Lp1K4KDgwEAFy9eRHp6ulQJx2w2Y/PmzU4bMtWFQqdD8MMP3/Vx45kz+GPfPvyxb1/585s2\nhTY6GsEPPyxtckLljp68gGYdh8BedAs2mRp/5O/DhRsCRddPYuywmAcedysn3gCwa9cu6YOWyWTC\n5s2bpapCQggsWrQIixcvhq4Bl4KUyWRQtWwJVcuWAIDQQ6cQE3InB9AKPYoP/YhbBw5IeywEtmsH\nze18IbBtW7f0q9ZpJN999x0mTpyIUaNGIT4+HnFxcX5RB5sal1azZyPi739H03HjoImMhOniRfz+\n3Xew3rxZ7bn3KjfUWAzuE4lL+cdhkwVBo9GgXVSvBndL3i/I5YhcuhSt/vIXhA4fDkVYGEqPH8eN\nb76BNiQE48ePl56q0WiwfPlyaU5vdnY23n//fbd0y1fH/cF9IqEVeqBMD63Q+1zZP09SKBToXWke\na7NmzbBp0yZp2sHPP/+MrVu3So/r9Xp8++23Lju+rmdPdFi8GM2nT4cuNhbCbEbxwYMw/PKLy47R\nUISGNoMcZigDHLAabyIwuBUCtaFo0qqbS8ddjUYj/fwrduHWarUAgAsXLmD37t1SdZyysjK8/PLL\nDf7vYU1jRouZM9F2wQI0nTABms6dYb58GTe//x5WV03JqsF9TSNZunQpPvzwQ8ybNw8//vgjbtaQ\nwBB5U9VFlw6LBWXnzkETWf2PsUwmw6V330WAWi0tpFC3aXPX8lkNTcXiyBKTAprQ8o1BFEoFjGW1\nv5Zcy2nR5dChAMo3IrFcu1YtHps1a4aRffsi/7XXyhf/BAcjpcrmOa7iq+M+y37enVarxcOVrkTH\nxMQgNTVVau/Zswf79u3D2LFjAQD5+fm4ceMG+vfv/0DHq7roUjgcsFy9CtylctTNPXtQ/PPP0mJ3\nTVQUAhrBnTS9Xo+fc36FSWWAsfQPyAIC4TAV4UphIEQzHYoNNU+NdIWKux4A0KFDB3z//fdSMn74\n8GGcOnVKahcWFuLLL7+strtmQyTXaqHr1Qu625V/HBYLTOfPQ92uXY3PL0xPBwICpMXC6oiIOucL\ntSbbISEhGDRoEI4cOYKSkhKkpKRg8uTJdToIkacFqFQI6lrzH2Vhs8FUUADbH3+g+NAhAECn1auh\nvL3FckNXsThSrSmGBTrkFxYhumPLRnVL3pcpQkOhqFTuqzLz1auwXL0K86VLUAJoFxkJ3E6eXInj\nvv9r2rQpmlaaRz1w4ED06NFDan/xxRewWq1Ssn3ixAmoVCqnahd1IQsIuOeUPfOVKzCePAnjyZMA\ngObTpqHpuHEPdCx/suKDXQhuNxTFly4AAWo4HA4EtYpFqbUYVrvs9oK9nh7pS5NKf+OGDBmCrpX+\nRu7btw95eXlS+9dff0Vubi4SEhI80jd3uZ/SfwEqFbS318pUJRwOlJ0/D9uNG9JU1ah33oGqRYs6\n9eO+dpA8f/48oqKikJWVhUGDBnlldTyRq8gUCnRas0ZadGm5cqXRJNrAncWRUR3b4tz5SygrK4VW\nyBv1LXl/oevZE9H/+7/liy7z8qCodOXKlXxx3Ge5yvqpvPkSAIwePdpp7u769evRv39/KdnOyclB\ny5Yt0fL23Nf6avnEE2g2aZK0VXdQT88kmN5WbFLAaLNCFqAEAgC5UgVYSiBTCsjspWjb2j1zhGsj\nl8sRXqngwJQpUzB69GipvXPnTqc54T/88AOEEG5ZI+IOFePFwV+uQhNqv3MHt45LT2QBAei0cqW0\n6NJ04QKUzZvXuT+1Jtvz58/Hu+++ixUrVmDDhg3YsmVLvT7pCCGwZMkS5ObmQqVSITU1FW0rTUjf\ntGkTtm3bJn0Ce+ONN6oNEkT1dT+LLhsqbWD5J3ylSoWYLlHQCj1vzfuRqosu3cHV474r+MrmFA1F\n7yp1ix977DGnK52vv/46/v73v0vJdnZ2NqKjo52mJtRVxaLLey28bGjMxt9hlYXDATnkShUC5Eoo\ntCFQOa6jQ0RzhAbf/+7J7qTRaKCpVJXjmWeegaNSycfPPvsMwyrtL/Ddd98hIiLCadGuL3HlHdyq\niy4fRK3J9tmzZ/Hee+8BKC8rc+vWLacdjepq165dsFgs2Lx5M3755RcsW7bMabOEEydOYPny5ejW\nrdsDH4OI7q6ijFrlK4RElbl63HcFlqt0r7i4OKd2YmIiBtyuKiKEwDPPPIMtW7ZIyXZ2djZ69uwJ\nVQ1lAemOMcN647NvjkGY1bDbbZArlLDbrqNZUwd6dmjns+Nvkyp3exctWuRUaz89PR2LFi2S2tu3\nb0f//v3Rxkeqf/naHdxaZ3h/+umnTu36DrjZ2dnSp6PevXvj+PHjTo+fOHEC69evx+OPP44NGzbU\n61hEVF3FIrNxI7rikYFdeSueqnH1uO8KVa9IcY2Be02fPl260llaWorR4ybj9CUz9h06hZs3b2LG\njBmwWq0AypPxnJycBl/Z4kE0DdOgQ0QzhIXq0LJdN3Ts2AmjhvbA9An9MHpYb78Zf9u3b+80DqSm\npkrz/YUQeP3112G326XHP//8cxQXF3u8nxW0gYDNasP5y7/DJgtCcKDNq1PPar2y3bJlSyQlJaF3\nb+egSE5OfqADGgwGp9tQCoUCDodDKmc1fvx4zJw5EzqdDs899xz279+PESNGPNCxiIio7lw97rsC\n78h4z88nLmHYhL8CKJ/C82N2Ll599VWpjFxBQQHmzp0rbcBkMplw+fJlREVFeavLPkMmk0GuDoNa\neQtlN89CqZZB3qoJBveJ93bX6qXX7UoeQHmynZ6ejna3q3mUlJTglVdekbaRF0JIU9HcvSFXhcF9\nIvHvLftR5niofDObyB5enXpW63fd53YpNVfR6XQoLS2V2pUTbQCYPXu2tGhjxIgROHnypM8m21yw\nQ0T3y5/GC1eP+67Asn/eU3UKj1wZiqSkJKktk8nw4osvSmXksrKysGrVKnz11VcAgOLiYpjNZqcF\neY1F0R8mnL9wGSUmwFh8AzflASj+4zoSxvT2mSkX9RUQEIAhQ4ZIbYVCgQ8//FC6M3L27FmsXr0a\n06dPBwAYjUbs27cP49xYjUatViOyfVtAcyfmvFnettZk29VXMmJjY7F3716MHTsWOTk5iI6Olh4z\nGAyYMGECvvnmGwQGBiIzM/O+FuWkpaUhPT3dpf28H1yw03jEx1e/CpGcnFzvmqTeil3yPG+MFw8a\nt7WN+4zbxqViUXXldmUdOnRwKmSg0+mknSwBYMeOHcjMzERaWhoA4ObNm1Cr1dKGKzVpKGPud/89\nChHUHQ5LEUI79oTpZgECQsPw6ns78eHyZzzWD0/SaDQYenvfAKC8DOWaNWukD2OZmZnYuHGjlGxf\nv34dBQUF0hoBV6ktbt2lptj1zPX8SkaPHo0DBw4gMTERALBs2TLs3LkTZWVlmDp1KhYsWIBZs2ZB\nrVZj8ODB9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(2, 4, figsize=(12, 6), sharey=True, sharex=True)\n", "axes = axes.ravel()\n", "for i,c in enumerate(sample_counties):\n", " \n", " # Plot county data\n", " y = srrs_mn.log_radon[srrs_mn.county==c]\n", " x = srrs_mn.floor[srrs_mn.county==c]\n", " axes[i].scatter(x + np.random.randn(len(x))*0.01, y, alpha=0.4)\n", " \n", " # No pooling model\n", " m,b = unpooled_estimates[['floor', c]]\n", " \n", " xvals = np.linspace(-0.2, 1.2)\n", " # Unpooled estimate\n", " axes[i].plot(xvals, m*xvals+b)\n", " # Pooled estimate\n", " axes[i].plot(xvals, m0*xvals+b0, 'r--')\n", " # Partial pooling esimate\n", " axes[i].plot(xvals, mp*xvals+bp[county_lookup[c]], 'k:')\n", " axes[i].set_xticks([0,1])\n", " axes[i].set_xticklabels(['basement', 'floor'])\n", " axes[i].set_ylim(-1, 3)\n", " axes[i].set_title(c)\n", " if not i%2:\n", " axes[i].set_ylabel('log radon level')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Varying slope model\n", "\n", "Alternatively, we can posit a model that allows the counties to vary according to how the location of measurement (basement or floor) influences the radon reading.\n", "\n", "$$y_i = \\alpha + \\beta_{j[i]} x_{i} + \\epsilon_i$$\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "varying_slope = \"\"\"\n", "data {\n", " int J; \n", " int N; \n", " int county[N];\n", " vector[N] x;\n", " vector[N] y;\n", "} \n", "parameters {\n", " real a;\n", " vector[J] b;\n", " real mu_b;\n", " real sigma_b;\n", " real sigma_y;\n", "} \n", "transformed parameters {\n", "\n", " vector[N] y_hat;\n", "\n", " for (i in 1:N)\n", " y_hat[i] <- a + x[i] * b[county[i]];\n", "}\n", "model {\n", " sigma_b ~ uniform(0, 100);\n", " b ~ normal (mu_b, sigma_b);\n", "\n", " a ~ normal (0, 1);\n", "\n", " sigma_y ~ uniform(0, 100);\n", " y ~ normal(y_hat, sigma_y);\n", "}\n", "\"\"\"" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [], "source": [ "varying_slope_data = {'N': len(log_radon),\n", " 'J': len(n_county),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'x': floor_measure,\n", " 'y': log_radon}\n", "\n", "varying_slope_fit = pystan.stan(model_code=varying_slope, data=varying_slope_data, iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "b_sample = pd.DataFrame(varying_slope_fit['b'])" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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pJKMg9SltMy9BBHnvYX/XNYrvz0Zxw4pikJaUAQCyKcgTMpEuSRicM0kYrqRMRETxYLQo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\nWPEeXTafKgjEXZT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the orbital period with horizontal boxes\n", "plt.figure(figsize=(16, 6))\n", "sns.boxplot(data=b_sample, whis=np.inf, color=\"c\")" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YtefSk9tB7P0WQr7Rjnaa3DydsZrBWMWk6t15k9te3G6KHbbGwIq6ecxKI2K1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\ny8hDSgKWayYHGw79sey9O8OIpepHwzc+CU2TjtnQ8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BtweDLn3cdTDE1hd9VhbzUfn48i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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "b = varying_slope_fit['a'].mean()\n", "m = varying_slope_fit['b'].mean(axis=0)\n", "for mi in m:\n", " plt.plot(xvals, mi*xvals + b, 'bo-', alpha=0.4)\n", "plt.xlim(-0.2, 1.2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Varying intercept and slope model\n", "\n", "The most general model allows both the intercept and slope to vary by county:\n", "\n", "$$y_i = \\alpha_{j[i]} + \\beta_{j[i]} x_{i} + \\epsilon_i$$\n" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [], "source": [ "varying_intercept_slope = \"\"\"\n", "data {\n", " int N;\n", " int J;\n", " vector[N] y;\n", " vector[N] x;\n", " int county[N];\n", "}\n", "parameters {\n", " real sigma;\n", " real sigma_a;\n", " real sigma_b;\n", " vector[J] a;\n", " vector[J] b;\n", " real mu_a;\n", " real mu_b;\n", "}\n", "\n", "model {\n", " mu_a ~ normal(0, 100);\n", " mu_b ~ normal(0, 100);\n", "\n", " a ~ normal(mu_a, sigma_a);\n", " b ~ normal(mu_b, sigma_b);\n", " y ~ normal(a[county] + b[county].*x, sigma);\n", "}\n", "\"\"\"" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [], "source": [ "varying_intercept_slope_data = {'N': len(log_radon),\n", " 'J': len(n_county),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'x': floor_measure,\n", " 'y': log_radon}\n", "\n", "varying_intercept_slope_fit = pystan.stan(model_code=varying_intercept_slope, \n", " data=varying_intercept_slope_data, \n", " iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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c0kWzLCnLuVV38dFbdSRZib1+isNT2h2eTgv4DkMYCDBoj2iPwXcFPIeKwe5J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\nUH+ItK0koyCNw9P18Tc93+2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G3X6K00mO4aSodJ9JRqNw0512mi5euBri+WsRWjUX42mB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2TNhWhQock48WHPvHSYkolbCPCijBz4ayh/FC4ODGboDrexwn77ZdmAZw7yzGO6ex\nzmvOhTOeiAjPMClk22k56Lc2v9Pt55zaH6tozO38gNAlp3662qBeifysYFsmHPlYZnnFzOxMxU5y\n191rOfjW/RXeerhGXlDZTb62iR/7gTZ+/h9eCsKeeL7bi/OjZzsz91HTv6JEqXFjq/bdU6yUV/ad\n04jMXEmzsS3aYZo1Wys2VQLXixDB+KKfsqR/fTClonW6zLBOSsyWLBQKeGGZ0H7ebsOVsBR2j4t1\nzuCAqGAMoWlIV22iXXOw23F1LOaj8aXP4zA4IcHJKMVaIC6OxUK93/Ww03Se6+dAkdCOhxcBK4HL\n0fJslePhMNEkqiQv4clFp1e3YUtqliELZMdmFxsl7NAA7qkny42Yy3cN7LRc9JoOru162G3z79Ws\n2brDPxunuD+IcT6lZ3i7UAcivqwqEs8c8fvWfVuvCPrtDa99LqCQs0mq2fBpxtCIwGXO8nRZ4HyW\nkg2ellhJd53lBIukWYmiEiiOQwLaQZf87xv7AQ47LpKcl4JYMrXLiqP82TLXYrys4J+rRIos2N6F\n5xxAO9xozpH0ZJltOAyVdMwxlfhRUmjYjy10NtME0qJCnBDokuUl7p4mWCc53Q0gG9x3DXz/zTr+\nyT+69dw+Tx/0XBbnF/y8X1iAUt0q61Y9+O4o1lle4nxrD7eMcqwT2raY0UtVq2XyFqwTuD5GP+/L\netKs3LKe8PJHP3smEXtEXNY8C42ajXbNxm7b0ZasJCtlVEu29SoqYNsGaj7H4P2Wq4t1t+k8dwX2\ndJnrRKZIF2pTg3B6jedbqNO8xJkIt0aLbZW5DdcyMFnmuHsWSwpVqUNOFD40cLmjNuQ1WSY/t+uE\nOFJl91lGpYi5+N/vNJny1BN6lircvmtitiJB6+EguiC6VF9939kU6rwAHOmom4GFfpsXmt2tQh2n\nBc4mmaZ6bWct95oObJtJW0fC4l5L/vNaxFWLiBjaUix8hIqYQgDj56BTt+E5BhzHhGsT/hK4FhZR\njoeDRMeyJoIR9T0TPdkbd+rcW6t1Xz2wUFbAbKkSxdidq4ljKt7x+TrHOpaLRE4lPn3UZDX8y29M\nEKfM21Zdte+a2G25+Kf/+RvP7TP0Qc9lcX7JTpyWGmeo/IHqKKRjt0H043eDbUkV6pMRoQ5JRrg9\n5CHgCMIP4M6+GVpSrNlhP+/i8N10VOSlCuwYzDZAh9mSl8BKfKadBnGuXREvOrYJQ5KczqcpFutC\nZ10rcVnNt3HQc7Df8bTg8XmNoquqkkLNgqH2k65tCgjHQ7fxfP3ccVrgRAq1UpmrnXjomZguM7xz\nGmurW1VVWl1MG5MJT0RHjiBE1f9lDGKFVVQgkSKf5rQrdeo29jqu/A42UZKdhqO93Q+HMR4Mkgsd\nNYVZluSKE9lp21KoQxt7sqPeVsfnBYNOziYpzqdbgjJTdfY2TACnE6Z3zSUEY7LItBo8kb02d/Ic\n69s21e2hZ8J1TdRcpmZd3fFw+zBEp2njdJTizkmEh8MEMwHGJJmyv4mjoGWjETj6ObfTojZF5a8r\ncplqYtKMe/REErBU526bBv7VN6e0bEmVsy35rNftS0HY05zL4vz+RxF6lGVgW0ThO7Rd9BqfDH/5\neR81+j4dpxjKDb/Q+y92JElWvYsRrsbg3YZ9qQh/n5OLgGkwS3E+YQrVQqEdJVSiArGczZqFhlDI\nunVHe1En84yCLvG8r1N6Z2uehUZg40qfhXOn5eqc8Q97FELzWDpqhXX0HVMHWGwrpJ/HWcVEYR6P\nNjtxxzIo8HJMrONCF69VTECPZRswYEi3VmkFOIM6DKCiEjtOCwY4rAsRVVW6Kw192hF3ZIXQaWyK\ntW0ZulDfP6O1arEudLCD6xgIXIaAxDk79EZIitdeh1CYbTQpIyNznMn4WzUCBnhZ22058D0CS85F\n37BOCgwmqeytubPOcnanWU6fsQongbyuZmij33bw6es1/OhnW+i3PAznGd45iXDvjCSwKGGhTvNS\nMJuW7KhthP9/e+8aI9lZn/s+675W3buqL9M9d489Nga2A2afCCJvvEUcIYXsXLCDdywTiShIOYkV\nbfIFdHaAREJOIiXn6OCgneQDCI4OjpzkRGxLuWxiQEeEJN4+DGADNrTn3veq6rqu+1rnw/99V1V1\n93T39PRMV0//f9II3DUzvXp1TT/rfd/n/zymlq2q5dGK3OGpixnrfkAmyU4/EmKd4usXmvSgL65D\nV+n/HJsw8d/+y1v27b2yV1ic7zJkQ4wc3RqO03NG3sSHW6i2EmqAQl/yYqzF9amLdjgjPGdRow+t\nrNkRvh1kyKHkpSurNObT7tERA63MFNgWtQKVcno2wlIrUUyiG1AL0PU1GqHrujG8IBZjNhrKOR0n\np23M1axsBXSrSOMTraiDbOXniJXabNVEpWDc8ucZptUjx/difbCCt4V72tCVrCe679O5q6ooUJQU\n8VAbkyYMYqqiwBHVjVIw1jpkepIPAfSQQQ5limnVkXfo/st59WJOw3qXzsYvLbuUaOjGQIqse9kx\naUXtBeQwL+Y1VPJ0Pj0rVtTDoUldN8pW1DJIBqB/czMT9LAVhFThWG+H6HnkrK636XyY2rfIaNf1\nyaToZe5wui5N7BTcO+vg4QcKOH+igHJOx2KTVtVXVzxRy0ojVUkij7ooXrToCLEWGfNybr/vx9mq\nutGmApoXvrGMVi+meWnQw4sl0s84hGQXsDjfGh03IrFujeZjAzQPKFfV1JBzOLeAbyTUpZyO6QkD\nBVvPjgOa3dEEN9tQszPravHuObffb2KxilprkXv4+hrlWHfFqlB2G5fzOipFaggqOjqtboo6DF2h\nmfd1ykVu9WVmeEJhH7aKatHEqRkLJyYHOcq3gnRgLzbIgS2/7zlTw2yNzl5pnGx/SNMUjc5gNEv+\nW5OiqQJodiOs98iE5IcJbHEO2vcjrIsHmL5HPcy2qWblFapCM+s9n2aZKfsaNMalKsLMJMyTwrFd\nEVWS5byOKEozgWt2Q3RF3oCmqVlWtwLQzhPSbOv7xKRFne4bhNoPE6yKFfVae2DOsnQVUxXa/kZK\nJRmLjSArwAgjGeCiIO9oiKIUqy3yl8gZ/VAkg0n39ERRx1zNwn1zOZw/6aBWNLGyHuDyiodrq8KY\nF5Poa6qS5XJPVsjzIFMaJ8VWuGmo6PQj/OHzl3B5xUffizL3fSGn49ycg48/eWbf3hd7hcX5CLH7\n9DI9S/U5bGwn1HI1kKbIyjxkRrjE0MgRXxUJbqUcO8K3wgsSrLVo1OnNRS8b06KCh1Ska5EHIp/T\noKu0wp4S55YpFDQ6NLp0dcUX57Qx4iTJBGl6wsSpaRunpuxsxGivxAkFUCw2fKyIUSmAhFOuFPdz\nLEx+PlnOIMWrnNMxUdCRAiPBG7oYLbJMDV4Q4/qanxm9/DCBbWowNQrKoAdIGhOivIRIFEhQq5Rj\naln5hZxVp1hXOreWHdg/vu6K2N0YKUjkTV0RPdlk/gujhIQ6r+PUtIXZqj3Scw3I+WwylK00g2y3\nTobJTJXJo9DqRZhf6OPqGp2NAzQhMFezMVs1ECfAYiPAct3D/JKLtVYIP0wRJ7SDYOiDh5BqwcCJ\naQunZ2xMFHX0vYSawer0UBRGdGZvGxocW0GtaGKipAtfio5a0cA3vtvEhfkOglCMYKk05/zuByt4\n+rHZfXsv7BUW5yOMTC+TZzMbayLLOT174jyM6WWBSEzaKNSyc/hY1ULe1oYywkmwh0120hEuHafs\nCN9MKjKql5s+Li669MO3L+oBYwqvyNsqSjmqBNQ1cvNOlk2xDavDD2mVe3XVx7VVD81uiL6XIEmp\nLrFg08PVqWkbp6YtVAp7d2XLMBy5opPv+aJDn2O/y1pk9/VCnVzJ0lVcE7P7cZJidX3wkOiYGmYm\nDJRyGvwwxUI9wLVV2m3oiXleGbtJTVqqCBBJsNamTmmADE4k+Kown6nZsU8pr6NW1KHpClw/xtUV\nX4xNxUgTMltKoZar/CBKUchpKDkGTk1bODFlY2bCHIl7lZGycvt7eLqEzrZNFHIamp0IP7jcw6Ul\nL9thmCgauP94DlMTVGixuh7Q+2nVQ6MTo+tGWYsVRHqalsWs0oPgzIQBx9IRx4nIn6fo4DAiL0re\n1igMpWhgfqGPN6576IoyI8tSMVMx8ehDE/hP75nat+//XmFxZjJG0svEeMLG9DLpBD9sIrVboQaE\nI172Wm8YX5OOcHlmzY7wzYQRraovLlEQxWoroJnYJAVSEuqcOFKxLMozLguDz5TYhnUD2ja9suLh\n2qqHekdkT4MemIqOhrlJC6embZw+ZqOc29s5chSnWFmnbOq1VphF68qdluH3xX4QhAkWG/T5GuLc\nlnLFaSs6jOjBQW7BFx0dczUTxyZMBBEliF1d8bOVtXyQNHWqC807KtIEcP2EHOBBjDgeJGXlcxrS\nhFbdsvs6J7wClkElGyvNAMtCqJMkha6rMHUFlk7z20FI3ePygev0jI1T0zZmJjbXgfa8OJunbnYG\n4045iwpxygUNy40AP7zax0Ldz1qppism7juRw0zFBJQUl5Z8vHGtj0YnQBCm2fspjgE/osz4KKF5\nZ0NTYFsabBEhahsaUtE2poAePMIoxaUld1BUlIou6LyOdz9Yxkd/9vi+fc/3Coszc0OGg+o3ppdl\nNYSHML3sZoRa/v7mUFWmfBqXFB2d5qzFCNfdUhO6X3TdCJdXPLy54OLqio+uFyEFvb9skyoRiw79\nYFQUak2aLNOs9FTFgG1qWavT5WUX11Z91NthlrGsiiS9uRptc545ZiNv3/zKd+PYXva+yOuYE67v\n/QxZcf3BaFaWK64qmC7TuSithAfXUS0YmK3RFryuKVjvydx6Fwt1ChMJI5mlrcIxFEBVEEYJ/EAm\ndCXQVRV5m6I4DVVFz0+ANBUtVeTCz1kkxM1OlIUhJbHYWjYUOAbFk4Zhgn5ArVmlnIbT0zbOHHNw\nrGpuMpwGIRkEV9bJZCiPFgyNksYcW8VyI8D8god14Q0p5jTUiiZOTluYqZiI0xRvLri4uORlUau2\nqQCKgjBM4IUJXC+BG4hoT1H3aRrU8pVCEaElwBvX3Ow9BFBWt66qODlt43//X9kQtiMszuPDcHpZ\nox1myULAIL2sViLBPixntVKoFxujAQw3Empg8NAiz6zXu4MyE0A6wo1MsNkRPiCOUyw1ffzouovL\nSx5WWkE2KqQCKOV15B1akcnZ26KjY7JEBp+q2LHxghgLaz4uDZU8RLEci1FQLeo4PmnhzIyNMzMO\n7JsUVfm+WKjT+0I+lE4UjGxFvZ8PYR03wsIarahlCpqpqzQipSroenHWia0qCqbKJNQzFcrRlrte\n19Y8XFrysFj30RFtcGlKRwuapmbz05qmIBTpZAWH2rdMU0UYpej7dO4vqzNzNn2drV6UeQOimHwF\nlq4gZ6sUyymE2jKo5/rUFJXazFatTQ818VCc6EozyLb05Q6dokC4q2kFHycpLQIKOso5HeU89VEv\n1n00u7Tdr6pkMksSMS8eplDUFEGQZnnzcTLY4v7xgot4cIIFTbjFy3kNX/z42/bte7tXWJyZPTPc\nKrNVellWmHBIcrH3ItQAnd23elG2Dc6O8N3T7Uf40fU+3lyi7Wu5kkkSaoMq5DTkLB15WwUUMhlN\niOSoqfKgi9oPE1xb8XBx2cP1VW8kdlMRdZQnpiycmXFwctq6qTHCICSz0WLdR2Noa7ZapLGjjQap\nW2W9G2KhTp9PmqtoDFKHAgUtkeoGkJHsWNXEbM0aSUeLkxSNdojLyx4ur8hZ4Th7LRFHDFFCIqvS\n7YVlqijaWuYvcUWKmWNqKNiiPlPkXq/3YngBOZ2lUOdtLetMdn2q3ywK1/f549T3vNXuQ2soTnQk\nslgBogToe3GWk63rKioFPXOzq6CjqERsXSOl+kcoKbwgERnx9DWrKrnSvTDG1y80aYxLfC5VIfd7\n3tbx5f+NxXlHWJwPD9lZrZiz3pheJs+rKYJvvNPL9irUwCB5a3h1PeoIV6nMgx3hI8RxgisrHq2q\nl71sljYFjeiU8yTStqlB1+l+yS7qqfIguQygUpVLKx4uL9HY19qQEUtVFUyVTJycom3wk9MWTGN3\nYu0FCZablPMtz4xlnOds1do0G3wryPKLRTGaFQ0Z18p5OkdtdqJspW3pKmZrFuZqm2e5Y3G2Pi9m\nhZea1OqUpClcT0ZvpsLlTQ1Qhq4gJ2auZcRlz6cVaMHW4JgaIOaW230agUrTFIamwjJJqMMwIYH3\nUygiv/34pIX7T+RxYsraMhjJ9eU5Nfk+kpRmpPteIkbvlOy+6xoZuVRFgetRSEmcAIWcCsegrHjL\nVKk0xI1E81iEMEzxP/6/OgI5rq3QgwAUoJw38H994q378j28FVicmdvGcHpZvR1lWcjAaHrZuNdD\n3opQS3brCK8W776q0L3SaIe0ql50R+aGdU1BwaE4UVMXkZiqSK4Ss71yvlfuULh+jMvLnugV99Ho\nhFmLlK7R9vHJSQunjzk4PmntaiUs4zwX6z7NLoO2ZWslIxvbM/bJLCgd5gt1Oq+VxyiVPIWPJCmN\nZsl0tLytYa5mYa629XszihJcXfPw5iLNCq+uB4hiOrPtezGllRkUu1ktGHAsFbpGK+RYiHAY0/ua\nOp9p6R2ECW0hR6lIJdOE8YzOqPt+DNdLAYVateZqFs6fyOH0jLPldYYRnbsvN+nrDqIEHTcW8bJk\nznQsFQVHh6bQSj8Iacvc9WPkbA3lvI57jtmYqVoIxFRAvR3gi/+4KEyv9OChaYChKjg+aeGzzzyw\nL9+3W4HFmbljyPQy2WW9Ob1MBtyPb3rZ8FmkfKoHSKhna7TFuZuYVC+I0ehEOzrC5TnbUXeE+2GC\ni4su5hdcXFklM1C20jNoVZ2zNCiqkmWty6x5irccHfnpuTEuLdMK/foaiav8cWfqKqbKBk5M2zgj\n+n93ej9Kc9di3c+8GNnZcNXC9IS5b6OIcpZ/+DxcRmo65qBHOputzus4XrO2PScPggTzSy4uL7m4\nuupnKVp9EXVpicKKUk7DdMWEZSqQeUbS7eyHVIZh6SpUlXwB0pilKtTZnrdpTjtOILabqezDsSiZ\n6/yJHO6Zy93w+KjZJRPccjOgushOiPVODMtbev1KAAAgAElEQVRUUMqTz6BaMBBESXbcVm/TuFwx\np+PkpIW33VPA7ISJz/zfl/DG1T66fowkTkWTl477T+Y4hGQ3sDjfvXRdOWMdbeprlellVRE3Oo7p\nZUFIPyQXGxuEOq9nZ5G7zTMPQjLbSUf4sDMeGDjCad76aDvC4zjFcjPAjxf6uLRE299+mIjoSwre\nKOWE81unukCA7uFwacRwCUerJ85nRZZzZ8iRL2Nv5Zn1ZGX7nPqeF2cVl/KhS1MUTFVMzNZMTJfN\nfdsZ8YIESw3K+Jard01RUC1R3rkfJNk5OW2/G5ir7byqb/cjvLng4sqKiysrHtZatPPl+XSfTUNB\nMUeRmVMlA1GSIoqAFGQ4S1Og7ycIQiqZ8KIErhcjTiim0zHpe1TMa0AKUaBBOeKmoWK2auG+4w7u\nO+6geIMxuU6fcr+X6j4ur3hoiHE726T88ftP5jBZ0tHsxtnuS8eNoCrU5rfU8DC/6KHv03VRbaqO\n//B2DiHZFSzORwN5TitX1RtNVeOeXjYs1MPu3r0INUDzt+vsCN8R2XV8ZcXD/HUXq60AXeFSztsa\nbFPLgjiSOIUpHmo0VUFNtBpNVcyR+0cd2CTWV1YoM5vSyyimNGfRkczJKQsnp+xtPRRdN8pW1DIN\nTDZZzdWoCnK/mrrkQ8HC2uBzUa0seRr6XpKt6jWFSjrmahamytsHuiQJzVdfXPTw5qKLS8se1jsR\n/CgWmdgKSg6VcMxMmHBMFX1R2BGLwotYbIHL9C55P+UZ90RBR6WgQwEobEW2emkKZiZIqO8/mUM5\nv7VQe2Iu/s1FFz++3kejSzshpq7izDEHbz2Tw0TBwNVVD9+/3MNiPcD8gou1dgCAHuJsURn57rdW\n8PRPszjvCIvz0WQ0vSwaLVfHIL1MVseNU3rZfgs1QA7b9q4c4STYR9UR3nWp6/jNRRfX13zaOg1i\nWCalY+UsCkBBSitquYLNmRqtAssGaqXRLeg4TlHvUPjHlRUPy+sBiUuWfqZhoqjj5JRN26o3cOR3\n+hG5sBt+5jnQVQUzE+S2niztXxd1W5ZxDPVeWzrlVCsAOqKPGyCD4myVhHpiFzWb1HHt443rffzw\nch+LjYBStkDzw458Lw7lH8gAEF+EhwQRZbX7YuvbD1MYGq2oJ4rkG9BUBZ1+jLY4wlDFA8W9cw4e\nOJVDtWhueX1xnGKx4eG1S3386Ho/u9d5WxN/Ng/HUvF//PVV0RdPf3+lYOBY1cRc1cIzv3hyX74P\ntwKLM3MoiOW4knCCD6eXyYQpeV49Tull2wn1XNXCzB6EGhjsNDQ6FLu6sYHM0NSh9q2j6QiX5QzX\nVn1cXh6UbQB0/mibCgq2RvO/SQpTI2OZDDWRZ9Ubqy2DMEG9QwUeV1Y80cAkZn81OlOtFEisZyZM\nVEsGio42cv9bvQiLG8TTEKvE2Zo5MhZ1K8idBVnGIQ1jOVHhCdC/q+Ho0LkaCfVus8a7boTLSy6+\ne7EnijUiRFGCVKEyibxFglt0dDEzrWRZ4LSVDdo1E+fcQUjtVTlLQ7lgYHaCzvw7bkSFHyntYNSK\nOs7N5fDg6RymKtaW15YkCeYXPbx2sYsrKx68kMoxJoo6vnexi3YvRhBSuphjqrBNBaemHXz8P5+5\n5Xt/q7A4M4eSQXoZrSbXu4P5U/nDVdZjjkt62Y2EujK0or6VBCppuGt2qWKwH4w6wicKg6rMo+YI\np3KGAMuNQJxPhqLCMkHe1lDIUcyjaVDfcZoChjCWWbqKWtnAlMgC3+h/kPf92pqPq6uUbtUTYz9k\ngiLH8Ikp2kKuFslJLt+T690Qi2JFLUXS1FUcEyvq6i5Ws7uBtqepjGO5OZwpTtcoDVcbo0PnalvP\nJm95n5MUi3UfP7jSww+u9LDcJD9AFCewdBX5nIa8RcEmOUuDY6qQG2JxnJLbOqCktvVehCAkw5ht\nUu/0saqJoqNlWezyAb1SMHDPrIMHT+UwN2lveW2uH+P1qz384EofjXaIf/lhGz03gqYqUFXa0lYA\n3Hsih//61Nlbu9n7AIszc1cQxakY2Toc6WW3W6gB4QhvR2h0t3aEU1Y6nVlPFPR9G/sZd+RqMiuj\nWA9om9eNYeiUQS3nezVFQSxmdxVxe8o5XcxWm6gURt9Lw81v19Z8XF/z0HFjOm+NUuRMFXmHiifm\nqtRjXS0aKBd0qApVSsq5ZrkTYulqFjQyUdgfoY7jFMsiU3w4sKWS02Gaqnj4jUaiQ+cm6X15M36P\nZifE61d7eOMazVf3AzKJKUqKgkNz65pGTnDKwVaRCNOYF1IMZ7MTYqUZZKtsQwNKeTK2lfM6kiRB\nvRNnDxsFR8e5WRsPnMrj1LS96X7FSYrlRoA/fuEyFhqU+w6kKDk6HFvllfNuYXFm9oJML5NO8GFh\n0lVFBKLQr4NOL7sTQi0/jwxGaXRCtDc4wkuizvCoOcK7LvVML4sRna4bodOPESWpaHDSoAHQNLof\niXAUA/ReqpWMrGFrU9Rr1oMdYqnhYaEeoudF6PkxwpD+fsqz1nBswqJ7X9QxkdfR6sck1M3BdrQt\nnMyzWwSN7BU6Q6YHlfpQRGglr8PQFPhRMjLHPVUmob5Z13nPizC/QIata2sB1ruhEGoKE5FHDABg\nGfQQY6gAFAWKQqNX611yaK936MFB1xTaip80MVE0YGhAozNor8pZGs4cs3H/yTzuOeaMXO//+f9c\nxep6gHqbyjTKearGrBYNPnPeDSzOzH7gh5ReVm/RnHXPG2z5GpqaOcHpfPDg0ssGQk3l87dLqAHa\nbWiKVXWjE6K1wRGetzXqtj5CjnB5Tk2Vh+T87rgx/CCBrtP8uW1S85PMtKbcavqhn7c1UdhhbmlU\nDCN6H661wuxz9LwYPY/mgQsOxWQWHC1bVVeKOtIkxWorwnLTz7adHVPDrFhRl/P78571ghiLdRLq\n1lAZRzmvQ1MVeH6MzlAH9VbRobuh51Fn9Y+u97FU99HqU3KXqipQFTpSMESmaJoia5hSFQW6rmSJ\nZ2utAGudCEGYQlOoWWq6TDnspqGKcgy6X7ah4dSMhftP5HDueA5//291fOsHLay1QoRhCsOg/ul3\nv6XMlZG7gcWZuR14QZytqqURRWLpatZjfZDpZTLTeekOCDUwMN01RYrZ+hF3hGfn1E1qUup7tPXd\n8ymQOWdTwUOSUC6zAiAW4ztQBs1tUxVq2CptIaBeEGOtRe/BlSZFgkqxTpLByjovah0rBSqF6Hsk\n8jLSM2dpmK1SdOdujVw7IcfArq8N3OWGpqKU16CAVrLyjHwQHWqhUri5zy9HwC4teVhqDHYuVFFE\nIdOv5XstSegMOmepUBQFlqmg2Y5wvUHhKT0vgaKQwa6c0zE9oSPv6HD9JNv6NnUVbhDjjWsuADqO\nUFUap/rgf5jB+95R3Yc7eGuwODMMRtPLGu3RLGyZXia3wvdTEHfLnRZqYHB+2mRH+Mg5tVxRuz6N\nI6Wp6JjOaTB0BUFIUZDyxEDmgNsGxYROlmgLfKsM7o4b0e5Omx4IOi7N/PbF3G/e1pB3yFRVcDQo\nKhCEVPAgw1YKtpZVS+5Xhv16V7rL/SFBVlDI6UBKo1m7jQ7dDjkKd33Nz2bWe15MPcyaglREhCaU\nAIokpU7nvK3BMlRoKj1UXV2jWtGuSyNvqqqg4JBrvJLXEcUpXr/WE+9pUJ+zrmC6YuDh+7nPeVew\nODMHAaWXRZnJLBgSpZylZefVB5Fe5out7zsp1BJ2hBPD59TNbog4lsEaJBqmqcAxVcQJkCY0/5uI\nBqjMWJbXMwf4VhMFsu2s3pbNbyF6PomV59EnkrnSlk7GtSgGwiiFY6owDAVFR8dszcTsLvLfd0Oa\npmh05GjWYIs9b6mwLQ1JQmlfG6NDZ2u7yysfpuNGWKzT+7zVozG4vp/QtrdO7VL9gFzx8vNFcYok\nUZC3VRi6gjRJ0RAPFnKLO00VOLaCxYaPMKRnKAXICjVOTnG29q5gcWYOmuH0soYo8tiYXlYtkhO8\nWrqz6WXbCnXNwrGJ2yfUAI2nNDtH2xE+fE69JjKt/SCBHyVQQWYmx1KhKCScqtieTTEQBENTUCuZ\nWbzoVt+zKE6polWIdbsfwvUT9LwYfpCKz0NFEH6YwPOpdSpnacjZWtYBvZcQnK2IkxRrooxjpTko\n4yg4GixdRRTTzsvG6NBjVeumQ4M2Brj4QQLXT6CqCjSVVtWu+FgY0fl9CmSGMxrZStDtxyImN8K1\nVR/DAqco9PfkLQ1f/q9cGbkjLM7MuEHpZTHq7WDH9LI7KUhSqDf2Dk+I5KPbLdTA7hzhchu8WhzP\nzPRbgc6pB2avIEqQJoAbxNBVRbQfKdCFmSyJaWxIdg3LnYaCrWWr6mpx61AdP0wyg+NaK0Tfj+AF\niQhEQXbumqQpui6FezgWnV/P1kzcM+tgdhelHrshEnnnC/XRes6So0HXVARRskV86c7RoVvR6kVY\nEtnl/SBGmtC90HUFqqJAUVKEEXVAB1GMIASCOEGapPBCaeAD/sf/bGAozh8K6J7lbA0vfPLtt3xP\nbpXttG+8C3cZ5oBQVQo5qRR0nJuTWcx0JlsX6WWtfoSLS+5Qehmtqqu3Mb3MMlScmrZxatqGHyZY\natCKuiHiPn9wpZcJ9X79UN6IaaiYmbAwM0GJTVs5wtv9CJeW6fdLo5Mc4dqPFd1BomkUxzkzYW4+\npxbiFEVpFv2paANRDqMUaUSHqY0ObeNeXHahKQomiqJdqzKYJrAMFXOTFuYm6V73vIG5jI5iqFGq\n58UoODoSk2IzW90QC3UP35nvkpGsRpGY98w6e3540zWqWjw+aSEIkyxPnDqvY9pFyenQNMD1EyoG\nafiD6NDJ3c9wl/M6ynkd95/MY70rhHooaQ2pgqJDuzZhlCBKUgRhir4XI0lSSiGLUmgqsp5qAGTi\nU8mFPu7wyplh9kAck1jLc0IZOQgM5kdrZeqyLhf0fSs+uBEbhXrjivp2CfVWbHSEN4ccx8Cg53ui\nYKBa0lGw7x5H+MZzaoDOo1WxLQvQzLGi0Go3jEjA03Sw5QrQPZqq0Kq6doNjlDRN0erJ3R16OIrT\nNNsOjpM0M7WFMW2Ja6qCYxMmzs46uPe4g8mSecsGv75Ps9oLQw1dusgjVxTRXBXtPTp0mPVumD0U\nSNOaIbq/dY0eitbFTk4Qpnj+pSW03WHPBP3v8ZqJ//ZfHrylr3s/4G1thrnNyLNCuaLZnF6mZ6Nb\nt9vxPE5CDYw6wuVW+LD5ztTVEZNZKafdFY7wrc6pARIuQ1ehqinCMEUgvA1hlEAR59dxLAxR6iBX\nfqpC59Xl/Narz0HcLZ1Zt0SoSBAm6AlHdLtPjmv5EFDO6Tg5bePsnI2ZipXNOu+V7Ny47mdGQkNT\nkLM1pCmypiqAfBzHJ8lxfrOr+TSl4JdF8T4fjkSdLBmwTQVhnOLP/vt1LNQ9+CHNUmsaRZnedyKP\n3/vVe/b8de4XLM4Mc4fZbXpZtWRsKl3YT7YT6tmqiWN3WKglXTfKtsEbnWhkBl1XFVREMIrMqD7s\njvCtzqkBenDLW6oo5kjQdcnglaYk3JqqQD7GDIxlqogWJWPZjb5/QZRkJTKyuAMA+l6ERjtCz6O2\nKFWhLfeCQ7WOJ6dsTE9QwMqtuPGbnTBrzQqGYkptU0Wapuh6ySA6tGhgrnbz0aHAYARuq0jUr3+n\ngYtLHkjmyAegAPh35wr42OOn9/R17Sd85swwdxhTHz2XlS1HMhd8pRVgpRUAGMwS10oGauX9TS+z\nDBWnZ2ycnrHhBUOu7w6NSn3/Sg9VaSa7g0JdcHQUHFq1AUOO8A4dE6y1A9HDOzgmkAazyiF0hG93\nTk3brjGtkHMa9VGnKXrCpa2BjgrkyjqMYiys0ZkuQCvQSSHU1aKRrXxNXcWxqoVjVXoPun6crarr\nBZpnD0SqXqsbod2jX5eXvezMt5TXURsy903cRHXrhPj9bzmVot4JM/GUu0qOSTPjcZJm3/fvX775\n6FBFUURojoEHT9MY2GKDPleUkLu9Lx5MTEPBZGn/ZsNvJ+N/hQxzF2DKvGTxg3I4vazRDrG8HmB5\nncRIppfJGev9Si+zzRsLdeMAhRqQ40FaZnzKHOFiDr3ZpVGu+UUy4JVymkgyoxGuw+QIHxaTB07l\ns3NqmR6GPv2+ggj60FQFfhBTnrTYEg7DFGpKRqdGm856Ly650MSujFxVD4uQY2k4MaXhxBQ9EHX6\nEQm1cIP3/Vh4BcjQ13XpLDlnaygXdBQdDZpK6WHy+ieK+o4rXVVVMFU2MVU28dbTKVZaARbWqIzD\nDeQMtQZdA4Iozf4tDEeHTpaMXe0uKYqS/bt58FSKy8suFACuoyFNUkxPUI93KTf+pkQWZ4Y5AGxT\nw/FJDceFGPX9ONuCbLTDzOkKDFKn9jO9bCuhXmz4tII5YKEGNjvCQ1HM0BBjbS3hlpeO8IKtZbGj\nE0X9UDnC5S7CPbPOpnPqrkfvAUvUS9qmiihJ0exE2Qo0UYAwpHngMEqx1KDkLYBWp1KoayVjZMeh\nmNNRzOk4e8zJphHWWvL9F2C9R+fW7T4lmBka/Zl2X0WzG+LiEomlHJ3bzYOSpinZQ2oYJYPRrDaZ\n5xQoyFkaNIWOZK6t+bi25g+Vgew+OlRVFZw/kUfO0rCyHsD1k2wW/PgNKifHCT5zZpgxZFfpZUU6\ns97PZikSajonbIj2IgBDQm2NRZOVdIQ3OuRS3skRfpBFJ3tlu3PqyRJtGasKMlGVrwdRAip6oi1j\nWYWpgIyJtAVuopy/sdchjBI0RdPW1VUP19d8tHsR/d2KAssgE1+5QK1WQ6PEKNiDlXW1pO/qwc4L\nEiw1fCzU/UE7FmgeWVFoNEt+f/O2liWS7bSrtFD3cWG+s+njP3GuiLmateN13W7YEMYwh5hUBExI\nJ/jG9LKCPYgarRa3znPeC4dFqAGaQ++4cSbWd5sjXLqTlzfMU0vBna7QjkrPpznoddHTnG4Y10pT\naoMChLO5TBMEk2Vz2++lFySot0NcXnbx5qKL1VaIUFZcmiqmyiZqZQN5S0XXS0YCe3KWlq2sdzPn\n3vPkaJaffZ26ClgGhZl7QQL59q/kdcztEB26UPcxv+Ci58XI2xrOzTljIcwAizPD3FXI+Va5qm50\nRtPLSjky8dTK+5dedpiEWtJ1o2zOekdH+B2YRd9PNp1TCwq2hhnhtI6TBGstWv3KsaYopoNqRcHI\nqhqg942swpwobD/u1+mHuLTk4cfXXVxZ9eCLUSZNUzAnjG+lPLV5tfrRyMOkY1I5hTSabWfOavWi\nTKiH55pNXUWSpvCCdCQ69PikhRlxrnwYYHFmmLuY4fIEmV4mM5BvR3rZdkI9WzMxMzF+Qg1sdoR3\nh/q+D7Mj/Ebz1JauYloIpW2q5GkQ5q84M5ZRIAoUIE1SGGL1qakKakUDUxVaVW+3fRzHCa6seHjj\nuotLSy5lbacpdI0egE5NWaiVDeiqgiAip/rwroY0QMoHpa1qStOUztnlaFYYD4Ta0FUkSZqJ98bo\n0KVmgPkFF103RsHhlfNNweLMMPtHnNAWqHSCr2+RXiYDUW51xZgJdX10BVct0hz1uAo1sNkRLgsc\nABxaR/hO59QzEyZqJQM9L8Zqi8RazuAnCVUzqiqQpNRfLR/kcpYmZqvpz99oZZokKVZbId641sPF\nRQ+tHu1YGLqaPSQer1nZWbIXUHjPcH1rdgQhjmk25gAkCX2NC3Ufy81g5GFE1xQEUZKt1PtejPVu\nhEpBmATFX8NnzruExZlhbh8y+1qOzAwXVVCmsyjxEIEfez2LlaaepcbhE2pggyO8M/pQA4w6wqtF\n/UA6v2+Gnc6pZyZMTE+Y0FRgrRVmYi1XpWGYZv3RcZLSyJRCD3jDxrIbhegkSYp6O8SVFQ9vLrlo\ndWk8CwptoZfzGiYK5CSX59A9L950BGFoCiYKtAVe25CwFw+XcbTD7PtlGSpURcFrl7oiBCgGUuD4\nJAWdnJiy8cjbK7ft3u+WWxLnNE3x6U9/Gq+//jpM08RnPvMZnDx5Mnv9C1/4Av7qr/4K1WoVAPD7\nv//7OHPmzL5dIMMw+0sYJRSjKUa3NqaXTRRpVX0r6WWHXaiBUUd4ox1hvTvqCJdnp1Ksxz3YYqdz\n6ukKObjb/cGqer1LqXKp6JFWFTKVAYAuEsssXc1W1ZPlrQ2JVD1JI4JXVzy0ezG6XowwTpC3NZTz\nOmxTRdEhAS44FPfZ7tMOUN/fulN82C8QhAmWhFDL45aXf9hGqxeJNioFtTL93lPTNp78j8du383e\nJbeUEPbVr34VQRDg+eefx3e+8x08++yz+NznPpe9/tprr+GP/uiP8OCDBx8izjDMzhi6mqVVAZvT\ny1ZbQTYna2iDqNFaydh1WYFtqjhzzMGZYw68IBYRokF23vva5d7YC7UM9KgWDWBu1BHeaFMwyoIw\nKwGbt2OLzng5wrebp55fdDG/6I6cU99zzEGc0up3rRVidT3Itp+jOBW91UA3jOEFCa6L+1DO6Zgs\nUw54RRjLNHWQkPb2MwWstgIsNgKsNH10Pcr+bnUj1DVKh5Mr30qe8rcLjoYkTtEUISlr4sESoN2f\ncmHwkPTvz5cQRBRb+28/aMMLEnhhgjQFkjRFOa+j3Y9veJ/GhR3/pb3yyit45JFHAAAPPfQQXn31\n1ZHXX3vtNfzZn/0ZVldX8eijj+KjH/3o7blShmFuC5vTyyiTud6hrfBbTS+zTW2XQm1l5qVxRFWV\nLNby7DEHwMARLke4hu9V5ggvDWWEj4lYW4aKE1M2TkzZm86pr656uLrqjZxT338ih7efLaDjRlhb\npy3wZidEnKZU4BEl0BIylq2J4pf5RboHNTGqNVWh7WtNU7JY0SguYGWdijLWWiGiOEXfjxGGMXRN\nvBfFKl+a1E5MWSjlcgijNLv38hdA2+6lnJYZ+9Zaoei8HhTUzNbMg7z9u2JHce52uygWi4M/oOtI\nkgSqOIz42Z/9WTz11FMoFAr4zd/8TXzjG9/Ae9/73tt3xQzD3FZsc7RDWKaXSTf4xvSy2pBY73QO\nu7NQA7WiIX54m2NvwpKr0VNDGeEDsb5RRjgJ9kRh9znVt5ONud/D59TyYWPjOfXZWQdxTJnYtAU+\nONNGMlhVh1GKxYZ4YLlMASJy+7smcrrnahbmapQYtrJOGdzy/DiOaTjb0FUowEgmvaWrqJUNnJmx\nUcpp8MJUVGeGaPVirPfoYYnmvQFNofIQiu48+Pu+EzuKc6FQQK/Xy/57WJgB4Fd/9VdRKBQAAO99\n73vx/e9/f1tx/uxnP4vnnnvuVq6ZYZg7SM7SkBvKZO55g0CUejvE9bqfbWnmTC3rsd4pvexGQl3v\n0Kr9+5cVVIv6oRFqgPKrj1uDWFY/TEZ6rQcZ4QNHeHVIrPcrQGavKIqSFVZslfvd6Ib4wdXeyDn1\nW07loCh5uP7grLreDhDGKTSQQCcpyWGzE6Hnxri07EJV6PsrxbqYoy3s45MWgijBSjPAQp26qqX7\nOm9rsA0Vqgp0+vHIsUJehPHcM+uglNfR82K8udCH68XwwwRBDDg2ACgo7aFL+nbyvve9b9PHdrzC\nd77znfja176G97///bhw4QLOnz+fvdbtdvGBD3wAf/d3fwfbtvEv//IvePzxx7f9+5555hk888wz\nIx+Th+IMw4w/eVtD3tay1WKnH42kl8ltUUBEOcqV9TbpZVsJ9eIhF2qAto+Hm6HCKMF6d7ANvt6j\njOyLQxnhMsVsHBzhN3tOfbxm4dS0PZLVvdoKsm7pbAtcVRClafZ34eogQ36ybGKyZGTb7tLotVin\n2lNZfVkt0ly9piro9OPMGX5lxaMHn7wG21SRdzRoKvU7ayoApMhZ4/X+uWW3NgA8++yzeO211+C6\nLp544gl85StfwRe/+EVYloV3v/vd+K3f+q2bvjB2azPM3UGapmj3R6NGh9PLio6eOcGrxZ2DPrwg\nxqJYUTe7g3KEwyjUWxEnKVpiNX0jR7icsx4nR/hu5qmnK2b2MBaECdZaYpu/NZhrljWYiqIgSVPo\nqpIlllXyA2OZHPHbaq6e0sH0zK/Q6cdYE2E83/5xG8uNAIrIAyeDGvDAyTz+03um7vyN2wDPOTMM\ncyBk6WXCXLYxvayU17Ko0Z3Sy1w/xlLz7hVqgO5Xux+LcJRwU5qWqatZ89ZWAR0HwW7nqYfNg+1e\nhNUWCXVzKAc8ilOo4utJUjojBmhqQK6oJ8vkbZAPbovDZRmiMnK2SmEp//1ba5hf7OPKig8vSDBd\nNnFuzsapGQfv//e1O3ynNnNLo1QMwzB7RVUHZ5j3zm2dXtbqRXhzyR1JL6uVyGk77G52LA1njzk4\ne8wZEerDvvU9jKoqqBR0VArkCE/TFF1vKHa0HWKp6WOpSeesenZ/D84Rvpdz6kpBRymfw7k5clDT\nuFaA1dbQTHOSIopSqKqCfpRgYW1gRJQ7MJMVAz/5QBm+GJ1arPvZKKCqKFhZD+CHKU7P2JC3Zb0X\n4ViY3OCrGR9YnBmGuWNoYrSmVjIA0PZoQ6wS6+2BYerHCzS/Wino2e8fTi/brVDP1iwcmzAP3Gi1\nVxRFQdGhykt5xt8fyghvdkbn0uXMr6zKPAhH+M2cU09XzGwbXM7d9zxq1lprDbLCVVWhxDJhLGt0\nKDzn4rIrUu4oB/zfnStAVRSaKKgH6Lox1jshoChwLJXeQ+Nv1AbA4swwzAGiaQqmyiamyvSDeTi9\nTAptvRMC1wehILIaU/YRbyXUi3U/+7OvXaIzyWPVwy3UkpylIbeNI1yOpWWO8LyGauFgHOFbzVOv\nrAdYaW49Tz1dMTPD4ekZMpZRrzStqtt9kWaXpghDmhyKQefQcmTNMSkH/N7jDlbWfSgKcGnJQ6sb\nIUmAc7P2oXgPsDgzDDM2bJVe1uhQGtRO6WUFR9ss1I0Aiw0/S5S624Qa2KUjvLfZES7Pru+UI3xk\nnvrM7uap80Nd5fefpFASuaJea8nObmGdZc8AABJNSURBVAVRJLfA6Tzb9WNcXfXwxjUXSw0fqqqg\n4KiIE5q7lvdqnGFxZhhmbDE3CM9Iell7NL3M1NVsVV0r0dbq2VkHZ2ePjlAD9IAzVTExVaEHnDge\nygjvRGh2Q1xZ9XBFjLtJR7gU6zvhCN94Tt3zYhLqHc6pbXOwEpe95mvtAGvrdCSSIoWiUAiKpilZ\nK9XwTnYUJWj1oxte27jA4swwzKFhY3qZ648GomxML5PVmNWScSSFGqAVa1XcA2DIES62v5vdaCRI\nxtLVkarMO+EIz9sa7pl1cM+sgyBMaDW9wzm1pg3Mc/fOySOREKsiXtQNYnhBjJylwgtTKKCHvVJO\nx3qHxZlhGOa24VgaTmyTXjacIJUztUysZ2vWjkIts77vJqEGNjjCZweO8EY7yka4hh3hhiYywoVY\n325HuLmHc2rTUMWRiIWZCXpw67oRLvyoA1VVYYcJ0jQddFEfAlMYizPDMHcNm9LL3Ih6rNu0pXtt\nzcO1tc3pZe86X0KcpJuE+tVLg7nZu1GogVFH+OmZgSNczlk3buAIl9vgt9MRvtdzaoBc4287W8AP\nr/aokSoBNHG8flq8P8YZFmeGYe5apOicETPD7f6gxKPRGcQ9yt9bKxk4N+fANlU02pEQaiqvOApC\nLRnkqdN/+8KY19yiBSpzhMut8NvkCN/LOfXD54tYavi4uOzB9RM4loqzMzbedX9p369vv2FxZhjm\nSKAoQ5WPs444e40yJ3izE6HjRri0PJpedmLKQhCkWG4FR1KoAXKED9eKhlGCZjfKRrha0hG+RL+/\n6OgUjFK4fY7w3ZxTu16Mnp9QG1iBMtx320l+0ByOq2QYhtlnVNG3XCkYwNwg5zqLGhWCA1AsZDmv\n48SkhSgGel50ZIUaIEf4dIVWpwA5wtd70YjJrONG2a4EnffLcJTd9YDfDDc6p/5/v7dO+d0KoKkq\nTk/bMAwF8wsu5mrjPU7F4swwDAMRciJczfcd35xett6N0OxSLrimKCjYGpIU8MMYqy3/yAo1QGfD\nw8lvcldisA0e4dqaj2trt98RPnxOfW3VQ8+L0enH8EOagwaQNVuNMyzODMMwW7BVelmzO6jHbA/N\nyiYJkCJFFCe4uhphteVDu0wlFUdNqIHRXYmDdIQXHB0pgNyGlfp+r9xvByzODMMwu2DjVq5ML5NO\n8I4bQdcUBGGK9W6MOImwsh7g2poHx1RRK5mYq5Gj2NyhKvNu46Ac4efmHFyY72z58XGHxZlhGGYP\nbJle1hnMWPf9GEFI27vLjQCXVzy8cU1D0dExN2lhtno0hVqy0RHuBQma3f11hMtz5fkFFz0vRt7W\ncG7OGfvzZoDFmWEYZl+wTRVzNSv7wS/TyxodyoFu92O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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "b = varying_intercept_slope_fit['a'].mean(axis=0)\n", "m = varying_intercept_slope_fit['b'].mean(axis=0)\n", "for bi,mi in zip(b,m):\n", " plt.plot(xvals, mi*xvals + bi, 'bo-', alpha=0.4)\n", "plt.xlim(-0.1, 1.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Adding group-level predictors\n", "\n", "A primary strength of multilevel models is the ability to handle predictors on multiple levels simultaneously. If we consider the varying-intercepts model above:\n", "\n", "$$y_i = \\alpha_{j[i]} + \\beta x_{i} + \\epsilon_i$$\n", "\n", "we may, instead of a simple random effect to describe variation in the expected radon value, specify another regression model with a county-level covariate. Here, we use the county uranium reading $u_j$, which is thought to be related to radon levels:\n", "\n", "$$\\alpha_j = \\gamma_0 + \\gamma_1 u_j + \\zeta_j$$\n", "\n", "$$\\zeta_j \\sim N(0, \\sigma_{\\alpha}^2)$$\n", "\n", "Thus, we are now incorporating a house-level predictor (floor or basement) as well as a county-level predictor (uranium).\n", "\n", "Note that the model has both indicator variables for each county, plus a county-level covariate. In classical regression, this would result in collinearity. In a multilevel model, the partial pooling of the intercepts towards the expected value of the group-level linear model avoids this.\n", "\n", "Group-level predictors also serve to reduce group-level variation $\\sigma_{\\alpha}$. An important implication of this is that the group-level estimate induces stronger pooling." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": true }, "outputs": [], "source": [ "hierarchical_intercept = \"\"\"\n", "data {\n", " int J; \n", " int N; \n", " int 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 sigma_a;\n", " real 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": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [], "source": [ "hierarchical_intercept_data = {'N': len(log_radon),\n", " 'J': len(n_county),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'u': u,\n", " 'x': floor_measure,\n", " 'y': log_radon}\n", "\n", "hierarchical_intercept_fit = pystan.stan(model_code=hierarchical_intercept, data=hierarchical_intercept_data, \n", " iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Vk7Ff32P9fNujM+mfP38e33//PS5duqTYJggCkpKSTBoYETUMp38sRcuA6tfc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\niCwPa+9bsPv37yMxMRHbt29HaWkpysr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#a_means = M_hierarchical.a.trace().mean(axis=0)\n", "m_means = hierarchical_intercept_fit['m'].mean(axis=0)\n", "plt.scatter(u, m_means)\n", "g0 = hierarchical_intercept_fit['mu_a'].mean()\n", "g1 = hierarchical_intercept_fit['b'][:, 0].mean()\n", "xvals = np.linspace(-1, 0.8)\n", "plt.plot(xvals, g0+g1*xvals, 'k--')\n", "plt.xlim(-1, 0.8)\n", "\n", "m_se = hierarchical_intercept_fit['m'].std(axis=0)\n", "for ui, m, se in zip(u, m_means, m_se):\n", " plt.plot([ui,ui], [m-se, m+se], 'b-')\n", "plt.xlabel('County-level uranium'); plt.ylabel('Intercept estimate')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The standard errors on the intercepts are narrower than for the partial-pooling model without a county-level covariate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Correlations among levels\n", "\n", "In some instances, having predictors at multiple levels can reveal correlation between individual-level variables and group residuals. We can account for this by including the average of the individual predictors as a covariate in the model for the group intercept.\n", "\n", "$$\\alpha_j = \\gamma_0 + \\gamma_1 u_j + \\gamma_2 \\bar{x} + \\zeta_j$$\n", "\n", "These are broadly referred to as ***contextual effects***." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Create new variable for mean of floor across counties\n", "xbar = srrs_mn.groupby('county')['floor'].mean().rename(county_lookup).values" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [], "source": [ "x_mean = xbar[county]" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true }, "outputs": [], "source": [ "contextual_effect = \"\"\"\n", "data {\n", " int J; \n", " int N; \n", " int county[N];\n", " vector[N] u;\n", " vector[N] x;\n", " vector[N] x_mean;\n", " vector[N] y;\n", "} \n", "parameters {\n", " vector[J] a;\n", " vector[3] b;\n", " real mu_a;\n", " real sigma_a;\n", " real sigma_y;\n", "} \n", "transformed parameters {\n", " vector[N] y_hat;\n", "\n", " for (i in 1:N)\n", " y_hat[i] <- a[county[i]] + u[i]*b[1] + x[i]*b[2] + x_mean[i]*b[3];\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": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [], "source": [ "contextual_effect_data = {'N': len(log_radon),\n", " 'J': len(n_county),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'u': u,\n", " 'x_mean': x_mean,\n", " 'x': floor_measure,\n", " 'y': log_radon}\n", "\n", "contextual_effect_fit = pystan.stan(model_code=contextual_effect, data=contextual_effect_data, \n", " iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.68837427, -0.68702399, 0.4069351 ])" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "contextual_effect_fit['b'].mean(0)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6omCMZZ3ZRZtgYn6tTQYXiunV1KaVQfzdhiasXxIoebiHZxEMOCfNJPIqsiJf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "contextual_effect_fit.plot('b');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, we might infer from this that counties with higher proportions of houses without basements tend to have higher baseline levels of radon. Perhaps this is related to the soil type, which in turn might influence what type of structures are built." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prediction\n", "\n", "Gelman (2006) used cross-validation tests to check the prediction error of the unpooled, pooled, and partially-pooled models\n", "\n", "**root mean squared cross-validation prediction errors**:\n", "\n", "* unpooled = 0.86\n", "* pooled = 0.84\n", "* multilevel = 0.79\n", "\n", "There are two types of prediction that can be made in a multilevel model:\n", "\n", "1. a new individual within an existing group\n", "2. a new individual within a new group\n", "\n", "For example, if we wanted to make a prediction for a new house with no basement in St. Louis county, we just need to sample from the radon model with the appropriate intercept." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "69" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "county_lookup['ST LOUIS']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That is, \n", "\n", "$$\\tilde{y}_i \\sim N(\\alpha_{69} + \\beta (x_i=1), \\sigma_y^2)$$\n", "\n", "This is simply a matter of adding a single additional line in PyStan:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": true }, "outputs": [], "source": [ "contextual_pred = \"\"\"\n", "data {\n", " int J; \n", " int N; \n", " int stl;\n", " real u_stl;\n", " real xbar_stl;\n", " int county[N];\n", " vector[N] u;\n", " vector[N] x;\n", " vector[N] x_mean;\n", " vector[N] y;\n", "} \n", "parameters {\n", " vector[J] a;\n", " vector[3] b;\n", " real mu_a;\n", " real sigma_a;\n", " real sigma_y;\n", "} \n", "transformed parameters {\n", " vector[N] y_hat;\n", " real stl_mu;\n", "\n", " for (i in 1:N)\n", " y_hat[i] <- a[county[i]] + u[i] * b[1] + x[i] * b[2] + x_mean[i] * b[3];\n", " \n", " stl_mu <- a[stl+1] + u_stl * b[1] + b[2] + xbar_stl * b[3];\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", "generated quantities {\n", " real y_stl;\n", " \n", " y_stl <- normal_rng(stl_mu, sigma_y);\n", "}\n", "\"\"\"" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [], "source": [ "contextual_pred_data = {'N': len(log_radon),\n", " 'J': len(n_county),\n", " 'county': county+1, # Stan counts starting at 1\n", " 'u': u,\n", " 'x_mean': x_mean,\n", " 'x': floor_measure,\n", " 'y': log_radon,\n", " 'stl': 69,\n", " 'u_stl': np.log(cty_mn[cty_mn.cty=='STLOUIS'].Uppm.values)[0],\n", " 'xbar_stl': xbar[69]}" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [], "source": [ "contextual_pred_fit = pystan.stan(model_code=contextual_pred, data=contextual_pred_data, \n", " iter=1000, chains=2)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YZdmgVp7j85Le3mNHS6cNqqCKYcXTyIwUyNoNvrj+LqOP0RxgrcSQI436SWCb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\nbml8esSv4xfdiYC4vmByNHmMa+bAuWqqEyDEG6W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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "contextual_pred_fit.plot('y_stl');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise\n", "\n", "How would we make a prediction from a new county (*e.g.* one not included in this dataset)?" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Write your answer here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Benefits of Multilevel Models\n", "\n", "Accounting for natural hierarchical structure of observational data\n", "\n", "Estimation of coefficients for (under-represented) groups\n", "\n", "Incorporating individual- and group-level information when estimating group-level coefficients\n", "\n", "Allowing for variation among individual-level coefficients across groups\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models (1st ed.). Cambridge University Press.\n", "\n", "Gelman, A. (2006). Multilevel (Hierarchical) modeling: what it can and cannot do. Technometrics, 48(3), 432–435." ] } ], "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 1 }