{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A Primer on Bayesian Methods for Multilevel Modeling" ] }, { "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](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": {}, "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", "import warnings\n", "warnings.filterwarnings(\"ignore\", module=\"mkl_fft\")\n", "warnings.filterwarnings(\"ignore\", module=\"matplotlib\")\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[srrs2.state=='MN'].copy()\n", "\n", "RANDOM_SEEDS = [20090425, 19700903]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, obtain the county-level predictor, uranium, by combining two variables." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "srrs_mn['fips'] = srrs_mn.stfips*1000 + srrs_mn.cntyfips\n", "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": {}, "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": {}, "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

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" ], "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": {}, "outputs": [], "source": [ "srrs_mn.county = srrs_mn.county.map(str.strip)\n", "mn_counties = srrs_mn.county.unique()\n", "counties = mn_counties.shape[0]\n", "county_lookup = dict(zip(mn_counties, range(counties)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, create local copies of variables." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "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": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "srrs_mn.activity.apply(lambda x: np.log(x+0.1)).hist(bins=25, grid=False);" ] }, { "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": [ "Here are the point estimates of the slope and intercept for the complete pooling model:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "from pymc3 import Model, sample, Normal, HalfCauchy, Uniform\n", "\n", "floor = srrs_mn.floor.values\n", "log_radon = srrs_mn.log_radon.values\n", "\n", "with Model() as pooled_model:\n", " \n", " β = Normal('β', 0, sd=1e5, shape=2)\n", " σ = HalfCauchy('σ', 5)\n", " \n", " θ = β[0] + β[1]*floor\n", " \n", " y = Normal('y', θ, sd=σ, observed=log_radon)\n", " " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [σ, β]\n", "Sampling 2 chains: 100%|██████████| 4000/4000 [00:05<00:00, 747.76draws/s]\n" ] } ], "source": [ "with pooled_model:\n", " pooled_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "b0, m0 = pooled_trace['β'].mean(axis=0)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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": [ "Estimates of county radon levels for the unpooled model:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "with Model() as unpooled_model:\n", " \n", " β0 = Normal('β0', 0, sd=1e5, shape=counties)\n", " β1 = Normal('β1', 0, sd=1e5)\n", " σ = HalfCauchy('σ', 5)\n", " \n", " θ = β0[county] + β1*floor\n", " \n", " y = Normal('y', θ, sd=σ, observed=log_radon)\n", " " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [σ, β1, β0]\n", "Sampling 2 chains: 100%|██████████| 3000/3000 [00:11<00:00, 258.81draws/s]\n" ] } ], "source": [ "with unpooled_model:\n", " unpooled_trace = sample(1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pymc3 import forestplot\n", "\n", "forestplot(unpooled_trace, varnames=['β0'], ylabels=['']);" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "unpooled_estimates = pd.Series(unpooled_trace['β0'].mean(axis=0), index=mn_counties)\n", "unpooled_se = pd.Series(unpooled_trace['β0'].std(axis=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": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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_trace['β1'].mean()\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 PyMC to easily specify multilevel models, and fit them using Markov chain 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", "\n", "Estimates for counties with larger sample sizes will be closer to the unpooled county estimates." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "with Model() as partial_pooling:\n", " \n", " # Priors\n", " μ_a = Normal('μ_a', mu=0., sd=1e5)\n", " σ_a = HalfCauchy('σ_a', 5)\n", " \n", " # Random intercepts\n", " a = Normal('a', mu=μ_a, sd=σ_a, shape=counties)\n", " \n", " # Model error\n", " σ_y = HalfCauchy('σ_y',5)\n", " \n", " # Expected value\n", " y_hat = a[county]\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n", " " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [σ_y, a, σ_a, μ_a]\n", "Sampling 2 chains: 100%|██████████| 3000/3000 [00:20<00:00, 144.12draws/s]\n", "The number of effective samples is smaller than 25% for some parameters.\n" ] } ], "source": [ "with partial_pooling:\n", " partial_pooling_trace = sample(1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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KNVMuO8Us3CvNo6PSRRdJAwNU0AOAZtwLZADQDBkgH7nFAqJQHCCb9X+f5bKTfbDWyS4lQZDTV3I559ZOcGztWqA3Ocm8dABoxa8LZEFI0lTKIzMnNLOwRT86P6SMkU4VKpIGwh4W0BAZIB+5xQKioLpggR8LTcvltQpklcr6pqhRFIWS5ACAxubmWq+vTLqkXNQ6MnNCd9z/uIolZ7FrxUrHTp7VkZkTIY8MaIwAKAX8+ANbKtU+jnoA5HdJ8qWl9WtyACCO3NkKYSsU/L9oyN/qcNz94FNaWi7XPFexVnc/+FRIIwI2RgAET/rqJktGfQqc3yXJy2XnBgBxF6XZCn5z/1anMbsUZmD73GLjqLPZ80DYCIASamjIufklm3X2t3mzU83MjwColwUI3KprUrglyQEAwetFdinqHnq0qBd+uKzHjv1Qr7/r7wKdfnbZcOMmgc2eB8JGAJRQIyP+F2PIZp0KZJKTXcnnu9vf5GTvFn52UnUNAIA4OjJzQsdOnlVlZXr6icUl3XH/44EFQbddv1+D/eurL527UGIdECKJAAhtKZfXiiAcPRrtAgOUJAeA9JibW5v67Me+4jSF7u4Hn1KlbnHu0nK552twduxwbocO7NSdb71afZna6SFnzi0HGogBXhEAoS3VxRAqle7X1gAA4IdCwb8CPXGbQudlDY4fFWHrnTnj3CQnCMpm1s+PDyIQA9pFHyC0pboYQiaTnrU1veirBADwx5GZEyoUL5XUp3LFarks9WfTc433suFBPd/keVcQ5bbdMtj1KIaAqEnPXwf4IptdK4JwzTXpmV62aZPzc0d5yh8ApJHbg6ZSlf1ZWi7r/HJ6Snfedv1+ZeqqEw32Z3Xb9fsDG8NG09wohoCoIQBC24xxgoFcLuyR+KPVtIDp6bUmsH70FOrW0FDvqucBSL5ThaIKxXCqhfVCox40knShXNGpQrHj/S6XK5pZONPx++THlLMjMyc8jeHQgZ3at2Or3BloO4cHdedbr9ahAzu7G0Abmk1zM1KggRjgBQEQPCmXpWIxmb1wWjWKrV7n5EdPoW6NjPSueh6AZAu7Wli9paXug4TnFpd0+qGfkF1ef0pz/PS5jva5XK7o/HJ5dUpXJ+9Tt03I3cyW1zFcMjSgoYF+Xbtvu75++xvbDn68BlvNNJvmZqVAAzHACwIgtJTPr2VA/Fxk6urFwkw/Va9zoqcQgDgLq1rYkZkTmp45r0f/+1LNyXW53P3alMuGB3XhBznJrl+A32xNSivFUln1h7qgF/M3ymz1agztBluNNJvmtpPpb4ggAiC0tLhY+9jvAKjbq2S9Nja21gSWnkIAvIjqhR0v1cL85p5cLxezqiz3rZ5cL5ebByftvH+tpld1ks2oNDnOBbmYP8jflR/BVhTWIQFeEQChpeHh2sdm/UW2trjT6cJeS9MOtwlskMGPG2h223AWQPCiemGn2VX6Xi5Sb3ZyXSw1n1Pdzvt36MBO/XhuoOn3O8lmNKjmLCnYxfxB/q78CLbq1yEN9GUCX4cEeEUAhJZyubUMyNBQdwFQ1AoKBGl01HvxgunptYZ+MzPpep8A9E4YV+mbnUQ3y7J0Yu8lQ+t+rmrtZjMG+rKq31vQ2Yzbrt+vwf7aHgy9GkM3wValspatc9ch5Tb368Ceiwl+EFkEQPDEzYB02w8nagUF/JLPSwsLGwcqk5Peixf8wR9s/BgAOtGqWlgvpu41O4lulmXplDFGWhe2rGknm9GfzWhzf1YDfc5pUhhV1Q4d2Kk733p1IGPoJtiyNprZTmAjNEJFoBoVFHjwwbBG44/paenoUecq2MGD/qwTeu65jR8DQKecq/TS6L7tmrr9jZLWgp5enMjedv1+3XH/4zXPDfZnNdCXVXHZ/9dz2VJGpTNbVh+3O3WsP5vR6J6LJUmjL7xRU38lHTrg6xBbOnRgpw7sce67v6tevY4k3Xw4o2Kpop3Dg7rt+v1kcJBYBEAIlFtQoFRKTkGBqam16WpuVqvbn+uXf1n6p3+qfQwAvdIo8HGDom7L7rsn0Tfd40x7c0+ub/lERp136WnOnQpnK0aVZec0p52pY0dmTqhQvFQVK80sFLR72xbNzjZfY5QUQQVbQBQQACFw2axzS0LwIzlZrEzGCYL8KpP93vdKt97q7PPKK53HABAkP7NBhw7s1NBKDPH1Hp9cG2M00J/VuQvO43ayGW7Fuoo9KMkpo33s5FlJTuYMQDKwBiiBJiakuTn/97u05NxQa2xMuuYaae9ef7Na7nrel77Un/0BQFr0ZzPKZjLKbe5vqyloo4p1FWs7bqjql7m5aJZVB+KKACiBZmedSmuuuTl/AqJy2blFQbncuuhAkHI5ac+e5GS1ACCuKp31PpXUvFBCpw1VN3Jk5oRmFs7osWM/bNmrqFCg0ADgJwKgFCgUagOiuMvnnZ9nfj59pbQBIAmcdTbLKlcqmlk403aj0uasrLXKn19WuWx19lx7tbabFUpwK7H5xZ1q5wZWnfQqqt/fzMIZ5c8v+/x+bvya5UpFkl19zdFRZ50vEHUEQAnViwxJpdLdlTW/LC6u3Q+qlPbQEH/UASTD3Fy405nX1tk4j4uliv7Nry3rxnd1d6XO2vXBTqlk2woGGpWDzhij3du2NPkXnWnWHLadXkWu+mCqWKp0FUx5fc3f/NxaSqpYqug3Pzer8ZtPaGSkZy8L+IYAKIHqMyTdTlvL56Vi0an13+D4Erjh4bX7fhUdaGVkRJH4o95OM9Uo6UVvEQCdKRTCnc7c6OT/3PM/pn94rLua2JUmB6h2ggq3947bo2igL6N9O7b6XgCh2VS7dnoVufwMpry64/5vq/56aGXleSAOqAKXQPUZkv7+zhuYVve4iYpczsnG7NghHT7cet2NX6VcoyCuPwNz1wG4glxns9HrNVNdsc7tA+S3y4YHdaLBuNrtVST5G0x5tbTc+HfV7Pk4SNK5AlrzlAEyxtxjjJk3xlhjzE822eYjxpgfGGNmV273+jtUbCSfX5vyVp8h6esizK3ucRMl2az3ogOzs5yAA/BPO4vXsV6zk3z74taeZIo7CSpcfhURqtdoql07vYqqNfv5qp/nM9sa5wrp4nUK3BFJb5D0vRbb/bW1dnTl9hvdDS2ehoaCn6LkZmncKW/uONyyzJ1mf6S1HjcAAOlvn3jB18XraXTb9fu1+Hc/IVvKSNaodGaLjJH6Kps6PgE9VWjeUrWToMLVqyJC7lQ7t7jCzuFB3fnWqz2X667WKpjyu+CCpNUpgs2eD+NcCGiHp1Nba+2j1trjfrygMWbYGHN59U3SLj/2HQUjI8GnT6uzNBcuOFPg6jMkS0udrcFwe9xs3uzbcNGmKJX7BtJgo+PUp/7hWODrLZKo+P2cVHHOlivL3c/GD7tPTz0v/fgOHdipA3su1rX7trfVq6jRftxgKtNf0rbd52qCqV6sEXrXa/ds+HwY50JAO/y+tv8OY8y3jTF/a4xpNjlpQtJ83e0Rn8eRKtVZmk2baqfAucrlzlO7uZw0QAPswLlBLeW+gcA1PU59P3++4T/o5XqLpLn7wafWFdSxViqWOq/MsNH6oTAydPX9+HrNDaZ++tWDeu7ru2uCqV6sEfrYoav17mvXgiAj6d3X7tHHDl3d8T6BIPkZAH1S0l5r7Ssl3S3pvxhjtjfYblLS3rrbdT6OI3XcLI075S2X6/1rViq9mReNNdUnCEGV+wYgaYPj1I/nGqfDu1lnEjVzc72t2tjsxLvSRZXRvmyTOVlqP9vh9ijKn19Wobis5XLvF8L6USmz2XolL2uEOvGxQ1crm8lIMnrtvu0EP4gV3wIga+0L1trllfv/TdJxSesKJlhrF621z1TfJD3r1zjSKpfzXhTAD9Ymq7lq1AVV7hvAxsep971hn2+L18PgpQFpodDbxeDNTrybrStpxWnIuXH05DXbUd+jqGKl88vlDdcY+cGPBfjN1iv5WXDBi9FR6cUXaX2AaPMtADLG7Ky6PyrpcklMio6Y6mpxiAc3s+cGt/TUAcLzs694iW+L14PWqAFpGNPDbrt+vzKmNtrJGKOBvs4q9jSaUlft9EM/oeIjr/S8r/r1MlbtrzE6VSiqUFyORNU1Pwsu1HOaz9qan3NyUrroIiqqIdo8rTw0xvyRpLdKeomkh4wxP7TWvsIY84CkD1trvyXp48aYV0sqS7og6T3W2hd6NXC0L59f6+lz8GDtSXWQhoacr0GcxLvTAaLQxLRT9Zk9DipAuJz1Fs79qdvfGO5g2nD3g0/pxFf3yy6vXft0p4f1K7gA7tCBndq3o6gnVkorZYy0b8dWPftiZ9dkN8zuWKPSyYu0bcfWjvZlS86Y2ulRdOO7CvrO032rgaZbdU1SaIFyLz6zR2ZOqGJfKmcFUO3PqQA/T0AnPAVA1tr3S3p/g+dvqLp/s4/jQg8sLtZWi5uaCicAcoORIE7kmaYHAI7nFpd04Qc5yZp1z78s4LFcMjSgbMYp0DM00K9LhjqfC3/Z8KCe3+D7+3Zs1SVD3ir5rGtQulKpzs2eePEPjy2rcqH29dxAMw6ZQq+cdVUvrXkujIAa6AQdXlJkeLi2WlxU1pQwLa8x0+F8eABopFeL4cP2My/fse45U3XPa/AjNV4vI0m7t23xvI9m2aKkVQrsRXU5ICgEQCmSy9VWi+sk+2NMd41V67nT8npR6nl0dG26XRzRgBaAnxqtvQmzgIO7fiR/flkzC2c6qrZ2ZOaEvvTf16+v6c861cna5a6XqS7IkDHtBVHNskWdBppBHstGR703ME1qQI104BQrZbqtFpfJSIM+/m1rNC3PL5OT8V77kyRk+ZqjqAWC4qy9WVsLM9CXCayAQ3Vp6dff9XeaP1VQpapyQbFU6ajaWqOiBZJUqnReuvrQgZ0aGuhXbnO/spmMTJvp+N3btqwLvboJNN2GokG0npic9N7AtNHPE6eKiPAuiccpAiCEqt1peV66a4ehnatmaTM93bssXxL4Uf4W8MpZe5NRNpPRgT0XBxb8VFefO7G4pO/n1wc6nVRb60VPoWrZbPuzHi4ZGtDm/uxqFsmPqmvNSlyH6dCBnTUZxThURGx2In9k5oRmFs5EompfFCXxOOWpCALQSLHonMx2U0jBnZa3uCgdPtx6X0F31/bK6xWzJHMPKvXvxdRUNIpvdKLZzwTAu2ZZmmqlM1tkSxkVS5WVk9EtKpYqev1dR3Xb9fubnlTXFC3IWKnsnJBnjFOStluDg9JyuaKZhRc9jcfVn82oP5vR6L7tsaoU2C43O3ZtTH7ORifxboBeLL1GUjSq9rWD41RnYpkBmp6W7ryTK8lhKa8cVc6f9+eKftBNXOsxPcsfza4QjY9Hs/iGF0m86gUEzcui+Mpyn1Qx6suYlZNR56qJezLa7Ip8ddEC07c27a3TnkL1lsvO1Dyv4wnb0lLypir1WqMA3a1mFwccpzoTuwBoeto56f7Qh5hOE5ZSae1+J+t2ojRdjOlZvTc21n3xDQDx1daieKO2Tkbrm3zWcooszCycaXttkatYKqt+Np3fJ8dzcxtP7a5fP7VR8FUuczLcLqrZpVPsAqCpKeeku1z2f9E8vOmrmjjZyRV9d5Flqz/6QWg0PQv+CzvLB6BWNhvchSg3S5PpLynT71xByxhTU1wgY5znSuXGi3c2Ohl1mnxerNzmfrmV385XBVHFUkXHTp7tKGvTbC2RnyfHG63vabR+KsoZqDiiml06xS4AGh93Trqz2fhNp0kKd0GoMd1d0Y/Cos44T88CEE1xWFA9OBjcmgE3S7N1x3n1XXxOO4cHtW/H1pUF9Ea5zf0aGuiXMca3EtKV5dr9VKz1lLWpXySfaVIALqiT46hPz+qi2F5kNOr9RDW75ItdEYSxMeeke2rKOVmNwxXlpM7HzWTi8f5vxJ2e5bUIQ5Cy2WQcXIA0ieOC6uqiA0ZS8XxOMwsF7d62pa3+NxtxsjTO/anb36jxrzXebve2LSr7cTJqVyIXs5bC8ZK1qZ8+NtCXrckmdTyeDjE9q/fc/5c3H3aKcOwcHvRU6ALxFqkA6B3veIc2b968+viWW27RLbfcolOnTummm25at/2+fbdqbOztOn78uN7znves+/5v/dZv6cbxP5DcAAAgAElEQVQbb9RTTz2l973vfeu+/zu/8zt605vepNnZWU00iFI+/vGP63Wve52+8Y1v6IMf/OC6709OTmp0dFQPPfSQPvaxj2l21rmcNj7u7OtTn/qU9u/fr4cfPqXjx59VqbRF5fKQDhz4mC666J/16U9/Wrt379bnPvc5/emf/um6/X/xi1/UJZdcovvuu0/33Xffuu8/8MAD2rJli/7kT/5Es7OvW33t2dlJFQojkpzOacXieZXL/ZqdfXz13775zXfoq1/9qiTp937v9/Twww/X7Hv79u360pe+JEk6duyYlpZ+TNJ2lctWhcKSpK1ypxpMTExotu6oceWVV+rP/uzPJEnvfe979fTTT9d8f3R0VJLzfj355JMqFour75skjY2N6c4775Qk/fzP/7x++MMfStLqz9bX1ydp88rP8mYtLdUeDN7ylrfoAx/4gCSpUChodnauZv+/8Au/oF//9V/XuXPndOyYM7Y77lj7fv1nr/53e+utt+rtb+/tZ29w8HUqlaxmZ4/WjH12dlIjI87v1/3s1XM/e1/+8pf1h3/4h+u+7+dn7/Of//zquNz3aGplLuE999yjr3zlKzXfGxwc9PzZu+OOOzRdtzBr165d+sxnPiOp88/e5Mql73e/+9169tlna75f/dl74on/T8vLpZr3/+DBg/rQhz4kqfVnb7xBSrH6s3fDDTes+2y1+rvXy8/e+fPn122PWu5xyv293XffbM3va2ZhUcVSWRd+8JeSpLNP/oN01Rv0sc89osl//8l1+wvjOFUuX61CYUnj42/R2/7Pj+qP/8c5Lf1ov0o/OiVJshf260fPzemfn5P6t+/W6+/6Z43pKX3ra59bt/9ujlPl8tWSnGDHPU49O/ekdn31P6h08hOyMqsno49/5S81+e83Pk796Ec75B73ZCur+5ak0pnndPrzv63xx+5efa7R3wr391oojCibzWpwpfHdhdPPqly6oDOf/20NbRvU5CMD+kcfjlPSxsepy4ZfruMnz8hecP7tC39zuyQnMLvv5SdrPnuFwldULg9qdvZxjY9PrPtbUf+3xo/PXibzOpXLyThOmdOT2iyp/2sf1af+flCHOE7p3Llz+p/fcFDfeeITqliri/b9qnZvG9QH/u37Yn+cit0UuLgqlbbo7NkRnT//Un372/9RTzzxYX3kI8NhD8uzwcET0rqloOiloSEpm+U9T7pSaYuKxUv14os/EfZQ4INiqXHx5e/noxlc/udH51uWqD6xuKTP/tNCx4UE2nXJ0ICGBvp00WC/vn77Gz1diV9aLqtS2SBbZYx2b/M+bS2bXVJ/v/Pz9mcz2rZ1k3Kb+3Vgz7BvWTEvGk3PyjT5WbLZJRnjR/Fv7zZvXptGjuT58uxzOnby7GrT4mKprGMnz+p/fO9MyCPrnrE2/BMsY8zlkubn5+d1+eWXhzuYLrhBdP1C+vFxp8zy/LzzOJt1FoTv2ePfovvq1x4fd9L4o6PO4+FhZ63NT//02vbtvK6770cfdb4ODUkvvuj8HNUV4do1vBL/uQtxvYzJ/dmGhqSbbmo9h73+vWi2TavX97KN35qNPYyxeLHRuKI65lZ6Pe7paef/ZaXirMkIu0reM888o71790rSXmvtM+GNJHrqj1PNPhuvv+vvdGJxSS/8zbWSpJe86zFJTpPIr0egT8r4uPO3fGjImfq79/b/R1ZaHa8kXfhBTpsuza8+9utnqD9OPfqoU9Dooouc593jlPt9d1svLtp3RvlnLqqd+maNZKwGdp2RMdJnj5xvGUzVXwx3L9x3cpxy/91G/2ZiQvriF52fvdm2R2ZO6KbXXaqKlcY+8kjT6Vmtjne9+HvGcSp8vRx3FP+e+XWcIm4PQD7v9MxxC95s2rR28o/OjIzQ9AvxRxXC5Inbgup2FvNHed2J26enGWvVduGAU4Xiavnpbkppb2Ry0jmebeTQgZ0aGuhXbrP3jFgjQVVejUMREHiT5DVoBEA95vaZef555/FLX+pc5c3lwh0XgPBRhTB56vvS7Bwe1J1vvTqyC6obBWzN9Kry2XK5okJxWeVKRTMLZzo6YW5SrK1GOydtpwrFlak/zuNuSmkHwQ063GAtrHGuFQGJR+PYuOt1sJnkEuEEQD1WfYXXWme+bJQqjSF+8nlnSiVNW3uv1+81TWKTye1Lc+2+7V1dse+FU4WiypXKalNNSTUBW7NAondZLKvzy+WaQOOO+x9vO9viZTJ/Oydtx0+fW1334PJaSrs+c9Trk//6oMN9D+tfd2Skdbapvgx4q+frRb1sd5IEEWzGLaPdDgKgHqu+wpvJxHvqWza71gNIcgI7TsKD5WYU5+elgwd5/3spqPeaJrEIypGZEzp28uzq4+oS3W7A9tp925Xb3K+RS4d6nsVy1yDXBy9Ly2UdP32urX2t6x+Uqd1rxpi2TtqaTalrlUVy3+P6gK6XQZCfQcfs7PpS4Bs9Xy/KU6aCmprnNVjsVhDBZtwy2u0gAOqx6iu811wT76lvmzY5QdyFC85jazkJDxprRoLDe42kufvBp9ZlNZqdMF0yNNDTLNapQnHdWKq1WtNTb/e2LU2/N9CX0b4dW9v6GTptyNrOe+xyM0adnphHKeiI6pSpIKfmeQ0WuxXU7z3KGe1uEAAFwL3CG+fgJ593qtScPy9Vl5PnxDBYrBkJDu81kiZKJ8rHT5+raVLaSDvT4C4ZGlDGVE3gqzj3s5mMDuy5uO3S1bu3bandn7xlkdp9j+szRp2cmEcp6IjqlKkkTs2L0u89jgiA4MkLLzR+Pi0nhlFZdxPlNSMbvUejo2tlZOMiyu810ImonDAdmTmhYqki01/ZMAhqdxqcMUbOKiajbCYjb6URGrtkaED7dmxVZmUXXrJIExNS8ZFXNvxes/e4k4xRvbCDjqGhtb/vUZ0yFaXg3y9h/97jri/sASDebryx8xPDctnpI5TPh5sda1UW1F0LUqk4U/7CPhnO5ZxblE7IW71HcS1ZHsX3GujUbdfv17v+tDYocE+YJr8WzBhOFYor645e03LbdqfBuUzncU8NpyGrc390z8Utt5+dlbYVL9WiOVvz/EYnpX6cmLvBxc2HM7ogJ1gLMuiob0vhTJly7k9FoPeV5ASgJxq8p3HOllT/3oulinYODzbtEYX1yAAFII5Xv6uNjkrXXbf2uPrg8v3vd7bP6em1KXVHjzpBUFgKBefWDGtBWgvqPQpqcSmQRIcO7NS+HVtXH4dxdf746XPrpiI102wdTiuZqn9mrQ2sJ83cnPT88b6a1+/LmA3fYy9ZuSMzJ1aryjX7Gdx1GrnN/Tqw52JOgut4yZbE8VwtqetzgkAGKADulZEgp4pVp6S75Y7/gQecjM1VV0kzM93ts/oEuVJxOpJHlbsWpFJJz5S/dgX1HgWxsBRIskuGBpTNSEObM6F0cvea1ckYs2Fhg1ZMxkplp3R1/cJ3SZ5OFJ3iBBlVrDSzUFgZT/O1RGderOj8ckX9A2tT2iot6nNvlJWT1hbvV+zBjn4GOLxkS+I6UwGdIQMUkl6vKXFr/ft5tTyblQYG/JmuVn2C3G558HI52PU47lqQXK67KX9JxnqZzsXxqiPQqeqsTqa/tLoGqDoE2Dk8qH07trZduMBlrVUlU2r4Pa/ra37ssoKeyz7fViPUYqm8rqR3q95BblbOXWtUn5VL4uL9sJAt6VwSj1NkgEIQ1JqSKF8tHxtzslRuRslrUOVWoysUgl2Pk8s5U/86nfKXBqyX6QxXHRElbtbjsWN5DfRlWmY92rV72xaVV6Yi9V18TpXlPhlJm/uzKpYyunbfdk3d/kaNd7EmqWLthuUPvKyvOf3Kf1Juz5IWj66dJLvBTLMT5/psT6a/pE2X5lu+nrvWaHTlZ/cy1kbPV//uXn/XUdaDwDdJPE6RAQoBa0ocnWSUqqfKpeG983MqIwBs5FShuK6JZ6usR7suGRqoqRKWMU7w05/t/nQkm/VWAMHLwvdOihNk6l677+Jz2vamf+5qob3Xyn1+lNNuV1CNRYFeIAAKAf1FarWTWq2eKuf1vQt6ypyf6qvrAIiGJE4JOX763LqSzK2mcHWieirS0EC/L8GPJA0O1hZAaLiNxzLBnZQMH+jLrss8dVuW2GupYz/KabcjyMaiQC8QAPlsbq71uhvWS9SanPR+kp/LOVkRr++dO2Vuft6ZMhfHIAhA9LTzdysq3Cv25UpFheLyupPVZgUK4tYrJWNMwylwF2/p91z1rlHg0aoRan82o8392dXslpdy1O7vJH9+WTMLZ9b9Tty+Os3WCLmC7nPD2qTGyIrFB2uAfFYoeFt7w3qJzmWz0p493t67RlPmeM8BpM3aFXun/07Fal01sYG+TMMgKG69UowxGujP6lzReeyuZZr58M963of7ntx0j/Neufs4dGDbhv+uP5vR6J6LNXva6R106EDz/kH1v5NiqdKwwtuhAztX+xE1q9x32fCgnm/yfC8ksbFot+p/n0FV7EtaJjooZICQaJ1MmQsavW0A9FrNFfuMVaa/tO6K/e5tW5SpW0TTKusRVc60OqNsJqMDey7uqKKcE3j0r/bW6bQqXTN+ZlFuu37/ut9dt9PvNtLJFMGkCysrFsdsdBQQAKVAuewUXfCj2ejSkjPNrxNhnOi3O2WuU938bLOz0a7Yl2ZJXOeBdKq+Mm/6Kuq7+Ny65y8ZGqgpyTzQl9G+HVt7XklsuexMyStXKg2ngXkxOur8rY8TP7Morcpp+83r2qQ0ISsWL0yBSzh3DYzklN52+9l0qlxe21+7ujnJ7yZwamfKXKcIYJKJq2pIisuGB3WiwYlY/RX76pLMQcgOlHV2aVkV65xMu9PAsoVL2sq4TE46f4dfeKHzsTjrN7aoWKqslpGWehf8ef2deLVROW2/eWksmjZ+/z7RW2SAEq56DUylUvs4TsiSQOp9A2EgqaJ6xb60Na/s8Nma55aWyzp++lyg42hW1Wy57DzuRTa4nd/J0FB3Ga5eLM6nsWitqP4fQ2NkgBKi2R/m6jUwmUztYzjKZach6/R0b7NEbhaLrEJngmogDCRR9RX7C/JWocxvjY5TzSrPNXveC2utCsWSpD6VK1anCssts0nN1m8US2X1ZzM9+bvdzu9kZKTz1+l2cX6jzFjag51GyIrFCwFQQjT74+yugTl7tvvpb0k0Pb02pa/XJ9VksLrTqIEwARDgnXPFXp4qlPVCo+NUs8pzbinpdllrVbFWpqolzrGTboapeRDUbJ1GxTZ82jdB/E42WpxffXLeeAqgOgqeorp2stfjcn+fkno+DRHdIQBKgWzWyf7kctH9oxSWqam1+61OqqsbqgZx4p3PO1MWg3q9qHMbCFcq0a3oB6A9u7dtqQpQHIP9WV19bb/+p0u978c9ea/Yi9Z9r2LtypS65gFQs/UbmUYNhWLGy+L8Zlmigb6Mp+CpXlRnOkR1XAgea4BShnKJtapPojc6qQ66oao73YsGrmtoIAwkT6PKc3e+9Wp9+W+GPB+r6tfv1Mg4KZxWU+qard8Y6Ms2+Rf+mZtzKqz2ipeS1c2yRItLyw3/LZXNEHcEQAnmLhgvlyVrWTzeyNiYM0Vw8+aNT6obNVTtpUbTvVxpLs2cy/W+oh+AYDnVy/pXe/a0u2ai0cm7JMlYmT7nD2mrKXWHDuzUnW+9enU7t4y000+otwoF5zjdK14W57cb0FDZDHHHFLiQ9PoENp9fWzDucrMJcb56ns9LxaI/PY1cF63MmNjoPQm6oepG072imsFLa1AGIFytTt4zxmj3ti0t9xP39Rujo4379HlZnN9sCuDFW/p1frk2e0ZlMyQBAZDPvK4T6fVJ7OJibfDjivPi8eqg7uhR/9bGeKmu4xaT2LFDOny49++fO91rcTGY1/NDVAMzAMnW7ORdxqp/oKx9O7a21VMortxeSI20Cu5uu37/anED12B/Vr974yskUdkMyUMA5CN3nUihEH6mZXh4LYNQLc6Lx6uDukol+EAuiIaq1XI55xaH4AcAwlJ98u5OeTOSBrcYvebA5q723U3vnThplSWKc2YMaIQAyEeN1omEcfLqVg8bGZGWl6WTJ6Vz56SXvcy/bIIJoTJOdVCXycQ3kAOAOIjLtNbqk3e95EUN9GVUOnmRL+t3uum/EzdxnwIItIMAyEdBrxNppLpZZCbjTKM6fdoJWPzMXmR8WBfabgPSXM75eZ58UrrqKjIjAOCX6mDHXUcSp2mt7sn7qUJRx0+fW21ieqpQCWT625GZEyoUL1XFSjMLBfUN5DQ62vsKcgA6QwDko6DXiTRSXT2sUqnNSkVJpw1IczlpYICGrgDgp+pgJ65Nm08Vijp28qwq1il9XbFrTVB7GQS5Zbgr9qAkp+T28uYXNX7zkiRva2Wy2fhk3LCxqP4eJyacr3G6sNFLlMH2WdDrROq51cMk52t1VspP1joB1tNPd1Zau1EDUgBIijSXqw/L8dPnVoMf11oT1N5pVIa7Yq3ufvApz/sYHOTENCmi2m9xdja+Fzd6gQAoYHNza1F4L1Q3i7zmmt5kSsplJ/ixVnr+eelnfqb9IMhrA1IAiKOongQlWbNmp62aoHarYQW6DZ4HEL6WAZAx5h5jzLwxxhpjfrLJNlljzL3GmO8aY+aMMb/i/1CToVDofQTuNovs1TSxUqn2cScZnLEx6cABJ1DrZbW8XvQNAoA4GxqKTnbKzZQNDTkzKLrRrNlpqyao3co2qQrU7PlOeM0ozs017gUEoJaXNUBHJP1fkh7ZYJtflDQi6QpJ2yXNGGMestY+0/UIETl9dZ+aTjM4vS7zXF0Qws++QQhPVE7agDgbGYlOdsodx+zs2rrQTu3etqVmDZDkvQlqN8p10+5aPd8Jr7+vbt/DdvE3GXHVMgCy1j4qSWbjKxlvl/Tn1tqKpJPGmCOS3ibp7voNjTHDkupXpuzyOmCEL5t11hdZK73kJdKXvhTNwKK+IERUG8C6ZcsJ0FqLykkbko3jVDi6zUy5hQ6Onz6nC5IyRoE0Qd3ZpBHrzuHBnr5uI0H3LeJvMuLKr7zwHknfq3q8IGl3k20nJM3X3TbKLiEiqqcoGOMEQVdeGd2T9vqCEM2yVH4sVs7npYWF9tdCuVmq+XmnGl4nBSUQvomJ3q7tQ+A4ToXAj8zUJUMDOrDnYuU292tooD+QEti3Xb9fg/1r8/c2XZrXlpf+SLddv7/nr11vZCRdvYuAToVRBntS0n11z+0SB5fIGxkJPr3eDbcgRKu+Qd0ecKun2m1U0rtRpqc6SxVm81x0h8o6icNxKgGCWuvkNmK96R6n9PbVN83rtuv3rz4PIHr8CoAWJL1M0jdXHtdnhFZZaxcl1XSnaTG9DuiYn32Dmh1MvQQxzYIkN0tVqVAND4gKjlO9F0Rg4kdGyes4Dx3YKTfZ9PXb39jdiwLoOb8CoC9I+lVjzP1yiiAckvQGn/YNREKzg6mXIKZZkORmqRYXw2ueCwBBi8vakbiME9jIkZkTmlnYomKpotffdZQMpbyVwf4jY8yzctL/Dxljnlh5/gFjzE+tbPZpScck/YukxyR91Fp7rEdjRkjcUqWSsxao25KlSVHde6nZ9Lfq9Uj1QZJbtpzgBwDSZ2go+OIFSI8jMyd0x/2Pr/bDOrG4pDvuf1xHZk6EPLJweakC935J72/w/A1V98uSbvV3aPEUtf4Kkn/rEyYn1zoJDwZf3CbSWpX0JtMDAGiEogXopbsffEpLy+Wa55aWy7r7wadSnQUKowhCokWxv8J993W/Lypcda/XfY8AAACqPdegRPtGz6cFARA8ocoVAADx1c3slKjMbEH7LmvSp+qyEPpURQkBEAAAQMJ5mZ3SLNCJyswWtO+26/frjvsfr3lusD8bSp+qKCEAAgAAq7jaH5yoVeci0Eke9/N08+GMiqWKdg4Phv45iwICIADoUqMmt0BcpfkkOMjgb60612skrVXnkpT6k1P469CBnTqwx7k/RZ8qSQRAiIGJCWlujko5iKZmTW4BeBeVrFOQwR/VuYDwEAAh8mZnpUIh7FEAjTVrcgtEUVQCjXppzDpRnQsIDwEQAsM0ISSR2+S2Ulnf5BaImrQEGlHqydcM1bmA8GTCHgDSwZ0mND/vTBOang57RIA/3Ca3e/cy/Q2Iiij15Gvmtuv3a7A/W/Mc1bmAYJABQiAaTRMKShyuBCLeaHILoF1U5wLCQwCEQDSaJvTgg8G8dhyuBAIAuuNe6IpT426qcwHhIABCINxpQouL0uHDXCkHAPjLvdDFOjxgPWbC1CIAQmCYJgQAQG9ErakqooWZMLUoggAAABBja01VncW2blPVIzMnQh4ZEE0EQAAAADG2UVNVAOsxBQ4IGfNyASD+hobCe22aqgLtIQBCxygvvcbL+9BsG+blxh//DwCMjIT32jRVBdpDAISOUV56jZf3gfcqufjdAgjTbdfv1x33P17zHE1VgeYIgAAAQGKElZENMxNMU1WgPQRAaFu5LJVKUj4f9kiCwxQnAIiHsDKyYWeCaaoKeEcAhLbk81Kh4Nw/elSang62r8/oqDQ3F9zrucI+sAEAAMAflMFOgXJZqlT8ydgsLq7dr1Skqanu99mOyclwF5oCAAAg3giAAlYuSwsLTuYkCNPTTsbG2rWMTTeGh9fuZzLS+Hh3+wMAAACCRAAUIHf62Py8dPBgMEFQdYamm4xNPu8EbpJT/nrzZumaa4Kd/gYAAAB0izVAAaqePnbhghOM9DqAqM7QdJqxmZ52skeVirOPLVukgQEpl/NrlGiEwgsAAAD+IwAKUPX0sU2bgpk+NjbmZGzOnu08YzM15QQ/kvO1VJKy2e7H5vUEP5+XisV0VZ2TKLwAAADQCwRAAcrlnGBkxw7p8OHgpo9ls07mptOMzfi48+/dDFCfT58aLyf41dknP9YwAQAAIN0IgAKWzUp79sRr7czYmJM9Wlx0sljHjgX32vXZp6CrzgEAACBZCIDgSS4Xzpqf6uyTMdL27cGPAQAAAMlBFbiUyGb9XVQ/NBTMIv2xsbW+P9ZKExPhrQWamHBuAAD4ZXSUojdA0MgApcTgoL+L6kdGglukv7y8dv/CBWcqXhjZqNnZ4F8TAJBsFLwBgkcGCJFXXz2v+jEAAADQDgIgRJ5bPW/vXunhh+k/BAAAgM4RAPkon5cWFijV3AtxrJ4HAACA6CEA8onbr2Z+Xjp4kCAIAAAAiCICIJ9U96u5cIF+NVExN+fcAAAAAIkqcL6p7lezaZPzGOErFMIeAQAAAKKEDJBPxsaka65ZW6jPWhUAAAAgesgA+SiXc24EPwAAIGg0VAW8IQACAABIAJqqAt4wBQ4AAABAapABSoGhobBHAAAAAEQDAVAKjIz4t698XioWna/tCmNuMsEfAAAAqhEAwbN83mn2Wqk4X6en2yv4EMbcZD+DPwAAAMQfa4Dg2eLiWrPXSoVmrwAAAIgfTwGQMeZKY8y0Mebpla9XNNjmI8aYHxhjZldu9/o/3HgbHQ1mStboaG+mmw0PO81eJecrzV4BAAAQN16nwH1S0r3W2s8YY94t6VOS3thgu7+21n7At9ElzOSkNDsbzOv0Qi7nNHt98knpqqvodwQAAID4aRkAGWMulfQqSf9q5anPSvpjY8wOa+3Jdl/QGDMsabju6V3t7gfhyOWkgQHnKwAkEccpAEg2L1Pgdks6Ya0tS9LK1+dWnq/3DmPMt40xf2uMaZYfmJA0X3d7pO2RI1C9mlbn9bWp5gYgQBynACDB/CyC8ElJe621r5R0t6T/YozZ3mC7SUl7627X+TgO9MDkZHgdpicnO6/mls9LCwtOxToA8IjjFAAkmJc1QMcl7TTGZK21ZWNMVtJlK8+vsta+UHX/vxljjkv6SUl/X7fdoqTF6ueMMR0OH2huenqtbPfBg9LDD7NuCUBrHKcAINlaZoCstT+QNCvpnStPvVPSTP36H2PMzqr7o5Iul/SUbyMF2jQ1tVa2+8IFynYDAADAexW4X5P0V8aYD0s6I+mXJMkY84CkD1trvyXp48aYV0sqS7og6T3VWSEgaOPjTrnuSkXatImy3QAAAPAYAFlrvyPptQ2ev6Hq/s0+jgvo2tiYU7Z7cVE6fJjpbwAAAPCeAQIio51qdLmccyP4AQAAgEQAhBgKqxodAAAA4s/PMthAolFSGwAAIP4IgAAP3JLa8/NOSW2CIAAAgHgiAArY6Gh7a1gQDZTUBgAASAbWAAWM9SvxREltAACAZCADBHjgltTeu1d6+GGqygEAAMQVGSDAI0pqAwAAxB8ZIAAAAACpQQAEAAAAIDUIgAAAAACkBmuAkGiUHAcAAEA1AiAkGmXHAQAAUI0pcAAAAABSgwAIAAAAQGoQAAEAAABIDQIgAAAAAKlBAAQAAAAgNQiAAAAAAKQGARAAAACA1CAAAgAAAJAaBEAAAAAAUoMACAAAAEBqEAABAAAASA0CIAAAAACpQQAEAAAAIDUIgAAAAACkBgEQAAAAgNQgAAIAAACQGgRAAAAAAFKjL+wBAF6MjoY9AgAAACQBARBiYXIy7BEAAAAgCQiAAI/IQgEAAMQfARDgEVkoAACA+KMIAgAAAIDUIAACAAAAkBoEQAAAAABSgwAIAAAAQGoQAAEAAABIDQIgAAAAAKlBAAQAAAAgNQiAAAAAAKQGARAAAACA1CAAAgAAAJAaBEAAAAAAUsNTAGSMudIYM22MeXrl6xUNtskaY+41xnzXGDNnjPkV/4cLAAAAAJ3zmgH6pKR7rbVXSrpX0qcabPOLkkYkXSFpTNJHjDGX+zBGAAAAAPBFywDIGHOppFdJ+uzKU5+V9CpjzI66Td8u6c+ttRVr7UlJRyS9zc/BAgAAAEA3+jxss1vSCWttWZKstWVjzHMrz5+s2m6PpO9VPV5Y2aaGMWZY0nDd0y+TpGeffdb7yCPo/Hnn6zPPhDqMdaDAD2sAAAS8SURBVPwc1/nzUqXifI3azwmgO1V/g7NhjiNsST5OAUCc+XWc8hIA+W1C0u82+sZ1110X8FB6Y+/esEfQmJ/j+sd/jO7PCaBrV0j6btiDCFHij1MAEHNdHae8BEDHJe00xmRXsj9ZSZetPF9tQc4Vsm+uPK7PCLkmJd1X99w+SQ9L+l9W9pMk85LCChV69dp+7LfTfbT777xu72W7VtvskvSIpOskJekycRI/w37tO2mf4z2S/l7SMe9DSySOU/F/7ST+//a67UbbcJyK12sn8XMcieOUsda23siYKUl/Ya39jDHm3ZJ+2Vr7M3Xb3CLpnZLeLGm7pBlJb7DWthzgSrGEeUl7rbXPtPUTRJwxxlprTZJe24/9drqPdv+d1+29bNdqm6R+jpP4GfZr30n7HCf1M+yHJL83Sfw/nsT/3163TeP/8SR+hv3ad9Q+x1H5DHutAvdrkv6dMeZpSf9u5bGMMQ8YY35qZZtPy4nG/kXSY5I+6iX4AQAAAICgeFoDZK39jqTXNnj+hqr7ZUm3+je0xPgPCXxtP/bb6T7a/Xdet/eyXZi/yzAl8TPs1775HCMJkvh/PIn/v71um8b/40n8DPu176h9jiPxGfY0Ba7ng0hoShbpwucYccdnuDneGyQBn2PEXdBT4HptUU60txj2QIAu8DlG3PEZbo73BknA5xhx58tnOBIZIAAAAAAIQlQyQAAAAADQcwRAAAAAAFKDAAgAAABAahAAAQAAAEgNT32AwmKM2Szpk5LykirW2omQhwS0xRhzkaT/JOlfWWt3hz0eoBPGmJ+W9H9IGpC0aK39tyEPKTI4TiEJOFYh7to9TgWWATLG3GOMmTfGWGPMT1Y9f6UxZtoY8/TK1yuq/tlbJf29tfb9ks4ZY34qqPEC9Tr5DFtrX7TW/htJT4UyaKBOh5/jR621v2ytfbek3caYoVAG32Mcp5AEHKsQd0Ecp4KcAndE0hskfa/u+U9Kutdae6WkeyV9qup7L5P0zMr9eUmX93aIwIY6+QwDUdPx59gY83OSnrTWFno+ynBwnEIScKxC3PX8OBVYALQSmR2vfs4Yc6mkV0n67MpTn5X0KmPMjpXHC3IOLlr5Wv9GAIHp8DMMREqnn2NjzC2SXmOtvT2osQaN4xSSgGMV4i6I41TYRRB2SzphrS1L0srX51ael6T7JY0bY/6jpB+z1n4znGECTbX6DMsYc6+klxtjPmmM2RvOMIENbfg5Nsa8RdLHJL1k5XOcppMmjlNIAo5ViDtfj1ORLoJgrV2SdEvY4wC6Ya39DUm/EfY4gE5Za78iaVfY44gijlNICo5ViLN2j1NhZ4COS9ppjMlK0srXy1aeB+KAzzCSgM9xc7w3SAI+x4g7Xz/DoQZA1tofSJqV9M6Vp94pacZaezK8UQHe8RlGEvA5bo73BknA5xhx5/dn2Fhr/Rrbxi9kzB/JKRf6EkmnJP3QWvsKY8zLJf2VpIslnZH0S9ZayjAicvgMIwn4HDfHe4Mk4HOMuAviMxxYAAQAAAAAYQt7DRAAAAAABIYACAAAAEBqEAABAAAASA0CIAAAAACpQQAEAAAAIDUIgAAAAACkBgEQAAAAgNQgAAIAAACQGv8/YlsNlTPYs54AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_trace = partial_pooling_trace['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": 21, "metadata": {}, "outputs": [], "source": [ "with Model() as varying_intercept:\n", " \n", " # Priors\n", " μ_a = Normal('μ_a', mu=0., tau=0.0001)\n", " σ_a = HalfCauchy('σ_a', 5)\n", " \n", " \n", " # Random intercepts\n", " a = Normal('a', mu=μ_a, sd=σ_a, shape=counties)\n", " # Common slope\n", " b = Normal('b', mu=0., sd=1e5)\n", " \n", " # Model error\n", " sd_y = HalfCauchy('sd_y', 5)\n", " \n", " # Expected value\n", " y_hat = a[county] + b * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=sd_y, observed=log_radon)\n", " " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [sd_y, b, a, σ_a, μ_a]\n", "Sampling 2 chains: 100%|██████████| 3000/3000 [00:12<00:00, 247.41draws/s]\n" ] } ], "source": [ "with varying_intercept:\n", " varying_intercept_trace = sample(1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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dy1NNjo9qdWmWU3pAj6jt+8IpxwjF0l5MoZSCRkRzynFhZW1HKeTEsTFq+yXhSiEViSVAvPG43whZlInavi8EWg9SHQQXVtZ0ZWNrx8emJzjCBHpFbd8XSiEZO7M4o8mu8/2T46PUjoE+UNv3hTk0AN5EM4eG6lDbBwBkizk04ADUsoF4EGjIyjDNy35vXZNqmQi3cMDjC4EGNzzW/IdR9/MhQOvH7WN8IdDQqNRCrG6EWLNYh+YLgYZGeR6QuXUNDsM6NF9oOQL74NY1OAzr0HxhHRoAb1iHBq7liGbQ9ALgAYGWoSqLGP1W2w/jeY4N4GDOFwKtYrT4huNx/xGyaKO27wuBVhGPAzGGQ5BhN2r7vhBoFclp8Gufdum+FQ03O0QOqO37Qm0fQzs+Pqpzyyd16dS8pieoMCMf1PZ9obYPwBtq+6C2j/7R0gKQCgItEnWUTMqu3LflNJ+IvHBA6AuBVqCVWJ2U9i3hjG7U9n1JPtBSGkxRPQIL/aC270vygcYAdbBrm9u6e+Wibtxs/VSapKkJ6vZAL6jt+0JtP3PHx0d1fnmuU7efmqB6DPSK2r4v1PYBeENtH9T2US8aXgA8IdAyUXU5pqzKP3OeiAkHdb4QaCWjVTmcpvcfgYp+UNv3hUArWfeA2PTgjP7t9ZoRctgPtX1fCLQKpToQLqysdY5K26aLdiSnW5ATavu+UNtH37qrytMTY7p0al7nlk8SZsgOtX1fqO0D8IbaPgaq7fMODQCQBObQMtKuGD/86JZGjphu3gw6wdwXMDBq+75wyjFSXhqUqRZf0KhoTjl2F6SOmHTiGNdBLQtXCnHES+BUrcnnSZiiadT2fSHQKuJxsN2rbs9RJTA4avu+UArJSLtifMSkoyOmIxJVY2AI1PZ9YQ4NgDfRzKGhOtT2AQDZYg4NfaGmDMArAg236bW5eNgtYzwWY4AycYDnC4GWKA/LBvrdBgIQseH2Mb4QaInaHQ4eAg5IDevQfCHQMlHWu5+50xe0vrnd+fvk+Kgunpov5WsDsWEdmi+0HNGX1aVZTU/cunXM6tJs05sENIZ1aL6wDg2AN6xDA9dyRNpolAE4CIGGylRZRDlsycCgaFqiHxxk+UKgRYKWYj087mdC1i9q+75QCgGc8xiyaKG27wvv0CKR41H67psnHv/8UR0dOcLpHbhBbd8XAg1unVmcYX4Cru31PYrmUNsH4A21fVDbRz5olwHYjUBDo8ooPAxb4c9xfhLl4MDKFwINO+TYqGviOROiaaC27wuBhh26B9ocw60OhFk6qO37QqBhX54H3mub27p75aJu3GyNJiZpamKMo2PUitq+LyysRpSOj4/q/PJc58r/UxNc6Rz142r7vlDbB+ANtX1Q208VTSoAOByBVoMyyxVlXmXe8xwZEAMONn1JNtBo6B2uyX1EmCIF1PZ9iT7QCK447X7dCDjEiNq+L9EHWg4DIRV1wCdq+75Q248AFXXAJ2r7vlDbB+ANtX0MVNvnHRoAIAnRz6HBp2ub27r37GWtb25LkibHR7W6NEulGUmhtu8LpxyRRFM0h3JQRqI55biwsrajFHLiGGWtsnClkAqlMOinLLbXhwBOA7V9Xwi0HjEA9WdhZU1XNrZ2fGyapQZIDLV9XyiFoBJnFmc02TWXMDk+SqUZyaG27wtzaAC8iWYODdWhtg8AyBZzaECPqGgDvhFoyEpZbchhb+NDySgNHOT4QqChUbHV7cvi9XkTtP3h9jG+EGhARgiscrEOzRcCDY2KZYBdWFnT1Y2tTr336Ijp/PIcp5cyxzo0X2g5Aj04szijqeL2PdMTY4QZJLEOzRvWoQHwhnVo4FqOQBlorgFxItCQrDKahMPU82OZH8TgOPjxhUBD47xW2IdV5fMiLH2gtu8LgYZKpBpSTSHAfKK27wuBhkrEPADPnb7QudO21LpTwMVT8w1uEbyitu8LtX1gl9WlWU13VfRXl2ab3iQ4RW3fF2r7ALyhtg9q+6gP7S4A3hBo6MlBJY/9qu0xz6MBveDAzhcCDZU1Env9ugQfYkVt3xcCLWNU64HhUNv3hUDL2DDvjKi2A9T2vaG2j4FQbQeo7XtDbR+AN9T2QW0f+aBdBmA3Ag21qqKIMswV8bvRtkS/OLDyhUDLDM3G/TW9bwjU+FDb94VAS1TTgzP6N/nD7yDUIkNt3xcCLVEpD4wLK2u6urHVaSYdHTGdX57jVA9qR23fF2r7iM6ZxRlNdS0ZIMzQFGr7vlDbB+ANtX0MVNvnHRoAIAnMoaFn1za3de/Zy51LXk2Oj2p1aZbTfcgWtX1fOOWYCc+tx5QLLBhINKccF1bWdpRCThwbo7ZfEq4U0iDPgeGdp31HuKIf1PZ9IdBKksNAuLCypisbWzs+Nj3BESnyRW3fF0oh6NmZxRlNds0PTI6PUlNG1qjt+8IcGgBvoplDQ3Wo7QMAssUcGvZEHRlAbAi0hFTVFizr9izdcijRIH0c+PlCoJXEU/U8BrHuL4IY3bh9jC8EGtCHvYKYkMsX69B8IdBKktqgtteplO6jUa6KALAOzRtq++gZ8wWoSTS1fX4mqjNIbZ9AA+BNNIGG6nAtx0xwVAgAtyPQGjZs22/YSn1qc39AnTi49IVA2yXWOvmg6n6+BChSQm3fFy59tQsDbrVyO2BA2qjt+8I7tD14D7X2aY7uW7lQowfqR23fF96hRej4+KjOLZ/UpVPzmp7g1hVAU7h9jC/U9gF4Q20f1PaB/dBGA9JHoMG1Kkok3D0AZeFAyRcCDT2hnXiwWPYPwVsuavu+EGiQFM+AjMMRWvWhtu8LgQZJ6Q+C1za3dffKRd242Rp9TNLUBMscMBxq+75Q20cWjo+P6vzyXGeZw9QEFWsMj9q+L9T2AXhDbR/U9lEvGl4APCHQMlJl8aPMKnzq83lIBwd1vhBoFaM92L8Y9hmhC4navjcEWkliGITRH0ILh6G27wuBVpLcBr+FlTVd3djqtIOOjpjOL89xugVZobbvC7V9DOTM4oymigr89MQYYYYsUdv3hdo+AG+o7WOg2j7v0AAASWAODVl44OFNfefZy7pxM+joiOnNS7N67onxpjcLkaO27wuBBpeqbI3euBn0kjc8UOrXzK0UhBZq+74QaGDJQQm87kOCtlrU9n0h0JDFoDf9ynd2rrQvtZYZXHnNCxvcIqSA2r4vlEKQhTcvzeroSKs8155DA4ZFbd8XavsAvKG2D2r7AIB8MYeGxlB5BlAmAg0Hqqu9V+btZ3bLofSCZnBQ5guB1gCvFe9Ued3fBG38WIfmC3NoDVi//x4GM7gNWvSOdWi+8A6tQbmG2sLKWueotm16YozTNYgO69B84R0aate9dmd6YkyXTs3r3PJJwgzRYR2aL6xDA+AN69Aw0Do0TjlGinYVAOxEoNWsiiJAmZX3XOf1gEFwYOlLNoFGo6w3de8nAhQxo7bvS7KBRoD5RYghFdT2fUk20FIdNKm8A35Q2/eF2n5kqLwDflDb94XaPgBvqO2D2j5QNVptgF8EGpJURymoyjsEtKU6F5wKDnB8IdAwEFqk9YhlP+cavNT2faEUAmBosQRv2ajt+8I7NAwkxyPyhZU1Xd3Y6jSijo6Yzi/PcYopY9T2feEdGtCjM4szmpq4tWSCMAO1fV+o7QPwhto+qO3XgVYTAPiURaBVNWFdVm07x/koIAUc4PpSW6Dl2oLqhbd9Q8ACvaG270ttgbZ7kPQ2iOeK8AIGR23fl8ZOOcY4kFLbBtCN2r4v1Pb7QG0bQDdq+75Q2wfgDbV9DFTb5x0aACAJWdT2kZ52XfrhjS2NjJhuPh46p3w4DYy6UNv3hVOOqFzMjdYYy0sJiOaU48LK2o5SyIljY9T2S8KVQjIUc1jEwPv+JXCbRW3fFwItcrkOaN1Hxm0cIaNu1PZ9oRSCKLXr0kfUWg/YDjNq06gTtX1fmEMD4E00c2ioDrV9AEC2mEODa9SiAfSKQEMlqmgHlnW7nm65lmpQDg64fCHQIue9Vu5dDPuP0PWL28f4QqBFbq/BLoZBGnsjvOLCOjRfCLQEpTQotk/pXNnY6nyM9WbwgnVovtByhGvHx0d1bvmkLp2a1/QE633gC+vQfGEdGgBvWIcGruUIlI0WGxAPAg3JqLoMw7IB7MYBjy8EGkpDu7J/3vcZgXswavu+EGi4jfdBFuUgrIZHbd8XAg23yX2g6741jUm6Y8T0+OPilBJuQ23fF2r7wC7dVeypiTGdX57Twz/xQp1bPkmYYQdq+75Q2wfgDbV9UNsHekU7DUgPgYYolVlcKaOOn/u8Y644MPKFQENfaEDurYn9Qog2j9q+LwQa+rJ+/z2EmhP7vQ4EXX2o7ftCoKFvKQyYc6cvaH1zu/P3yfFRXTw13+AWIUbU9n2hto8srS7Ndq7ePz0xptWl2aY3CRGitu8LtX0A3lDbB7V9+EMLDEBdCLTM1VnwqOJq9bulML+HeHDA5guBVgJaf36k/loQ2L5Q2/eFQCvB7kEm9UEV9SPIfKK27wuBVgEGn1uoxyNl1PZ9obaPSlGPR8qo7ftCbR+AN9T2MVBtn3doAIAkMIcGN9oV6Ic3tjQyYrr5eOicxqEKDY+o7fvCKUdUwlPTk5JOdKI55biwsrajFHLi2Bi1/ZJwpRC4ChIvPOwTQjVN1PZ9IdASE/PA2X2028ZRLzyjtu8LpRC40a5AH5F0dMQ6YUYVGl5R2/eFOTQA3kQzh4bqUNsHAGSLObTMUDMGkCoCLUJltfbKvJ1LzGUUYFAcIPpCoPXBQ/3bq6b2DUGKJnH7GF8INBFUMWu/dgQbmsA6NF8INOU1GLZPkVzZ2Op8jLVewGBYh+YLLcfMHB8f1bnlk7p0ar5zWxfWzwCDYR2aL6xDA+AN69DAtRxRLRpdADwj0DJURglmmMp/TnOWSBsHeb4QaM6l2MBs4jkRoqgCtX1fCDQnUgyuOhFYaAK1fV8INCe8D8gLK2u6urHVaQMdHTGdX57j9AqyRm3fF2r76MmZxRlNFTX/6YkxwgwQtX1vqO0D8IbaPqjtozq0uQB4R6AlrKqiSVlX6fc+bwgchgM9Xwi0CtBY7A1X6EfsqO37QqCViCCLQz+vE+GHg1Db94VAK1HKg9+1zW3dvXJRN262fnpN0tQEV+hH3qjt+0JtHz05Pj6q88tznSv0T01QUQao7ftCbR+AN9T2QW0f5aLBBSAmBFqk6i6glFXV70XKc5FICwd9vhBoh6C5WL8Y9zkhnCdq+74QaIfoHqhiHGgxGAIKvaC27wuB1ofcBjmq+sDBqO37Qm0f+6KqDxyM2r4v1PYBeENtHwPV9nmHBgBIAnNokNSaL7v37GWtb25LkibHR7W6NEsFGTgAtX1fOOWYCG8NzNwKNChVNKccF1bWdpRCThyjNFUWrhTigLdgaUrT+4FARR2o7ftCoJUs1oF0YWVNVza2dnxsmoo+cCBq+75QCoGkVv14suvc/+T4KBVk4BDU9n1hDg2AN9HMoaE61PYBANliDg1Roi4NYDcCDS4M04oc5tY2sZZ44AMHVr4QaDhQ0/X7qjX5/AjT+HH7GF8INNwm9RBrGkGWDtah+UKg4TYxDLhzpy90LtMltZYZXDw13+AWIUesQ/OFliOitLo027mtzfTEmFaXZpveJGSIdWi+sA4NgDesQwPXckR+aJkBaCPQUJm6yyXD1Pd7FcP8IurDAZUvBJpjtA39Sf01IbD7Q23fFwLNqdQHTtSHkKoOtX1fCDSnGIQO1n1jxbbpiTFO+aBW1PZ9obaPKHXXpacnxnTp1LzOLZ8kzFAravu+UNsH4A21fVDbB/pFSw1IB4GGqFRZlqmi9s9caNo4IPKFQEMHzcryedqnhGv5qO37QqCho3vA8zQQoxwHvaaE3WCo7ftCoGFPqQ9w1P5RBmr7vlDbR5ao/aMM1PZ9obYPwBtq+6C2j7zQMAPQjUBD5eoomFC5RxM4qPKFQEsYTcXhxLj/COF6Udv3hUADIkJg+UJt3xcCLWEpD34LK2u6urHVaScdHTGdX57jdA9qRW3fF2r7iNKZxRlNTdyq3RNmaAK1fV+o7QPwhto+Bqrt8w4NAJAE5tAwsGub27r37GWtb25LkibHR7W6NMsMjpVCAAAThklEQVSpP2SD2r4vnHLMCDV0RCKaU47d1wQ9YtKJY2PU9kvClUIaEmNQxML7viVw80Zt3xcCrQS5DmoLK2u6srG142PTExyhIh/U9n2hFIKBnVmc0WTXfMHk+Ci1ZWSF2r4vzKEB8CaaOTRUh9o+ACBbzKGhZ1SUAXhGoGGgJmE/t2vJtTSD9HGQ5wuBFiHvVfbdqtheQhIecPsYXwi0CMQWYHVo7xOCDU1iHZovBFoEvAzac6cvdC5zJbVq+hdPzTe4RUCzWIfmCy1H9Gx1aVbTXbdsWV2abXqTgEaxDs0X1qEB8IZ1aOBajogfrTEAgyLQUJqyyyv9LA3Yj5f5R6SJAzBfCLQE0Yq8xeO+IGTTQW3fFwItQb0MmB4H+hwQZmmhtu8LgZYprwPrtc1t3b1yUTdutkYJkzTFLWngFLV9X6jtw5Xj46M6vzzXWR4wNUEVGn5R2/eF2j4Ab6jtg9o+qkWjC4BnBFqiqi59lFGp34vXuT1gLxzk+UKgDYCGYHU871vCFrtR2/eFQBvAfgOb58EYw+t+fQk3SNT2vSHQSpTqILewstY5Cm2bLtqHnF5Bzqjt+0JtH4fqriZPT4zp0ql5nVs+SZghe9T2faG2D8Abavugtp8DWlUAsDcCrWZlFkfKrM6nOv8HVIkDTF+yDTQaiTt53x8ELjyitu9LVoHmfdAGEBdq+75kFWgpHOW3T3Fc2djqfOyISSeOcUV6oG7U9n2hth+Z4+OjOrd8UpdOzXeuSE9dGGgGtX1fqO0D8IbaPgaq7fMODQCQhKzm0BC/a5vbuvfsZa1vbkuSJsdHtbo0S1UajaC27wunHFG5GNulKRSIIhbNKcfu65xSzioXVwqBpDgDxJvY9yGBXA9q+74QaAlKeTBbWFnbsWRBal35n6NiNIHavi+UQhCVM4szmuyao5gcH6UqjcZQ2/eFOTQA3kQzh4bqUNsHAGSLOTS4Ri0aQK8INFSiipZgmbfLaUu5QIPqccDlC4EWqdhr5V543I+EbDy4fYwvBFqk9hv0PA7Q6E/7NSTY/GMdmi8EWmJSGwTnTl/oXOZKatX0L56ab3CLgFtYh+YLLUe4tro027lNzvTEmFaXZpveJKCDdWi+sA4NgDesQwPXckTzaH0BaAqBlpk6SyPU7JE6DuB8IdAqQtuwGjHuV0I4XdT2fSHQBhTjwIp6EWTpo7bvC4E2IAarvV3b3NbdKxd142brp9wkTXF7FySK2r4v1PZRquPjozq/PNep2k9NUGVGuqjt+0JtH4A31PZBbR8Ho5EFIGUEWiL6Lan0WqlnrhDYHweJvhBoDnhuTJa1bQQjUkRt3xcCzYH2YO852IbV/dwIN6SC2r4vBJojVQ70Cytrurqx1WnzHB0xnV+e4/QIMARq+75Q28/EmcUZTXVdtZ4wA4ZHbd8XavsAvKG2D2r7wG600IB8EGhwp6pyTJlX/6fYAokDJm8ItMyl3Kyskvf9RuDWg9q+LwRa5nJYMpADAqwZ1PZ9IdAgKd0Bkav/o0rU9n2hto+kcfV/VInavi/U9gF4Q20fA9X2eYcGAEgCc2hw4drmtu49e1nrm9uSpMnxUa0uzVKBhmvU9n3hlCP6FmsjMtXiS4KiOeW4sLK2oxRy4hiFo7JwpZDIxRoUsfC+fwnc+FDb94VAcyTnAW1hZU1XNrZ2fGyaej2co7bvC6UQuHBmcUaTXXMPk+OjVKDhHrV9X5hDA+BNNHNoqA61fQBAtphDQ9KoVQP5INAQhTIaisPcPibnwg72xwGTLwQaSuW9Gj8oD8+LUPWH28f4QqBhaB4G+1QRYr6xDs0XAg1D8zzotk8Jda9x44oOKAvr0Hyh5YikHR8f1bnlk7p0ar5zCxnWC6EsrEPzhXVoALxhHRq4liP8oP0FoG4EWubqKHQMU5c/iOe5O+SBAzdfCLSS0firT+z7mkCOH7V9XyiFlCj2ARb14vslftT2feEdWok44r7l2ua27l65qBs3Wz/tJmmK28EgMdT2feEdGipxfHxU55fnOlX5qQkqzUgPtX1fqO0D8IbaPqjtI000yQD0gkBD7YYpQwyyBIC5TVSFgy1fCDR0pNq6q+N5EZp5orbvC4EGlGB3aBJweaC27wuBhg6vg/Dc6Qta39zu/H1yfFQXT803uEVAC7V9X6jtw73VpdlO/X96YkyrS7NNbxIgidq+N9T2AXhDbR/U9oFuNNCAvBBocK+MluKgV/z3Oq8IHzho8oVAw0BSrfjvRuUfB6G27wuBhr7lEmZ1OWh/Ena+Udv3hUBD32IZZKn7o2rU9n2hto9kUfdH1ajt+0JtH4A31PYxUG2fd2gAgCQwh5axa5vbuvfs5c480+T4qFaXZqkdAz2itu8Lpxwj5LllGEthBK5Fc8pxYWVtRynkxLExavsl4UohNfAcJh40vX8IVNSJ2r4vBFqfUhowF1bWdGVja8fHpic4wgR6RW3fF0ohGTuzOKPJrvP9k+Oj1I6BPlDb94U5NADeRDOHhupQ2wcAZIs5NAyEujIAbwi0TFTZPhz01iwHSal8g3RxYOcLgVaipivrKfG2LwlY7IXbx/hCoJVokEHP28CNve33OhF0eWMdmi8EWsNiHRDbp1q617FxpQTkhnVovtByxECOj4/q3PJJXTo137lFC+twkBvWofnCOjQA3rAODVzL0RPaTwBQLwKtBIcVO/artcc6fwaghQNXXwi0Q1TZQuz1axN8gE/U9n2hFAIAA6K27wvv0A4x6LujudMXOneCllpXsr94ar6szQLgALV9X3iHVpHVpdlOnX16YkyrS7NNbxKAklHb94XaPgBvqO2D2j78oxUGoCoEGkoxSBu0n6v00/SERxyg+UKgZS6WiyOXvZ0EJMpAbd8XAi1jsYRZFXY/dwIOg6C27wuBlrG6B/GFlTVd3djqNIqOjpjOL89xigbRorbvC7V91ObM4oymupYyEGaIHbV9X6jtA/CG2j6o7SNuNMYADINAQ+nKKJv0U+nfD0UPVI2DMF8ItIzk1mps4vkSonmhtu8LgQaUqDtECbf0Udv3hUDLiPcBljsUIDbU9n2htg83uEMBYkNt3xdq+wC8obaPgWr7vEMDACSBOTS488DDm/rOs5d142bQ0RHTm5dm9dwT401vFnAbavu+EGgYWB21+Bs3g17yhgcq+/reizLwjdq+LwSaQ7mtF2tSjPuaEPaD2r4vBJpDuQ9Y0698p27cvNU7OjpiuvKaFza4RcDeqO37QikE7rx5aVZHR1pFt/YcGuARtX1fqO0D8IbaPqjtAwDyxRxa5qgdA0gFgRaZKlt5ZdyypVvu5RakjwNCXwi0IcVY+65LbPuGAEa/WIfmC4E2pPX774lu4Mbedr+OBBwOwzo0Xwi0EsQ88LVPmVzZ2Op87IhJJ46NcaQJHIJ1aL7Qcszc8fFRnVs+qUun5ju3bmE9DdAb1qH5wjo0AN6wDg0DrUPjlCNcoTUGYFAEGoZWVSmm7GUE3WKe94QfHID5QqBFiFbl8GLbhwSwT9T2fSHQnItt4MVwCK64UNv3hUBzLrcBjmUEiAm1fV+o7cMVlhEgJtT2faG2D8Abavugtg90o4EG5IVAgwtVl1/KXAKQ27wm9sdBky8EWkZoTJYjlv1I8FaP2r4vBFpG9hrgYhmc0b9eXltCbzjU9n0h0DKX4oC2sLLWOWpum54Y43QQSkdt3xdq+0hOd5V6emJMl07N69zyScIMpaO27wu1fQDeUNsHtX3kiaYZAIlAgwNlFlPKquenOLeI8nEw5QuBBkm0HXdran8QpHGhtu8LgZYhwgsoB7V9Xwi0DKX2LmDu9AWtb253/j45PqqLp+Yb3CLkgtq+L9T2Eb3VpdnOlfmnJ8a0ujTb9CYhE9T2faG2D8AbavsYqLbPOzQAQBKYQ8PArm1u696zlzvzV5Pjo1pdmqW2jGxQ2/eFU44ZiqHlmFpxBX2J5pRj93VDj5h04tgYtf2ScKWQyMQQLE2Jad8Qvvmitu8Lgdag2AfChZU1XdnY2vGx6QmOUJEPavu+UArBwM4szmiya75gcnyU2jKyQm3fF+bQAHgTzRwaqkNtHwCQLebQIkdtGABaCLQaVd3c49YpQL04oPQl+UCLqf7thfd9RuDCC24f40sSgeZ9AAaQJtah+ZJEoOV4xN59hYK26YkxTnkANWIdmi+0HCPVvf5lemJMl07N69zyScIMqBHr0HxhHRoAb1iHBq7liOrR6gLgFYGGHfop2By2TCDHuU3khQM8Xwi0hDXd/hzm/ycMEQNq+74QaIlpOsTKQJghFtT2fSHQElNlGCysrOnqxlanEXR0xHR+eY5TLMgWtX1fqO2jZ2cWZzQ1cWupAGGG3FHb94XaPgBvqO2D2j5QJxpugC8EGpJXR1GmrDsdHISyjD8c1PhCoGEgKbQpYxPrPk85iKnt+0KgYSDdg1SsAy2Gk3JQ9Yravi8EGoaW68A2d/qC1je3O3+fHB/VxVPzDW4R6kZt3xdq+8CAVpdmNd21jGF1abbpTULNqO37Qm0fgDfU9kFtH2miSQagFwQaSlFXMaSOeny3XOcH0RsOtnwh0JyiOehDKq8DwVwNavu+EGgNS2XAhB+EV32o7ftCoDWMwedw1OPhFbV9X6jtwz3q8fCK2r4v1PYBeENtHwPV9nmHBgBIAnNocOva5rbuPXu5M382OT6q1aVZatFwg9q+L5xyRC2abnNSvolKNKccF1bWdpRCThwbo7ZfEq4Ugp40HS5NaOo5E6Rpo7bvC4GWoVgG2YWVNV3Z2NrxsekJjoDhB7V9XyiFwK0zizOa7JqPmBwfpRYNV6jt+8IcGgBvoplDQ3Wo7QMAssUcGtyjGg2gFwQaalNG03CY28fEUoZBPDjY8oVAQ0fqdf66nx8Bmj5uH+MLc2hARVI/QADr0LzhHRo6vL6j4PYx8Ip1aL7wDg3ucfsYeMU6NF9YhwbAG9ahgWs5on60vAB4QaBlqKqywjCV+oN4ndsDOKDzhUArEa22asS2XwngfFDb94VAK0FsAy6qQZDlh9q+LwRaCXIeyK5tbuvulYu6cbP1U22SprjFCzJBbd+XvgPNzO545JFHqtgWROqN33qXXvH29+va5mM6Pv4E3Tf/DK2vrze9WYjUXXfdNSnpegjhs81uSceIJF2/fv22T9w3P6FXvP3jurb5mO7ke79UXft7pNd/03dtv11h7esfAUB/eq5qV83MvkbSu5vejow9P4Twnl4eOEig3SHpzkG2ag93qvWN8nxJtx/+pC3X587zzut5S4M9dzfv0MzscyTNSPq4pJt7PMT7a/uIpLua3og9HLbfRiQ9TdKDIYQ/7+UL9n3KsfgmW+/33+3FrLN+8rqXo7G65Prced55PW8p/udeDKb7vkPw/vzMTF63q3DQfnu4n6/Jpa8AAEkg0AAgbf+q6Q2oC4EGAAkLIdzX9DbUpelA+6RaRw+fbHg7mpDrc+d55yf1557686tK6ftt0KvtAwDgStPv0AAAKAWBBgBIAoEGAEhCbYFmZs80s/ea2e8Vv0/v8Zj7zGzDzB4qfr2+ru2rgpm91sweMbNgZs/a5zEjZvZ6M3vYzK6a2T+oezur0ONzT+r1liQzGzezd5rZR8zsA2b2K2Z2bI/HjZrZW4vX/HfN7Oub2N6y9PG832hm17te81c2sb1l6eX7HDv1+r0yiDrfof2CpNeHEJ4p6fWS/t0+j1sNITy7+PV99W1eJX5V0tdK+n8HPOY7JE1Jmpb0PEn3FdfLjF0vz11K6/WWpCDpp0IIXxRC+DK1rnRw/x6P+0FJnwohTEn6Bkm/ZGZjNW5n2Xp93pJ0f9dr/pr6NrESvX6f45Z+vlf6UkugmdmEpK+Q9JbiQ2+R9BVlpbJXIYT3hBA+esjDXizpDSGEx0MIj6r1A/J3qt+6avX43JMTQvjjEMLFrg89IOkL93joi9U6yFMI4Yqk35T0gso3sCJ9PO+k5Pp9Powqv1fqeof2VyV9LIRwU5KK3/+g+PhuLynehv53M3teTdvXpOPaeXR3TXvvl1Ql+3qb2RFJ3yvpv+7x6WRf90OetyQtm9kHzexXzexLatw0ONPD90pfvJVCfkGt20Z8maTTkn7NzMYb3iZUJ/XX+2clbUn6uaY3pGYHPe9XSpoKIfx1Sb8i6TfMrOf7XSE5pf6M1BVoH5X09PY3bvH7FxQf7wghfCKEcKP487ni86lPtF7Tzrfbx7Vrv6Qq5dfbzF6r1rzoi0MIj+/xkCRf98OedwjhY+2PhxBWJY2pvNtRISI9/Iz0rZZACyFsSHpI0rcXH/p2Sb9dzBl1mNnTu/78bEmTkj5SxzY26G2SXmZmR4o5xRdJenvD21SLVF9vM3uNpK+U9KID7uP0NknfUzx+Wq37bf1GPVtYjV6e967X/G+pdX+xj9WzhfCix5+R/oUQavkl6YslXZb0e8XvX1R8/J2Svqr485skfUjS+yU9KOmFdW1fRc/5dWrduO6zkj4h6cN7POcRST+vVtPnYUnf3fR21/jck3q9i+f0pWq1uD6i1kHcQ5L+S/G5hyR9QfHnJ6oValeLx35j09te0/P+H5I+WLzm75b03Ka3fcjnvef3Ob8G+14Z9hfXcgQAJMFbKQQAgIEQaACAJBBoAIAkEGgAgCQQaACAJBBoAIAkEGgAgCT8f5jj0Ds2mRW3AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from pymc3 import forestplot, traceplot, plot_posterior\n", "\n", "plt.figure(figsize=(6,10))\n", "forestplot(varying_intercept_trace, varnames=['a'], ylabels=['']);" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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PndCUAbfL2pyHqb314C06sH1z+uPjh37SP29vJ0navX61nruunsb17aDXbvsvLXnz5UzLExIS9GrPRL35wM3asWKRT/ogHHg7RJAhhUD4KO7f54xxbNX0SenLs8axBQsWSMocx479tFuSM3EsISEhxzg2rm8H4hjgJxzBQsD9vGuHvvnofQ1473OViIzS/CfvVsu61yi2dn1J0rV3Pazr7hmYaZ1V0ybqrlem6Pih/Zo4caIq3/2klr79qpIe+JuMKdwwzDotE9Vv3AxdOPu7xvXpoCbtuqQv37RykUZvOqZD32/RtEH3KrJktBpcfV3RGh6GOEoLFF/F+fufNY6980hvNW7XOcc41i0hVt9tOpYpjq2b8666D3rBkTi2aeUivbBmX7Y41m/cDEkijgF+wBEsBNwve35QrWatFFUqRiVcLrVv317bli7Ic50Il0sXz53TxXNnFRkZqV/379HJo4dVr9W1Ra5PVKnSqtGkhX49sCfbc3GNmqnjg4O1dvbkIv8fAEB4yBrH6rb6L6/iWAmXizgGhBGOYCHgqtZvos/H/0O/J/+myJLR+mzBApk/NU1/fu2sydo0f7ZqxLdQ90EvqFS5Ckq6/zF9NHKwIqOjtfyjmer+wF/VecDwfP/XrKceVmTJaM0s5dLhk2dlIrLvY/g9+Tf9tGWDrn9wsH4//mu25+OaNNeK98YXrdEAgLCRNY59v2qJasa3SH8+Yxx76F13/MgYx+4YMUELxj7rVRyTpNSLF4ljHt5OJMbEY/AlEiwEXJV6l6t9v79qyoBeiipVWl2vaqGtp9zPXX17P13/4GDJGC2eMEqfvvaMej03TnGNmmnAewslSbt3b1fZytVkrTRj2F9UwhWpboOeV9lKVbL9r94vTlLN+JYanhCrYZ9u1NTH7kp/bu/mrzSubwcZE6Gk+x5V1fqNtXv96uwVzmVsPLxHQAQQDrLGseqXN1VECfcmVtY4NnjwYF3+15cyxbE9G9Z4Hcck9zlYWeNYQkKCjp5LK3ZxrDgPUUXwIcFCUGhz691qc+vdkqSTH76mShUrSFKm4HLVbX/OFEgkyVqrkSNHquNTE/TJmOHq9PAwHT/0k9Z88La6PvKUV3XIOEY9L4f+s0VV6l7u1WsjZwREAOEiYxz7/H9HqlzVOEnZ49inw+5RxghirdXSyWN15+i3HYljl84ZzgtxDPAtzsFCUDj92y+SpOTDB/Tvf/9bLW+4TZJ08pef08tsW7pAVes3zrTexnkz1b17d5UqV0EXz7mH/JmICF08d9Yn9Tz8wzYt/b/XlHjH/T55fQBAaMoYx7Z9+WmuceyKK67ItN7GeTPVuG0n4hgQRjiChaAwfch9OnPiuCJckXp/4nh9U859BOuz11/Q4R+2ysioYlwt3frUK+nrXDh7Rhvnz9KMNV/q1a0n1PauhzV96H0q4YpUn1FvOVa3S0MuDhw/pTIVY3Xz0H8w8xIAIJOMcazHsDEqlUsc+2LmO5rqybkuxbH7x38oST6NY+P6dtDFc2eJY4AfkGAhKDw0ZX76/Y4JsfrGM7yh98gJua4TVSpGD771sSIjIyVJda+8Rn+bvSLX8v/v7U8yPa4YV1t/+3ClJKle62tVr3X2mZvqtb5Wz63YreEJsV4NZQMAFC8Z41hGWeNY9eqx0s/ueHIpjl3iyzgGwH8YIggAAAAADiHBAgAAAACHkGABAAAAgENIsAAAAADAISRYRZCSFn4X6gMAQCLGIbx5+/nm+wBvMItgEXCRVABAuCLGIZzx+YYvcQQLAAAAABwS8gnWwoUL1ahRIzVo0ECjR4/O9vxrr72m+Ph4NW/eXB07dtS+ffskSfv27VOrVq3UsmVLNW3aVJMmTZIknTp1Si1btky/xcbG6m9/+5tf2wRA+n71F3q1Z6Je7tFGy955Pddyc+bMkTFG69evlyT9+uuv6tChg8qUKaNHHnkkU9mnnnpKtWrVUpkyZXxad8AXrLV69NFH1aBBAzVv3lwbN27MViavGLZv3z517NhRzZs3V1JSkg4cOJC+PKd4CCB3Bfk+SlJSUpIaNWqU/p08evSoJGnFihW68sor5XK5NGfOnGzrnTx5UjVq1MgWxxAaQnqIYGpqqgYOHKjFixerZs2aatOmjXr06KH4+Pj0MgkJCVq/fr1iYmI0ceJEPfHEE5o1a5aqV6+uNWvWqGTJkjp9+rSuuOIK9ejRQ3Fxcdq8eXP6+q1atdJtt90WiOYBxVZaaqrmjhmuByZ8qHJV4zT+7i5q0v4GKcsQjVOnTmncuHG6+uqr05dFR0drxIgR2rp1q7Zu3Zqp/M0336xHHnlEDRs29Es7ACd99tln2rlzp3bu3Kl169apf//+WrduXaYyZcuWzTWGDRkyRPfcc4/uvfdeLV26VE8++aSmTZuWZzwEkLOCfB8vmT59ulq3bp1pWe3atfXuu+/qlVdeyXGdp59+Wu3bt3e83vCPkD6C9fXXX6tBgwaqV6+eoqKi1KdPH33ySearnHfo0EExMTGSpMTExPQ9dlFRUSpZsqQk6fz580pLS8v2+jt37tTRo0fVrl07H7cEQEb7t25UpZp1dFnNOnJFRqlF11u1Y9ln2co9/fTTeuKJJxQdHZ2+rHTp0mrbtm2mZZckJiaqevXqPq074CuffPKJ7rnnHhljlJiYqOTkZB0+fDjX8hljWEqa1fbt29WxY0dJ7th4KV4WJB4CxV3WSS4K8n3Ma2KMOnXqqHnz5oqIyL4pvmHDBh05ckRdunRxpvLwu5BOsA4ePKhatWqlP65Zs6YOHjyYa/nJkyfrxhtvTH+8f/9+NW/eXLVq1dKwYcOy7a374IMP1Lt3bxljnK88gFyd/OWwylerkf64XJU4nTiaOXBt2rRJ+/fv10033eTv6gEB4W3MyxjDXBFGkbUbq//rUzV60zH9+dWpOnXqlJ7+8geN3nRMwz/7VtUbNlX1mrWUcOdAvXckyh9NAkLGpUkxLt2Wb9+j5WfLpj9OLV9VLy7dlqmMK8K9/XjfffepZcuWGjFihKzNezbCtLQ0DR48WC+//LI/mgUfCekEK6cPaW7J0Pvvv6/169dr6NCh6ctq1aql7777Trt27dLUqVN15MiRTOvMnDlTffv2dbbSAPKXz3c7LS1Njz/+uF599VV/1goIKG9inpQ9hnV7/Hnt2bBW4/p20J6Na1SuSnWVKOE+U6BCtRp6bPZyDfnka22cP0unfj3qfAOAsJLD91HZv4/Tp0/Xli1btHLlSq1cuVLTpk3L81UnTJigbt26ZdqZgtAT0udg1axZU/v3709/fODAgRzHjC9ZskQvvviili9fnj4MIqO4uDg1bdpUy5avUO87bpckffvtt0pJSVGrVq181wAAOSpXJU4nfv5jz/zJo4dUrnK19MenTp3S1q1blZSUJEn6+eef1aNHD82dOzfbOHcglI0fP15vv/22JKlNmzYFinlSzjGsXOVquvvVdyVJ58+c1tYv5iu6bLlM65WrXE1V6zXS3k1fSZ3iBeAPa2dN1jcfuROkmk0TlHzkUPpzJ44eUtnKVbOtU6OGezRG2bJldeedd+rrr7/WPffck/v/WLtWK1eu1IQJE3T69GlduHBBZcqUyXEiNwSvkE6w2rRpo507d2rPnj2qUaOGZs6cqRkzZmQqs2nTJj300ENauHChqlSpkr78wIEDqlSpkkqVKqXjx49r9erVGjRoUPo1ERaOm6xaSbfkeY0ErokA+EbNpgk6tn+Pfju4T+WqVNe3n3+sPv/4Y2az8uXL69ixP76bSUlJeuWVV0iuEHYGDhyogQMHSpI+/fRTvfHGG+rTp4/WrVun8uXL53pO4QcffJBtBMbvx39VqfIVFRERoWVTXlfrW+6UJJ04ckgx5SsqMrqUzp5M1t5vv1bbu/v7tmFACLqm9wO6pvcDkqT/rFyktbMmq0XXntq/ZYOiy5TLtCNQklJSUpScnKzY2FhdvHhR8+fPV6dOnfL8H9OnT0+//+6772r9+vUkVyEopBMsl8ulN954Q127dlVqaqruv/9+NW3aVM8884wSrmylnrfeoqFDh+r06dO6/Xb3kanatWtr7ty52rFjhwYPHixjjKy1GjJkiJo1a6ZPPQnVd4vnqt+4DwLZPKDYKuFyqcewUZoy8A7ZtDS17tFXVes31t+fflpXeWYLzUudOnV08uRJXbhwQR9//LEWLVqk+Ph4PfHEE5oxY4bOnDmjmjVr6i9/+Yuee+65TOumpNn0cfNAMOnWrZsWLFigBg0aKCYmRu+88076cy1btsw0e+Ds2bO1YMGCTOvv3rBan//vSMkY1b3yGt0yfIwk6eieH7TgtWclYyRrdd2fB6paQ45eAXlp1Lazvl+1RK/ccpUio0up13Pj0p8b1ydJj85cpvPnz6tr1666ePGiUlNT1alTJz344IOSpG+++UY9e/bU8ePHNW/ePD377LPatm1boJoDh4V0giW5A063bt0yLXvhhRckSaM3HVOnl2cq676C0ZuOSbEJunPq0vRlv2Up88S89T6oLYCCaty2sxq37Zxp2cgRIzR60zFtz3Jk+Yaxc7RE0hLP8oc/+uP7OzwhVqM3HdPcTcd0Wd8n9EjfJzKtm/UoNUemEayMMRo/fnyOz2VMriRp9+7d2co069RDzTpl3znRMDFJj81e7kwlgWLCGKNbnnwpx+cenblMklSyVIw2bNiQY5k2bdqkz2x9SdYdfP369VO/fv0cqS/8K+QTLAAAQp23R04vpllFcqQVCGqXZh4sKHbwhY+QSbAYtgPAH3y9octvGXJSmA0xNtwAIDiFTILFXgAA/sCGLgAgELzdAccOu+Bl8rvgWRZeFXaaLzd68lrnySsre/U6AJwxauMvmR47+b0OZHlk4sutg4DGLG8Fy+eUmAfkLmtcygvxJCwVKGaF9IWGAQAAgOIoJc37fUiFWQfeC5khggAA3yjMMJPiNDSF/gEQjLwd0i5x1MtfCpxgPf/8867HHnvMsX9cmOBjz5wscNnkZJdX5fNap0KFCl69DgBnZP0+Ovm9DlT5Y7+V8Pq3z9uJNAozw9zEbVkvVpG3/k0v86p8bl5//fU6kg48++yzKY68oIfTMcvb/nmwScWginHelCfmAbkLlu9pYcpfWgeFV9CYVeBzsJ5//vk6kvYUtWIAAGRR99lnn93r5AsSswAAPpJvzPImjT0gqW6RquO2x6HXCUXFte3Ftd0SbaftxU9h2n4g/yJeyy1mFef3Ji/0S+7om5zRLzmjX3IWTv2Sf8yy1vr19txzz1l//89guRXXthfXdtN22l4cb8He9mCvH/0SfDf6hn6hX+gXb2+BmEXw+QD8z2BRXNteXNst0fbiirYHr2CvX6DQL7mjb3JGv+SMfslZseoXb6+DBQAAAADIBdfBAgAAAACHkGABAAAAgENIsAAAAADAIY4lWMaYG4wx3xtjdhljhufw/CBjzHZjzHfGmC+MMX/K8Ny9xpidntu9TtXJX4rY9lRjzGbPba5/a150BWj7w8aYLZ72rTLGxGd47knPet8bY7r6t+ZFV9i2G2PqGGPOZnjfJ/m/9kWTX9szlOtljLHGmNYZloX1+56hXKa2F4f33RjTzxjzS4Y2/iXDcwH5nTfGXGaMWez5v4uNMRVzKTfGGLPVc+vtr/oFkhd985IxZpsxZocxZpwxxrsrKIeYgvSLMaZDhs/5ZmPMOWPMrYGor7948XmpbYxZ5Pm8bDfG1PFvTf3Li34J6e09bxW0XzxlyxljDhpj3vBnHX3KiakIJZWQ9KOkepKiJH0rKT5LmQ6SYjz3+0ua5bl/maTdnr8VPfcrBnp6RX+03fP4dKDb4OO2l8twv4ekhZ778Z7yJeW+LsKPkkoEuk1+ansdSVsD3QZftt1TrqykFZK+ktS6uLzvebQ97N93Sf0kvZHDugH7nZf0kqThnvvDJY3JoUx3SYvlvjZkaUnrM35/w/VWwL75L0mrPe9/CUlrJSUFuu6B7pcs5S+T9Js8cT5cbwXtF0nLJHX23C9Dv6SXC9ntPV/2i+f51yXNyCl+hOrNqSNYV0naZa3dba29IGmmpFsyFrDWfmmtPeN5+JWkmp77XSUtttb+Zq09LneQu8GhevlDUdrfPcMYAAAFiklEQVQe6grS9pMZHpaWdGnaylskzbTWnrfW7pG0y/N6oaIobQ91+bbdY4TcP7DnMiwL+/fdI6e2h7qCtj0ngfydv0XSVM/9qZJyOsoQL2m5tTbFWvu73MljKMWhwipI31hJ0XIn1SUlRUo64pfaBU5B+iWjXpI+yxDnw1W+/eIZqeGy1i6WJGvtafql2CpQvxhjWkmqKmmRn+rlF04lWDUk7c/w+IBnWW4ekPRZIdcNNkVpuyRFG2PWG2O+CsHhBQVquzFmoDHmR7k3OB/1Zt0gVpS2S1JdY8wmY8xyY0w731bVcfm23RiTIKmWtXa+t+sGuaK0XQrz993jv417OPQcY0wtL9f1harW2sOS5PlbJYcy30q60RgTY4yJlXvUQa0cyoWbfPvGWrtW0peSDntun1trd/i1lv5XkM9MRn0kfeDzWgVeQfrlcknJxph/e37rXjbGlPBrLf2voJ+XUN7eK4x8+8UYEyHpVUlD/Vw3n3M59Do5jcfOcW+9MeZuSa0ltfd23SBVlLZLUm1r7SFjTD1JS40xW6y1P/qgnr5QoLZba8dLGm+MuVPS3yXdW9B1g1hR2n5Y7vf9V8+em4+NMU2zHPEKZnm23fODOVbu4WJerRsCitL2sH7fPeZJ+sBae94Y87Dcey2vL+C6ha+YMUskVcvhqacKsr61dpExpo2kNZJ+kXsYXIpT9QukovaNMaaBpCb6Y+TFYmPMddbaFQ5VMSCK2i8ZXqe6pGaSPneiXoHmQL+4JLWTlCDpJ0mz5P49nOxE/QLFoc9LKG/v5ciBfhkgaYG1dn+4ndrpVIJ1QJn39tWUdChrIWNMJ7k7vb219nyGdZOyrLvMoXr5Q1HaLmvtIc/f3caYZXL/KIXKF65Abc9gpqSJhVw32BS67Z73/7zn/gbPEa7L5T7vIxTk1/aykq6QtMzzg1lN0lxjTI8CrBvsCt12a+16hff7Lmvtrxkevi1pTIZ1k7Ksu8ypillrO+X2nDHmiDGmurX2sGdj+Ggur/GipBc968yQtNOp+gWSA33TU9JX1trTnnU+k5Qo9zmGIcuJz4zHHZI+stZedLySAeBAvxyQtMlau9uzzsdyf15COsFy6DcmlLf3cuRAv1wjqZ0xZoDc5+tFGWNOW2tznUAqVDg1RPAbSQ2NMXWNMVFyHy7PNEOKZ9jMm5J6WGszdvLnkroYYyp6ZhjpotDaE1TotnvaXNJzP1bStZK2+63mRVeQtjfM8LC7/thomSupjzGmpDGmrqSGkr72Q52dUui2G2MqXxoy4dmT1VDuk/5DRZ5tt9aesNbGWmvrWGvryH3e4aUEI6zf97zaHu7vu5S+N/+SHpIuDSUL5O/8XLmPHMvz95OsBYwxJYwxlTz3m0tqrjA7HyAX+faN3Ech2htjXMaYSLlHYIT7EMGC9MslfVU8hgdKBeuXbyRVNMZU9jy+XqG1XVMYBfmNCfXtvcLIt1+stXdZa2t74uUQSe+FQ3IlyZlZBK17BpBukn6QOxt/yrPsBbk3LiRpidwnxm723OZmWPd+uU923yXpPqfq5K9bYdsu9+xMW+Qe/79F0gOBbosP2v66pG2edn8pqWmGdZ/yrPe9pBsD3RZ/tV3Sf3uWfytpo6SbA90Wp9uepewyeWbSKw7ve25tLw7vu6RRGdr4paTGGdYNyO+8pEqSvpB7B8cXki7zLG8t6f8896Pl3tjZLndS3DLQfR1EfVNC7h2EOzz981qg6x0M/eJ5XEfSQUkRga5zkPVLZ0nfyb1d866kqEDXPdD9ojDY3vPV5yVD+X4Ko1kEjadRAAAAAIAicuxCwwAAAABQ3JFgAQAAAIBDSLAAAAAAwCEkWAAAAADgEBIsAAAAAHAICRYAAAAAOIQECwAAAAAc8v8BOzAgpuo++TsAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_posterior(varying_intercept_trace, varnames=['σ_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": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
meansdmc_errorhpd_2.5hpd_97.5n_effRhat
b-0.662840.0709580.00181-0.792839-0.5138951519.0620230.999551
\n", "
" ], "text/plain": [ " mean sd mc_error hpd_2.5 hpd_97.5 n_eff Rhat\n", "b -0.66284 0.070958 0.00181 -0.792839 -0.513895 1519.062023 0.999551" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from pymc3 import summary\n", "\n", "summary(varying_intercept_trace, varnames=['b'])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "bp = varying_intercept_trace[a].mean(axis=0)\n", "mp = varying_intercept_trace[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": 27, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/fonnesbeck/anaconda3/envs/dev/lib/python3.6/site-packages/pandas/core/series.py:851: FutureWarning: \n", "Passing list-likes to .loc or [] with any missing label will raise\n", "KeyError in the future, you can use .reindex() as an alternative.\n", "\n", "See the documentation here:\n", "https://pandas.pydata.org/pandas-docs/stable/indexing.html#deprecate-loc-reindex-listlike\n", " return self.loc[key]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "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": 28, "metadata": {}, "outputs": [], "source": [ "with Model() as varying_slope:\n", " \n", " # Priors\n", " μ_b = Normal('μ_b', mu=0., sd=1e5)\n", " σ_b = HalfCauchy('σ_b', 5)\n", " \n", " # Common intercepts\n", " a = Normal('a', mu=0., sd=1e5)\n", " # Random slopes\n", " b = Normal('b', mu=μ_b, sd=σ_b, shape=counties)\n", " \n", " # Model error\n", " σ_y = HalfCauchy('σ_y',5)\n", " \n", " # Expected value\n", " y_hat = a + b[county] * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n", " " ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [σ_y, b, a, σ_b, μ_b]\n", "Sampling 2 chains: 100%|██████████| 4000/4000 [00:20<00:00, 197.72draws/s]\n", "The estimated number of effective samples is smaller than 200 for some parameters.\n" ] } ], "source": [ "with varying_slope:\n", " varying_slope_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,10))\n", "forestplot(varying_slope_trace, varnames=['b'], ylabels=['']);" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "b = varying_slope_trace['a'].mean()\n", "m = varying_slope_trace['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": [ "## Non-centered Parameterization\n", "\n", "The partial pooling models specified above uses a **centered** parameterization of the slope random effect. That is, the individual county effects are distributed around a county mean, with a spread controlled by the hierarchical standard deviation parameter. As the preceding plot reveals, this constraint serves to **shrink** county estimates toward the overall mean, to a degree proportional to the county sample size. This is exactly what we want, and the model appears to fit well--the Gelman-Rubin statistics are exactly 1.\n", "\n", "But, on closer inspection, there are signs of trouble. Specifically, let's look at the trace of the random effects, and their corresponding standard deviation:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(nrows=2)\n", "axs[0].plot(varying_slope_trace.get_values('σ_b', chains=0), alpha=.5);\n", "axs[0].set(ylabel='σ_b');\n", "axs[1].plot(varying_slope_trace.get_values('b', chains=0), alpha=.05);\n", "axs[1].set(ylabel='b');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that when the chain reaches the lower end of the parameter space for $\\sigma_b$, it appears to get \"stuck\" and the entire sampler, including the random slopes `b`, mixes poorly. \n", "\n", "Jointly plotting the random effect variance and one of the individual random slopes demonstrates what is going on." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = pd.Series(varying_slope_trace['b'][:, 10], name='slope')\n", "y = pd.Series(varying_slope_trace['σ_b'], name='slope group variance')\n", "\n", "jp = sns.jointplot(x, y, ylim=(0, .7), stat_func=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the group variance is small, this implies that the individual random slopes are themselves close to the group mean. This results in a *funnel*-shaped relationship between the samples of group variance and any of the slopes (particularly those with a smaller sample size). \n", "\n", "In itself, this is not a problem, since this is the behavior we expect. However, if the sampler is tuned for the wider (unconstrained) part of the parameter space, it has trouble in the areas of higher curvature. The consequence of this is that the neighborhood close to the lower bound of $\\sigma_b$ is sampled poorly; indeed, in our chain it is not sampled at all below 0.1. The result of this will be biased inference.\n", "\n", "Now that we've spotted the problem, what can we do about it? The best way to deal with this issue is to reparameterize our model. Notice the random slopes in this version:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "from pymc3 import Deterministic\n", "\n", "with Model() as varying_slope_noncentered:\n", " \n", " # Priors\n", " μ_b = Normal('μ_b', mu=0., sd=1e5)\n", " σ_b = HalfCauchy('σ_b', 5)\n", " \n", " # Common intercepts\n", " a = Normal('a', mu=0., sd=1e5)\n", " \n", " # Non-centered random slopes\n", " # Centered: b = Normal('b', μ_b, sd=σ_b, shape=counties)\n", " υ = Normal('υ', mu=0, sd=1, shape=counties)\n", " b = Deterministic(\"b\", μ_b + υ * σ_b)\n", " \n", " # Model error\n", " σ_y = HalfCauchy('σ_y',5)\n", " \n", " # Expected value\n", " y_hat = a + b[county] * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a **non-centered** parameterization. By this, we mean that the random deviates are no longer explicitly modeled as being centered on $\\mu_b$. Instead, they are independent standard normals $\\upsilon$, which are then scaled by the appropriate value of $\\sigma_b$, before being location-transformed by the mean.\n", "\n", "This model samples much better." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [σ_y, υ, a, σ_b, μ_b]\n", "Sampling 2 chains: 100%|██████████| 4000/4000 [00:20<00:00, 193.45draws/s]\n", "The number of effective samples is smaller than 25% for some parameters.\n" ] } ], "source": [ "with varying_slope_noncentered:\n", " noncentered_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the bottlenecks in the traces are gone." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(nrows=2)\n", "axs[0].plot(noncentered_trace.get_values('σ_b', chains=0), alpha=.5);\n", "axs[0].set(ylabel='σ_b');\n", "axs[1].plot(noncentered_trace.get_values('b', chains=0), alpha=.5);\n", "axs[1].set(ylabel='b');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And, we are now fully exploring the support of the posterior." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = pd.Series(noncentered_trace['b'][:, 75], name='slope')\n", "y = pd.Series(noncentered_trace['σ_b'], name='slope group variance')\n", "\n", "sns.jointplot(x, y, ylim=(0, .7), stat_func=None);" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)\n", "plot_posterior(varying_slope_trace, varnames=['σ_b'], ax=ax1, color='LightSeaGreen')\n", "plot_posterior(noncentered_trace, varnames=['σ_b'], ax=ax2, color='LightSeaGreen')\n", "ax1.set_title('Centered (top) and non-centered (bottom)');" ] }, { "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": 39, "metadata": {}, "outputs": [], "source": [ "with Model() as varying_intercept_slope:\n", " \n", " # Priors\n", " mu_a = Normal('mu_a', mu=0., sd=1e5)\n", " sigma_a = HalfCauchy('sigma_a', 5)\n", " \n", " mu_b = Normal('mu_b', mu=0., sd=1e5)\n", " sigma_b = HalfCauchy('sigma_b', 5)\n", " \n", " # Random intercepts\n", " a = Normal('a', mu=mu_a, sd=sigma_a, shape=counties)\n", " # Random slopes\n", " b = Normal('b', mu=mu_b, sd=sigma_b, shape=counties)\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " \n", " # Expected value\n", " y_hat = a[county] + b[county] * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=sigma_y, observed=log_radon)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [sigma_y, b, a, sigma_b, mu_b, sigma_a, mu_a]\n", "Sampling 2 chains: 100%|██████████| 4000/4000 [00:28<00:00, 138.89draws/s]\n", "There were 24 divergences after tuning. Increase `target_accept` or reparameterize.\n", "The acceptance probability does not match the target. It is 0.7014054977792086, but should be close to 0.8. Try to increase the number of tuning steps.\n", "The estimated number of effective samples is smaller than 200 for some parameters.\n" ] } ], "source": [ "with varying_intercept_slope:\n", " varying_intercept_slope_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,16))\n", "forestplot(varying_intercept_slope_trace, varnames=['a','b']);" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "b = varying_intercept_slope_trace['a'].mean(axis=0)\n", "m = varying_intercept_slope_trace['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": [ "### Exercise\n", "\n", "Reparameterize the `varying_intercept_slope` model to be non-centered, and compare the resulting parameter estimates." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "# Write your answer here" ] }, { "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": {}, "outputs": [], "source": [ "from pymc3 import Deterministic\n", "\n", "with Model() as hierarchical_intercept:\n", " \n", " # Priors\n", " σ_a = HalfCauchy('σ_a', 5)\n", " \n", " # County uranium model\n", " γ_0 = Normal('γ_0', mu=0., sd=1e5)\n", " γ_1 = Normal('γ_1', mu=0., sd=1e5)\n", " \n", " \n", " # Uranium model for intercept\n", " μ_a = γ_0 + γ_1*u\n", " # County variation not explained by uranium\n", " ϵ_a = Normal('ϵ_a', mu=0, sd=1, shape=counties)\n", " a = Deterministic('a', μ_a + σ_a*ϵ_a[county])\n", " \n", " # Common slope\n", " b = Normal('b', mu=0., sd=1e5)\n", " \n", " # Model error\n", " σ_y = Uniform('σ_y', lower=0, upper=100)\n", " \n", " # Expected value\n", " y_hat = a + b * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n", " " ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [σ_y, b, ϵ_a, γ_1, γ_0, σ_a]\n", "Sampling 2 chains: 100%|██████████| 4000/4000 [00:28<00:00, 140.82draws/s]\n" ] } ], "source": [ "with hierarchical_intercept:\n", " hierarchical_intercept_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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0xhgflZ4LpH3TOkwfci7gJJBoMwzmD5vKmrF9oz7K+n7PQQoLy95JhDviuG5pidwv8+d7K2eJpoTX9hmjgBtVtQuwz/36G2Ceb5EZY3xU9io+NAAiUCaBhGsTtUNhtH2HJ5PkB2TMZfPne084lZ3XJNJaVV+PWDcJuC7N8RhjYmjSxFm8Cp87PH/Y1Bi9yR1rH+7D2of7xHx0FF4mVnrZs+CDsHfhiUQi1iWnfdM6UdfHG9IEoFo1OPLIlA5pkuA1iWwRkWbu6zUi0gM4DusnYkzaJEoSO3Y4ixexEka8RFJe2z98KuxdcncdJZ0FwxOOs6zYso9qEbvLE6FuzWoEAk5rrEinngq/+x1s3ZpUGCYFXps2TAR+CryJM7fIpzhDwj/uU1zGVDqh82Ss+mCvCSIT1j6c/Ii3jS//PdumQCqPrVaN6YOMdV6HN+cNOVz8MxPWjO1Lwwnu+sPR9zd+fNIhmBR5HTvr4bDXL4jIDKCOqi7xKzBjTOaVPDpyhlyPJrh3R9RP23Y9j21Tyl/vsWLLPhAFzVwdSi51vKxoUhr4QFXXJZNAROQxESkQERWRjnHKXSUii0TkW/drs1hljTHlEf0EHWqdFa/Mzkk3o1pUZtTc8BkIVaHX4zMIfyyVjGPvfj+p8iZ7vA7AeIqIfCIi20XkoLscEpGDibcGYApwNrA2zjG6AvcDvVW1I87js10e929MlVWtmrMkL9HQ6dFP/L179yYQCESdv6O4TJQOggC1AtG2qTyttqoir3ciLwOzcBJBB3c50f2akKp+oarrExS7A3hMVTe72+xS1cJoBUWkoYjkhy9AS0/fiTGVTDBIqZ7jELv3uJde5Y7Ydw5vvfUWkSf+yMdBsVp5OU2H48/5Eas1lslNXq9fjgZG+DyHyElAgTu4Y13gLeChGMe8HRjpYyzGVHjh09R6Tx7ZN33IufQeN6PUY4v2TeuwNsEdy5FHwg8/lG3Wax0D/eX1TmQS8Gs/A8FJaJ2B3jhNM34GXBuj7HigTcTS0+f4TBVRlUds/eGHHxg8eHC2w3DrZpw7lTVj+0bU1US3daszUGJks17rGOgvr3ciY4HZInIvzui9xVT1/DTFshZ4Q1UPAAdE5B3gDOCFyIKquhMoNc5mvOezxphEnBv+du3asXv3bpzrtNS1b1qn7COtQNC9ozCVidc7kTeAAuD/gBcjlnR5CbhQHNWBC4Bv0rh/YzLKaw/zkkELs+/MM8/km2/K/283fci5Zeo2ej3yhac7ClOxiJdqDhHZAxzlzrWe/EFEngR+iVO3sg34QVVPFpFpOHUtc0UkD3gM5zFWEfAhcKeqehrJ361cLygoKCA/Pz+VMI0BEncK9CrUYirUIS7WfsNvogOB2B3oYu0vJFq80Y7ZeeQHLHrwosiSgKJu3wxnu2g/AEG1JDlu21Z6/5HHC48x2joomb8j1rbR3jds6LyOnPfDJG/NmjW0cSqO2qjqmmS39/o4ayZOxfeCZA8AoKq3AbdFWd8n7HURMMRdjDE+6DzyA7Zv2RTlk2ij78Z+RByqd7CnyMZrEikAPhKRtylbJzIi7VEZkwNE/OvJHLqSz+TYTkVFRaz98Hl2z30HuDFKCSV/WGjOkIrTmstkl9ckcgQwFagBtPIvHGOqhsyOk+XcZeTl5XF452bqdOjJvrLTlEfdxphEvI6dFe2yxRiTJc6cHpGDJEZ2ACy5jVqyZAkdOnSg8c/vQvICHpJIZjRokNp21vcjd8RsneVWVIdet421ZCJIY3JZpltXtRk2NWqVd/hkUQsWLKBXr17F73e4tz4NatfwO7yMsL4fuSPencgioJ77eiXR728Vm1PEVHGFUQfn8U+sahrFufu4+eab+ctf/kKjRo2KP/vJT34CwMIHLqbzyA9i7MEPpafgBQgE+pYZpsWJ6aLicvVrBoCLMxSjKY+YdyKqWi/sdZ6qBtyv4YslEGM8iJxlMNoc5ekgIjRu3JihQ4eycuVKoo1PtfCBi6OuLy9nHpDEMykGi4oIBEoaLewpPMTuA6WzivPexmevCDzViYjIk24z3cj141X19vSHZUzlEe9k6rW/7zUTZxMs6h63zP6C+UBfRo0alUR0seYNiT2ib/6wadQKCEsfKqmTiTVqrxeWKio2rz3Wb4ixPtbYVsaYNLlm4mxmrdqesFygdr2EZaIrGVG3ZKBGjVhKKwwqJw6fVjw9baoJJBm1ajmLyS1x70REZGCoXNjrkLY4vc+NMeXmnKiDRUr+sPc567hGvDioB0DUBLJt6hNEts7a9PfyD5wYeddUs9V2DqxvFLVsYVCLe8/nD0vteG3awOJNP3oqu39/ascw/kp0J3Ktu9QIe30tMAA4Drje1+iMqRLKXunPWrWdaybOjrlFrdadwt6lv34jXM1W2zn2nmmJC6Zg/nw48abY36fJfXGTiKqep6rnAWNDr93lfFXtr6pzMhSnMVVO6A6k6NABds15HbSouDa6bqdQ893yJY90PSJKZiKpQF7p087CBy52W2OVcN5bZ8eKwGudyJ9EpC6AiARE5EYRuc4dNNEYE0esCaEiT6aRVIsQUdaP+wU7P5vkrCwzWFVJvUX+sKl0f2h6xD7iD92yf3/qj4nCp7qNNmqv8750fUusn0V4i7E1Y/u6701F4DUJ/BNo774eDdyJM1Di434EZUxl45w8S06SiRIIwA9Tnyh+fcGQP0PYNdtZx0Wvp/h+z8EyicQPka2zwPtEUkceWXb2QVNxeU0ix1Mygu81OMO1nw/8yo+gjMmW8P4coav7TCs64FQ0d7/wF8XrPn78FgJ5eQTy8lgztm9xpXs03+9JacYGINHc7CUJIjKBJGPr1swOPGn85TWJBIEaItIJ2KWq63BmFqzrW2TGZFishJGORBJ/yPTwSTeK2PXlG5x1XCP+Ne5W/K40jyY8YZzZ9ijObHtURo8fYk16Kwavo/i+D7wGHAW84q47CdjoR1DGVBUXPDId6BW2Rlj65niaN2+erZByhjXprRi83on8D85Q8M8DY9x1jYH7fYjJmCohWKR89eJjpVeKcN3Ly8q132b1cmeQRbuTqPw8JRFVPaCqfwEmAU3cdTNU9ZX4WxpTNTnDlBQRLCoKq2dxfP3114TqXOp1u7zMtt57f5d9zNWsXg2+HN47pZj9YHcTlZ+nJCIiDUXkJaAQZ0RfROTnIpLMID3GVAmxhylxEscZZ5xBkTsAY43GraPuwxnM0IvSTWjTnUBOPdVZjInF6+OsCcAu4Fgg1PRjNnC1H0EZkw2xWiZVS7JeOzKBhFpbhZz0s+vQBJXlmRiLKlys/iTjxzuLMbF4TSIXALep6ne49+WquhVo6vVAIvKYiBSIiIpIxwRlTxCRH0XksXjljEm3aAnjsEK736feQmvXrJdLvd/X+SpP22Vq+HhjysNrEtmFU5FeTERaA98lcawpwNnA2niFRCQAPOuWNyajDsfo3R25Pi/PWSLn0Og9bgaqyv5Vc4vL1u/eL23xpSuRiCRqdmyMN16b+D4HvCkiw4E8EemB03N9gtcDqeoX4Eyak8AwnB7ydbF+KCZHOY9+tMxjp8XffsuuGX/lx4L5wHCQPAJ1GmYjxLjspsaki9ck8jBOpfrTQHXgrzh3C39KZzAi0hlnjszzgD/EKdcQiPzPbJnOWIxJ1g/vP8neRR+TV/MITrtqMP95PbWh5do3rZPxOhFjUuW1ia+q6nhVPUlV66hqB/d92iYlE5HqwETgJlUNJih+O1AQscxMVyym6opVie6lcn3vt59Q7/RLafGbicx7dbyn8bFKEwJ5eTHHnDImF3m9E8mE5jhzlExzH3k1BERE6qvqbyLKjgf+HrGuJZZITDmtHNMXGVv62qiaOOtLc8r8uGIOocmhWvzPM1Q/skWKR06+giJ0CZfrdRvpu9Q0uShnhnJX1XWq2lhV81U1HydRTIySQFDVnaq6JnwBNmQ4ZFNple57EZlAPv300+LX+779pPh1sgkkNJhitASS6vDxxmRaxv4iReRJEdmAc8fwsYgsdtdPE5GumYrDmFQtX76cyy67jPPPP794XePLU5wX1oNUho83JtO89ljvHmP9GV4PpKq3qWpLVa2mqker6snu+j6qOjdK+ftV9U6v+zfGb9988w2ffvopY8aMKV6XaF62eCd+6/dhKgOvlzaxZrn5IF2BmKqtWjVnyS3Ko48+yp/+5DRCvOKKK1i9ejXDhg3Dpm41xhE3iYhIntv5T1x5YUt74HBmwjSVXTDoLLkhNCkV3H333cyePRtw+jg1btw4znb+yuSMgImm1TUmJNG132FKhh+NTBhFwENpj8iYLFqwYAFwSvH76dOn06tXrxilo9+NxKoUL6/KPhtgrrcyM9ElSiJtcP5TPsMZskQouUzbqqo20HMFFfqHtavN0g4eLD21bOwE4lgzti/ycMnraCrLudHL30p55g+xKqKKKe7jLFVd6zahPVZV1+KMe/UjsN4SiKkMdu7cyV133cUtt9wCwLubapf6/L4pi8p9jIIkmutm6nGVX/bvtzlEqppk5hP5B87QJ98D+0XkHyLSyNfojImhvAMIHjp0iD//+c+0a9eOxx9/nMLCQoa/9Q2T56wrVW7ynHVpSSSRfU9itdqq7I+sTOXjtXXW34DawKk4gyJ2AWrijKFlTIUyd+5cOnbsyG233cYpp5zCvHnzeO6553jl641Ry7/85fpyH9PPx4aBgLMYkw1eG1WeBzQPe4S1RERuADb5EpUxPjh06BDVq1enWbNm1KlTh3fffZdLLrmkeGTpYIwzfaz1meDl0IetjaTJIq9JZBmQDywJW9faXW9MTtu4cSPDhw9n48aNfPTRR7Rq1Yp58+aVmZYgIEJQFal5GD1QrdR6Y0x0Xh9n/Qv4SERGi8jNIjIa+Ahn+JKBocW/ME242rWdxcS3d+9eRowYQfv27Xn55Zfp0qULh93L9mjz2vTv3irqfmKtT5fytGgyJtu83on0AFa6X3u461YBP3EXcJr9Wh1JBhQWZjuC8vO7ifG8efO45JJL2Lx5M1dffTVjxoyhTZs2cbcZdXknwJltLWTAma2L1/tl/37rI2EqLknjlCBZJSL5QEFBQQH5+fnZDcZn6TgBZ7ufSOTxk40nVvnt27fTqFEj9u7dy7XXXss999zDmWeemVRsDRvCrl3x4wk/fqxYQsO4hOoswsvF+8yYTFqzZk3oAquNOyJ6UjyPViQiR+FMnHC0qj4qIi2APFW1IdgriMgTV2WyePFi7rzzTlavXs23335L3bp1efvtt7MaUzJ9PuyRlqmovPYTOQenEv0aYIS7uj3wfz7FZXyQW+NTpcf333/PTTfdROfOnZk9ezaDBg3C77vrziM/IDRwQ/6wqZSMDFTa1q3e+31YJz1TUXm9ExkPXK2q/xKRHe66LwHPQ8GbyqVLF+fr/PnZjEJp164dhYWF/O53v2PEiBG+D5DYeeQH7D4QLRMrlWeAE2O885pE8lX1X+7r0GXXwSS2N5VMQUF2jltUVMTKlSuB4wEYNGgQN910E8cff3xaj9OgAezcWXZ99ASSvIo+vIkxIV6b+P5XRC6KWNcLSMd4EMZ4MnPmTLp3706PHj0IXfmPGzcu7QkkaYGgsyQhmUddxuQyr0lkKPCiiEwCaovIs8Dfgbv8CsyYkBUrVvDLX/6Ss88+m82bNzN+/Phsh1TKsXd+yLF3fpjtMIzJCk9JRFXnAJ2BxTh9QQqAM1T1ax9jM4bVq1dz8skn89FHHzFq1CiWLVvGtddeS7bqH+rXjD5IVaz1xlR2nuo0RKQmzvwhj4Stqy4iNVX1gG/RmSqh+0PTcZ6OQv6waTSpLTx6zhGce+65tG3blieeeIJ+/fpx9NFHZzdQYOEDF7uts0rUrxlg4QMXZykiY7LLU2dDEfkcuNu9IwmtOxMYq6rn+heed1Wxs2Fo5Fav/T68dJDzqmFD52u0yudkYjlj1HS+33OQtQ/3AaDx5cPZOePvBHdvYd3aNbRs2TLu9n605vXyvaVyfOtQaHJReTsbeq0T6YTTpDfcV4TPI5qAiDwmIgUioiLSMUaZP4jIYhH5RkTmRanMN2EqQ7+P7/eUnklw25QxSLXqNOk3ImYCqahs3nJTGXm43hbPAAAZwElEQVRNIruAZhHrmgH7kjjWFJwpdtfGKfMV0E1VTwEGAq+KiA01mILyTtrkp5IOes4ZNbiv5JK/0UW30PzGP1O77emets8fNtV9b4zJBq9J5E3gJRHpKCJHiEgn4AXgNa8HUtUvVDXu7D6q+qGq/ui+XYhTe3qU12OY3BfthB+o07D4db1TL0byYldSx0oYlkiMyQ6vSWQ4zlwiXwF7gDnAUuD3PsUFcB2wKtrYXO50vfnhC1C5nn346MTh0wi/knfeZ4YWBdkzv+R4h7ZFv65oVq9GpkIyxpRDwiQiInk4w70PAeoARwN1VfVWv1pmuWN1/RHoH6PI7TjNjMOXmX7EUvkohcHSD+YLg+p7IlFVpk6dynd/vYXtHz1TvL5647JzdTSrV4Mvh/f2NR5jTHokbOKrqkUi8o6q1nNX+drPVkR6AJOBy1Q11syJ43E6O4ZriSWSlEUmlnTbs2cP1157LUptmvxiOFujDrArrBnb19c4jDHp5fVx1uduk15fiUg34FXgClX9T6xyqrpTVdeEL4ANSZ9jNm3axMiRIwkGg9SvX59PPvmEFv/vaY44vkfijY0xFYLXJLIWeF9E/i4ifxSRB0OL1wOJyJMisgHnjuFjEVnsrp8mIl3dYs8AtYFnRWSBu/g7rZxJu3379vHAAw/Qvn17xowZw3x3qN9TTz2VtY9eHmMrb03JYt2p2B2MMdnhdRTe2jhNdCHFCmxVvQ24Lcr6PmGvu6Wyb1N+tQLlbw9cVFTECy+8wPDhw9m0aRNXXnklY8eOpW3btqXKrRnbF3m45DVQ/N6LaNsbY7LDUxJR1Rv9DsRkipRJGLUCwtKH+sQo710wGGTMmDG0atWK1157jbPOOqvc+8yGBFOxG2PCJDM9bgfgCqCZqt4iIicANVV1oW/RVTF57sPFoqLYZXqPmwGcE7E2ubuIpQ/1QUY7r8t7Jb906VLGjBnD008/Td26dfn0009p3rw5kqs9HT3I7kRbxlQsXqfHvRL4HDgGp/8GQD1gnE9xVUmJhsXoPW4GH9/90zLrRTRh73RnkMPEU7p6pVrE/v0/0rFjR6ZMmcKCBQsAaNGiRYVOIMaY5HitWH8Q6K2qNwGh0Zq+IYmxs0x0TZo4ixcrtuyDYPJDjnd/aHqZMaocySeSYDDII488wu7duzl48CC//e1vWblyJT/9adnkZoyp/Lw+zmqKkzSg5MyjlPdy1rBjR+Iy5RU9gaQmLy+PDz/8kGrV/pfatWvz9NNPp23fxpiKx+udyDzg2oh1v8IZBsVUcv/+9785//zzWb9+PSLCe++9R506dcmLM8aVMaZq8JpEbgNGichnQB0R+RBnWJI7fIvMlNG+aZ2MHm/VqlVceeWVnHXWWSxdupTVq1cDMPqjVewuPMTuwkMc9/tp3DdlUUbjMsbkDq/T4y4FTgSeBu4D/gZ0UtUVPsZmIkwfcm6MT+JXZCc7mKGqcvfdd9OhQwemTZvG/fffz4oVKzjnnHO4b8oiJs9ZV1w2qMrkOesskRhTRXltnfWkqv6oqq+p6qOq+oqq7hWR8X4HaCJJlCW+L4f3jpFISm9b5LYtFhF27tzJtddey4oVKxg5ciR16jh3QS9/GX3U3VjrK6tcnq/FmEzy+jjrhhjrI+tJTA6INmmTMyquk3ScviElZ0BVZcqUKZx00kl89ZVTzTVhwgSef/55WrRoUWrfwRhtkGOtr6yKiuL35zGmqojbOktEBobKhb0OaQts8yUqk7L4kzaV7Vg4b948hg4dymeffUaHDh04dOgQ4LTCiiYgEjVhBJK8LK9iOceYSitRE9/QnUYNSt91KPA9cL0fQRkvop2Fk32+onTt2pUmTZrwzDPPMGjQIKpVi/8n0b97q1J1IuHrjTFVT9wzhqqeByAio1T1vsyEZBKLfhnv9EpPvK1zF+AknGHDhjFs2DAaNGjg6cijLncGVXZHTSEgQv/urYrXG2OqFq8DMN4HICJNgboRn632IS6TgnidCrUoSCj5vPnmmzjDoAljxoxJ+jijLu/EU7Wc16vGlH/gRoCAdTkxpkLylERE5CLgr0DziI8UsH//HLd/9Tx2fPpX4FIA2uTgMLWHD2c7AmNMKry2znoGp3NhHVXNC1ssgWRc/BrpyFF5f3j/Sba8PpLWDUquF04//XRfIsukRINVGmMyw2sSORJ4VlX3+xmMia/d76O3vAoJ9QX58o7QRJHC30f8hscff5zFixfjtV+JMcZ45XUAxueBG3EeaZksOZzgyvvTO85i1KhRPPzww8BuAPr16+d/YMaYKstrEjkTuE1EhgGbwz9Q1bPTHpVJyQknnMCGDRv4xS9+wdtvZyeGUHcRe9RkTNXgNYk85y4mhzVr1owXX3yRs88+24bkMMZkhNcmvpP8DsQkVi1BYth6wUium7aHNXZvaIzJkLgV6yJyfqLFy0FE5DERKRARFZGOMcoERORpEVklIitF5H9S+YbSLVMD7XUe+QHh410570tbOSb+fOgizq8z1tAn4ax1kzEmHRLdiTyf4HPFGUMrkSnAn4CZccpcA7QD2gNHAfNF5GNVXeNh/xVasKiI3QeCpdbtPhCk88gPWPjAxQAcOHCATlfegTMavzHG5IZEw56kpVeaqn4BzhDjcVwNTFTVImCriEwBrgQeTUcMFVF4Ymnfqz/rv3gzi9EYY0xZXvuJZEJrYG3Y+3VA1FH9RKShiOSHL0BL/0MMj6H8j7mumTibYJzxxA9sXMqyZcsAKOp4SfkOZowxPvDaOivX3A6MzHYQ5XHNxNnMWrU96meHd33Pjs8m8eOSz3mw6D+8+OKLVGvQLMMRGmNMYrl0J7IOODbsfWsg1nR544E2EUtPX6NLs1gJBGDjxJvYv+JLmvTsz4QJE5Led+TQJ5kSbTIsY0zllkt3Iq8Dg0TkLZyK9cuBqI1VVXUnsDN8XYL6lgqlToeetOp1A0ueKJnCpX3TOqWe9ZXmfO+JkoefI+XGmwwrW0nNGOO/jNyJiMiTIrIBp97iYxFZ7K6fJiKhgZ7+AawGVgBzgAcr+zDzGqOd7d5F/yqVQACmDzk3xl68J8/Dh220XGNMemXkTkRVbwNui7K+T9jrIHBzJuLJBSfV2ManL4wDLk6iw0bludsyxlQOuVQnUiVs3LiRG2+8kQ9G3YhuWwsISPivwRKFMabisCSSYVOnTuWll15i6NChbN6whkAgQCAvz603SF8CsR7pxphMyKWK9UopGAwyadIkatSowYABAxg4cCAXXngh+fn52Q6tXCInR1wztm/UynWrVDemchOtJJerbofDgoKCgrSeoGMNbe5lyPOPP/6YoUOHsnDhQi699FLefffdMmWquWn88OHE+0zUAC0XfpU2FLwxFcuaNWtCU2a3SWWYKXuc5YNly5ZxySWX0Lt3b3bv3s0rr7zCO++8k+2wjDEm7SyJpCBRp7p169Yxc+ZMHnnkEZYsWcLVV19dqfqxGGNMiNWJJCnac389fJAjz72BO85vy4gRI+jduzfr1q2jQYMGWYjQGGMyx5JIOe377wx2fDaJ4O6tfNv0SlQVEclIAgn1QA8G45czxhi/2OOsctr23mMEaten2a9G89prr2X0sZX1QDfGZJvdiSQpdKcRclSfO6jT8bziWQWNMaYqsTOfRzt27GDIkCFs++djpdbX7XRBVhKINaE1xuQCSyJxnDh8GqFWWI1btOaJJ8bz65+0R4vKVkL43amuTViLMFD3fe6xnvLGVC2WRGI4cfg0dm9aWfy+xtHtaX7jk8xs+gvWPvJznCFKhDVj+2YkgUSelxVyNpEYY6oOqxOJorCwkMKgEqjXuHhd06seREQoDGb+MjvWEe2C3xiTbXYnEmbdunUMGDCAs88+G9UiAkeUNNPN5c6C9gjJGJMtlkSAPXv2MHz4cE444QTeeOMNevXqZZ0vjDHGgyqfRBYuXEi7du0YPXo0/fr1Y/ny5YwePZraNWtELV8r4N8diUj0QRZjHTF3742MMVVFlUwiqsrmzZsBOOGEE+jVqxdfffUVkydPpnXr1gAsfahPmYRRKyAsfahPmf2lS1GRs0QqGNu3TMIQd70xxmRTlRsKfuHChdx5550sWbKEZcuWccQRRyTYr/M1laHgvQgfCj6R0DFr1YL9+8t3XGOMARsK3rPNmzczaNAgunTpwty5cxk6dCjVqlXMxmmWQIwxuaJinkWTtHz5ck477TQOHjzI4MGDue+++2jUqFG2wzLGmAovY3ciInK8iMwWkeXu1/ZRyjQVkakislBElorIMyKSUqIrKipi4cKFALRv354hQ4bw3//+l3HjxqUlgaSrWe2RRzqLMcZURJl8nDUBeFpVjweeBp6NUuZeYImqdgY6AacDv0z2QDNmzKBbt2706NGDzZs3IyI8+OCDtGvXrjzx+2LrVmcxxpiKKCOPs0SkKXAa0Ntd9TLwlIg0UdXwU6gC9cQZ0bAmUAPYGGV/DYGGEatbAgwaNIiPP/6Y1q1bM3HiRJo2bZrm78YYY0xIpupEWgEbVTUIoKpBEdnkrg9PIn8E3gS+A+oAT6nqrCj7ux0YGe1As2fPZsyYMQwePJjatWun83swxhgTIdcq1q8EFgIXAPWA90XkClV9I6LceODvEetaAjNnzJhB165dfQ/UGGNM5pLIeuAYEQm4dyEBoIW7PtytwEBVLQJ2icg7wHlAqSSiqjuBneHrQmNbNW7cGGOMMZmRkYp1Vd0CLAD6u6v6A/Mj6kMACoCLAUSkBtAL+DYTMRpjjEleJltn3QTcKiLLce44bgIQkWkiEnr+dDvQU0QW4SSd5cDEDMZojDEmCRmrE1HVpUD3KOv7hL1eRUkLLmOMMTmuygx7YowxJv0siRhjjEmZJRFjjDEpsyRijDEmZZZEjDHGpMySiDHGmJTl2rAnOSeXJn7MpViMMQbsTsQYY0w5WBIxxhiTMksixhhjUmZJxBhjTMosiRhjjEmZJRFjjDEpsyRijDEmZZWpn0gAYMOGDdmOwxhjKoywc2Ygle0rUxJpD9CzZ89sx2GMMRVRe2BVshtVpiSy2v16DrAum4GEaQnMBHoCuXKLlIsxQW7GZTF5YzF5l4txtQY+o+QcmpTKlEQOul/XqeqabAYSIiKhlxsspvhyMS6LyRuLybtcjCsspoPxysViFevGGGNSZknEGGNMyiyJGGOMSVllSiI7gQfcr7nCYvIuF+OymLyxmLzLxbjKFZOoTVJhjDEmRZXpTsQYY0yGWRIxxhiTsgqdRERkgIgsFJHDInJLgrKDRGSliKwSkadExJfvXUSOEJFX3WMtFZFLYpTLE5E/ichiEVkkIh+ISItsxuSWPVVEPheR/7rLz/yIKdm43PK13JjmZjsmEblMROaJyLfu73BomuM4XkRmi8hy92v7KGUCIvK0+ze9UkT+J50xpBjTH9yfxzfuz+ciP2PyGldY2RNE5EcReSwXYhKRq9z//2/dr82yGZOINBWRqe55damIPCMi8fsTqmqFXYCOwEnAC8Atccq1wekd2gQncX4IXOdTTCOA59zX7YHNQN0o5S4H5gDV3PfjgGeyHFMdnF6rZ7rvqwFH+fj78xRXWPnHgeeBudmOCegOtHBfNwBWAj3TGMcnwAD39QDgkyhlrnP/lvPcv+0NQL6PPxsvMV0EHOG+PgWnsra2XzF5jcv9LADMAF4CHst2TEBX4L/A0WF/R7WyHNP40M8GqA58CVwVb78V+k5EVb9V1f8CRQmKXgFMUdWtqloETASu9imsq4EJbnwrgLlAtKt5BWoCtdy7onr4NwyC15h+DXyhqnPcsodV9QefYkomLkSkJ85J/R8+xuM5JlX9UlU3ua93AUuAY9MRgIg0BU4DXnZXvQycJiJNosQ6UVWLVHUrMAW4Mh0xpBqTqn6oqj+6bxcCAhzlR0zJxOUaBvwTWO5XPEnGdAfOCXszOH9HqlqY5ZgUqOeek2oCNYCN8fZdoZNIEloDa8PerwNaZflY7+FcFW12lxMAv26xvcZ0EnBIRKaJyAIReV5EjvQpJs9xiUgdnCukm32MJamYwonIicCZOFd66dAK2KiqQQD366YocWTy79prTOGuA1apqp9jRHmKS0Q649wlPeFjLEnFhPP/1tZ9fPwfEblPwsYgyVJMfwSOB77DOS99qKqz4u04p8fOEpH/4PyjRNMs9APJpEQxJbGr04AOwDHAXpyT5Dggbt2OzzFVAy4AegDfu/E8DgxMNqY0x/Uo8LSqboz3vDvDMYX21xx4B/hd6M7EgIicg3NC6p0DsVTHefpwo6oG/TtPJ60a0BnnZ1QD+ADnQuCFLMZ0Jc4d5AU4T0feF5ErVPWNWBvkdBJR1dPStKt1lH7U0BpYn8qOEsUkIqFjbQ071qdRit6A80xyl7vdZOCvWY5prRvTd+52L6UaU5rj+inQR0RGALWAI0Vkoap2zmJMoUcEHwOPquprycYSx3rgGBEJuCe9ANCCsn+zoVi/Dot1Lf7wGhMi0gOYDFymqst8iieZuJoDxwHT3ATS0AlT6qvqb7IUEzi/qzdU9QBwQETeAc7AnyTiNaZbgYHuY/9dbkznATGTSFV5nPUmcLmINHGf9Q0C0vlPH+514LcA7lVzN5wrjEgFwAXuVRJAH+DbLMf0GnCGiNRz318MfONTTJ7jUtXOqpqvqvnAr4BFqSSQdMYkIkcB04GnVPW5dAagqluABUB/d1V/YL5b7xEZ6yBxWvo1wWms8WY6Y0k2JhHpBrwKXKGq//EjlmTjUtV1qto47G9oPE5dkh8JJJnf30vAheKojnP178v/WxIxFeD83yMiNYBeJDov+dUSIBOL+4PYAOwDdrivT3I/exC4Kazsb3EmXFkF/B8Q8CmmOjj/3CuBZThXY0TGhHNF/VecCtlFwFTgmGzG5L6/zv2jWYjzmKaZj78/z3GFrT8Xf1tnef39PQrsd/8xQ8uNaYzjRJyWMcvdrye466cBXd3XAfdvOfR3/Ru/fi5JxPQ1zl1c+M+lU7bjiih/P/63zvLys8rDeWS8BFjsvs7LckzH4VwcLcJpOfY0bgvSWIsNe2KMMSZlVeVxljHGGB9YEjHGGJMySyLGGGNSZknEGGNMyiyJGGOMSZklEWMSEJEZGRgh9363w2nWici9IpLWvi+m8rIkYjJGRH4tInNFZK+IfCci74vITzNwXBWRdn4fp7JQ1dGq6mvSNJWHJRGTESIyBKen8GicMapaA88Al2UzrsrIHdLCmIywJGJ8JyINcHp7/05V31LVfap6SFXfU9W73DI1RWS8iGxyl/EiUtP97AYR+SJin8V3FyLyd3EmZ5oqIntE5EsROc797HN3k2/cO6CrxZkA6NKwfVUXkW0icqrH72egiCwRkR0i8qGIHOuunyARkx2JyDtuAkVEWojImyKyVUQKROQ2j8fz8v3/nzv68j7gPBHpKyLzRWS3iKwXkfvDts13t79eRNa53/vwsM+LH62JyLkisiHi2GtEpFdY2ddFZLL7s18kzuRHvxeRLe6xL/TyfZqKyZKIyYQeOMO8vB2nzHCc4dRPxZnM6AzgviSO0R94ADgSZ8iShwBU9Wz381NUta6qvoozwN2AsG37AN+p6oJEBxGRy4F7gV/iTAQ1k5I5Gl4CrhZ3lD9xhtG/EHjFHbPtPZyxkY7BGSfpdknfzH+/xvme6wFf4AwFdB3OYIN9gZvd2MP9FGcKgguAESLSIcVjX4ozz8uRwHxKJso6Bufi4dkU92sqAEsiJhOOArap6uE4Za4BHlTVLeoMCvcAcG0Sx3hLVb9yj/EiTjKKZTLOqMD13ffX4n2yq98CY1R1iXus0cCp7t3ITJxJfXq6Za8AZqszRHw3oImqPqiqB1V1Nc7w5L9K4nuM5x1VnaXOBFWFqjpDVRe57xfiJLpzIrZ5QFX3q+o3OMntlBSPPVOdyagO44w71gQYq6qHgFeAfBFpmOK+TY6zJGIy4QegscSfq7kFpYcxX+uu82pz2OsfgbqxCron9VlAP/fk9jOcxBN6JLXXXe6NsvmxwJ9EZKeI7AS248zed4w6A9G9QslIqb8O7dfdrkVoO3fbe0lhDpMYSg3pLSLdReRT99HZLuAmoHHENp5/Zgl8H/Z6P84FQzDsPeXYt8lxlkRMJswGCnGGKo9lE2XnfAlN8rQPOCL0gYgcnYaYJuE80roS525hI4Cq3uQ+9qqrqqOjbLce+K2qNgxbaqvqv93PXwaucO9MulMyNPt6oCBiu3qq2sdDrF6+/8iRVF8C3gVaqWoDnCl/U5mNKfLYAZw7DWMASyImA9SZeGsE8LSIXC4iR7iV2T8TkUfcYi8D94kz50tjt3yo38Q3wMkicqqI1MIZyjsZ3wNtI9ZNwZldcjDJTQI0Afi9iJwMTqMBESme11xV5+MMhf4cztSiO92PvgJ2i8g9IlJbRAIi0lGc+TcSSeX7rwdsV9VCETkD564oFcuBWm5FfXWceqqaKe7LVEKWRExGqOo4YAjOSWgrzpX5LTgnc4BRwFyceUwWAf9x16Gqy3EqaD8GVuBUHCfjfmCS+xjpKnef+3HuEtoAbyXxfbwNPIxTWb4bZ+6Vn0UUexlnMp+XwrYL4lRAn4oz8c82nETTwMMxU/n+/xd4UET24CTklCZhcy8A/teNdSPOnYmfc6abCsbmEzFVljjT7R6vqgMSFjbGRJXTc6wb4xcRaQT8P5JrAWaMiWCPs0yVIyKDcB6nva+qnycqb4yJzR5nGWOMSZndiRhjjEmZJRFjjDEpsyRijDEmZZZEjDHGpMySiDHGmJRZEjHGGJOy/w8KxUv1+ctLBQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a_means = hierarchical_intercept_trace['a'].mean(axis=0)\n", "plt.scatter(u, a_means)\n", "g0 = hierarchical_intercept_trace['γ_0'].mean()\n", "g1 = hierarchical_intercept_trace['γ_1'].mean()\n", "xvals = np.linspace(-1, 0.8)\n", "plt.plot(xvals, g0+g1*xvals, 'k--')\n", "plt.xlim(-1, 0.8)\n", "\n", "a_se = hierarchical_intercept_trace['a'].std(axis=0)\n", "for ui, m, se in zip(u, a_means, a_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": {}, "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": {}, "outputs": [], "source": [ "with Model() as contextual_effect:\n", " \n", " # Priors\n", " σ_a = HalfCauchy('σ_a', 5)\n", " \n", " # County uranium model for slope\n", " γ = Normal('γ', mu=0., sd=1e5, shape=3)\n", " \n", " # Uranium model for intercept\n", " μ_a = Deterministic('μ_a', γ[0] + γ[1]*u.values + γ[2]*xbar[county])\n", "\n", " # County variation not explained by uranium\n", " ϵ_a = Normal('ϵ_a', mu=0, sd=1, shape=counties)\n", " a = Deterministic('a', μ_a + σ_a*ϵ_a[county])\n", "\n", " # Common slope\n", " b = Normal('b', mu=0., sd=1e15)\n", " \n", " # Model error\n", " σ_y = Uniform('σ_y', lower=0, upper=100)\n", " \n", " # Expected value\n", " y_hat = a + b * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n", " " ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [σ_y, b, ϵ_a, γ, σ_a]\n", "Sampling 2 chains: 100%|██████████| 4000/4000 [00:32<00:00, 124.40draws/s]\n", "The acceptance probability does not match the target. It is 0.7084623255238152, but should be close to 0.8. Try to increase the number of tuning steps.\n" ] } ], "source": [ "with contextual_effect:\n", " contextual_effect_trace = sample(1000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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meansdmc_errorhpd_2.5hpd_97.5n_effRhat
γ__01.4262040.0498690.0010881.3244871.5218292156.5886870.999664
γ__10.6996420.0858950.0018100.5201230.8543342005.2300910.999683
γ__20.3938730.1968700.004075-0.0165760.7598702201.4316011.000343
\n", "
" ], "text/plain": [ " mean sd mc_error hpd_2.5 hpd_97.5 n_eff Rhat\n", "γ__0 1.426204 0.049869 0.001088 1.324487 1.521829 2156.588687 0.999664\n", "γ__1 0.699642 0.085895 0.001810 0.520123 0.854334 2005.230091 0.999683\n", "γ__2 0.393873 0.196870 0.004075 -0.016576 0.759870 2201.431601 1.000343" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "summary(contextual_effect_trace, varnames=['γ'])" ] }, { "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": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "69" ] }, "execution_count": 52, "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 PyMC:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "with Model() as contextual_pred:\n", " \n", " # Priors\n", " σ_a = HalfCauchy('σ_a', 5)\n", " \n", " # County uranium model for slope\n", " γ = Normal('γ', mu=0., sd=1e5, shape=3)\n", " \n", " # Uranium model for intercept\n", " μ_a = Deterministic('μ_a', γ[0] + γ[1]*u.values + γ[2]*xbar[county])\n", "\n", " # County variation not explained by uranium\n", " ϵ_a = Normal('ϵ_a', mu=0, sd=1, shape=counties)\n", " a = Deterministic('a', μ_a + σ_a*ϵ_a[county])\n", "\n", " # Common slope\n", " b = Normal('b', mu=0., sd=1e15)\n", " \n", " # Model error\n", " σ_y = Uniform('σ_y', lower=0, upper=100)\n", " \n", " # Expected value\n", " y_hat = a + b * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, sd=σ_y, observed=log_radon)\n", " \n", " # St Louis county prediction\n", " stl_pred = Normal('stl_pred', mu=a[69] + b, sd=σ_y)\n", " " ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [stl_pred, σ_y, b, ϵ_a, γ, σ_a]\n", "Sampling 2 chains: 100%|██████████| 6000/6000 [00:36<00:00, 165.74draws/s]\n" ] } ], "source": [ "with contextual_pred:\n", " contextual_pred_trace = sample(2000, tune=1000, cores=2, random_seed=RANDOM_SEEDS)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { 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wquWfmr0iy3K1atU0fNlHkqQadzVTjbuyjwCscVczjfsw4/9ZjY6J8PnhfQByRhcfAMBJBJTD6HcHEMzo4nMY/fQAghktKACAkwgoAICTCKhCwv0kAPAN96AKia/3kyTuKQE/Sku3CvXkfQZ6X8vDTQQUAOcxYCg40cUHAHASAQUAcBIBBQBwEgEFAHASAQUAcBIBBQBwEgEFAHASAQUAcBIBBQBwEgEFAHASAQUAcBIBBQBwEgEFAHASAQUAcFLQBZS1VkOHDlXNmjXVsGFDbdmyJVuZM2fOKDo62vuKiIjQ8OHDJUkvvfSSoqKiFB0drebNm+vrr7+WJK1du1axsbGKiopSbGys1q9fX6jnBRRlhw8f1uynOmlKl3v0fNfm2rhwZrYyW1e/rqnd79XU7vfqnnvu0bZt2yRJqampatKkiRo1aqT69etr7Nix3n2stRozZoxq1aqlunXrKj4+vtDOCdcWdM+Deuedd7Rnzx7t2bNHiYmJGjhwoBITE7OUKV26tJKSkrzLsbGx6tKliySpd+/eGjBggCRp5cqVGjFihNasWaOIiAi99dZbioyM1FdffaW2bdvqyJEjhXdiQBEWGhqqDr8dr8p1G+niubOa1ud+1YxrpYo1anvL3FL5v/TUnBUqWaacGn3zqZ566iklJiaqePHiWr9+vcLDw3Xp0iU1b95c7du3V1xcnObPn6/Dhw9r586d8ng8On78uB/PEj8VdAG1YsUKPfroozLGKC4uTikpKTp27JgqVaqUY/k9e/bo+PHjatGihSSpTJkykjKe2Hnu3DkZk/HUzpiYGO8+9evXV2pqqi5evKjixYsX8BkBRV+lSpVUuW6YJKn4TeGqUL2Wvj9+LEtA/axRE+/7uLg4JScnS5KMMQoPD5ckXbp0SZcuXfL+3s6YMUMLFy6Ux5PRmVShQoVCOR/kTdAF1JEjR1S1alXvcpUqVXTkyJGrBtSiRYvUo0cP7w+0JCUkJGjKlCk6eS5VT85cnu1Jn1+uW6mbazbQ81+fkXRGEk/4BPLLqaOHdHTXl6raIPaqZWbPmaP27dt7ly9fvqzY2Fjt3btXgwcPVtOmTSVJ+/bt05IlS7T8zTdVoXx5xcfH64477ijwc0DeBF1AWWuzrbsyfH5q8eLFWrBgQZZ1gwcP1uDBg9XzmZlaP2eKuk9I8G77dt9OrYmfqH4JS/Ov0gAkSRfPn9Wro/rq4ZGTVCK8dI5l9n26QRvmzlXXF1dk+fLYc946XThzWq+OfEwXl32k22rW1dkLqfr45GV9/tlnWr58ufr166ePPvqosE4H1xAUgyQSEhK8Ax4iIyN1+PBh77bk5GRFRkbmuN+2bduUlpam2Nicv6k1bNtZX7//jnf59LdHtWDkY+o2YbpurVo9f08CCHKXL13Sa6P6KrpDVzW4/+EcyxzbvV3LJ/5WK1as0E3lbsm2vWTpsqoe20y7P84YxFS2YqT3WJ07d9YXX3xRcCcAnwVFQA0ePFhJSUlKSkpSp06d9Morr8haq02bNqls2bK5du/16tUry7o9e/Z43+/6aK0iqtaQJF04c1rzh/ZWu9/8UdWimxbcyQBByFqrNyYMV/nqtdTikYE5lkk5lqxXRz2u7hMTVKtWLe/6s6dO6MKZ05KkS6kXtC/xA5WvltGNV69Ve+3bnNFi+uCDD7LsB/8Lui6+Dh06aPXq1apZs6ZKlSqlefPmebdFR0dnGb23dOlSrV69Osv+06dP17p16xQWFqYzYeHqNmG6JOmTJXN08vABrZ/9N62f/TdJUr8Xlyn8lvKFcFZA0bZx40ZtfXupbqtZT/E9W0mSHhwyRqe/yRgp27Tr4/rn7Mk6f/qUVjz73/rkhf/RiR+kIa+t05nvvtWysUNkL6fL2nRFPdBRdVs+KEm6t+8wLRkzQFHL5yg8PFxz5szx1ykiB0EXUMYYJSQk5LjtynCSpP3792crM3XqVO/7K/u3Wz85Uq2fHJlPtQRwpebNm+vZLd/lWuaXT7+gXz79gqSMQUk//n5WqlVfQxe9l+M+JUuX1ePxixjE5Kig6OIDAAQeAgoA4CQCCgDgJAIKQNBLS8/+/yPzszyuT9ANkgCAnwr1mGwzwuSGQRWFgxZUJr4RAYBbaEFl4hsUALiFFhQAwEkmp8lTcxEw/WBp6VahnqtPApsTX1tQ1yr/hzuZRQLIL9f6j7pXysvv542UH9XoVp//vlzP36QiLE8Xosh28dFlB6Cg+Pr3ReJvzPXwSxff9QxIYBADAAQXv7Sgrufbx6hGtxZQbQAALgqYLr5A7LK7ss/c1z7u69kn0Mu7WCfOOf/LF9ZnuMbXe1Dcs/IhoMaPHx86bNiwfPtge/57n8qnpIT6tE+gl3exTpxz/pd3sU6cc/6Xl6Sz34dqxvZ/57n8wPrZH7iYm0AKwKlTp1aTlDx27Ni03MrleRTf+PHjq0k6cKMVAwBAUvWxY8cezK2AL118yZKC6TnmBxRc55tXXJeccV2ujmuTs2C/LsnXLGGt5ZXDa9y4cdbfdXDxxXXhunBtuC6F9WImiasb7+8KOIrrkjOuy9VxbXLGdbkGX2eSAACgUNCCAgA4iYACADiJgAIAOImAyoUxppsxZrsxJt0Yc5e/6+Nvxph2xphdxpi9xpjR/q6PC4wxc40xx40xX/m7Li4xxlQ1xrxnjNmR+TuUf//LP4AZY0oYYzYbY7ZlXhcGSuSCgMrdV5K6SPrQ3xXxN2NMiKQESe0l1ZPUyxhTz7+1csJ8Se38XQkHpUkaaa2tKylO0mB+XiRJFyW1ttY2khQtqZ0xJs7PdXIWAZULa+0Oa+0uf9fDEU0k7bXW7rfW/iBpsaSOfq6T31lrP5SU9/lrgoS19pi1dkvm+zOSdkiq7N9a+Z/NcDZzMSzzxVDqqyCgkFeVJR2+YjlZ/MFBHhhjqkmKkZTo35q4wRgTYoxJknRc0lprLdflKgJmNvOCYoxZJ+m2HDaNsdauKOz6OCynWSX55odcGWPCJb0habi11rfZVYsoa+1lSdHGmHKS3jTGNLDWcg8zB0EfUNbaNv6uQ4BIllT1iuUqko76qS4IAMaYMGWE02vW2uX+ro9rrLUpxpj3lXEPk4DKAV18yKtPJd1hjKlujCkmqaeklX6uExxljDGSXpa0w1o7xd/1cYUxpnxmy0nGmJKS2kja6d9auYuAyoUxprMxJlnS3ZLeNsa86+86+Yu1Nk3SEEnvKuOG91Jr7Xb/1sr/jDGLJH0iqbYxJtkY84S/6+SIZpJ+Jam1MSYp89XB35VyQCVJ7xljvlDGl7611tpVfq6Ts5iLDwDgJFpQAAAnEVAAACcRUAAAJxFQAAAnEVAAACcRUAAAJxFQAAAn/T9rrgrXNJVCmQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_posterior(contextual_pred_trace, varnames=['stl_pred'])" ] }, { "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": 56, "metadata": {}, "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", "- Estimation of coefficients for (under-represented) groups\n", "- Incorporating individual- and group-level information when estimating group-level coefficients\n", "- Allowing for variation among individual-level coefficients across groups\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## References\n", "\n", "Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models (1st ed.). Cambridge University Press.\n", "\n", "Betancourt, M. J., & Girolami, M. (2013). Hamiltonian Monte Carlo for Hierarchical Models.\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": "3.6.7" }, "latex_envs": { "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 0 } }, "nbformat": 4, "nbformat_minor": 2 }