mamacneil/Forced_PyMC2

## Forced_PyMC2
{
	"cells": [
		{
			"cell_type": "markdown",
			"metadata": {
			},
			"source": [
				"# Bayesian implementation of forced-response model in PyMC3\n",
				"\n",
				"### Based on Blair et al. 2015\n"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 1,
			"metadata": {
				"collapsed": true
			},
			"outputs": [

			],
			"source": [
				"# Import python packages\n",
				"%matplotlib inline\n",
				"import pandas as pd\n",
				"import numpy as np\n",
				"import scipy as sp\n",
				"import matplotlib.pyplot as plt\n",
				"import pymc as pm\n",
				"\n",
				"# Helper function\n",
				"def indexall(L):\n",
				"    poo = []\n",
				"    for p in L:\n",
				"        if not p in poo:\n",
				"            poo.append(p)\n",
				"    Ix = np.array([poo.index(p) for p in L])\n",
				"    return poo,Ix"
			]
		},
		{
			"cell_type": "markdown",
			"metadata": {
			},
			"source": [
				"The first step is to simulate known data from which to test the model. According to Blair *et al.*, the forced-response model involves a randomization device that forces a yes with probability $p_{fyes}$, a no with probability $p_{fno}$, and an assumed truthful answer with probability $p_{truthful}=1-p_{fyes}-p_{fno}$. So the first step is to assign these probabilities: "
			]
		},
		{
			"cell_type": "code",
			"execution_count": 2,
			"metadata": {
				"collapsed": false
			},
			"outputs": [

			],
			"source": [
				"# Dice randomizer setup in Blair et al.\n",
				"p_fyes = 1/6\n",
				"p_fno = 1/6\n",
				"p_truth = 1-p_fyes-p_fno\n",
				"randomizer = np.array([p_fyes,p_fno,p_truth])\n",
				"\n",
				"# True underlying probability of yes\n",
				"p_interest = 0.34\n",
				"\n",
				"# Number of observations\n",
				"nobs = 250"
			]
		},
		{
			"cell_type": "markdown",
			"metadata": {
			},
			"source": [
				"In Blair's description, they use $Z_i$ to represent the true (unobserved, latent) distribution of yes ($=1$) and no ($=0$) in the population. So we'll first simulate this from the data:"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 3,
			"metadata": {
				"collapsed": false
			},
			"outputs": [
				{
					"data": {
						"text/plain": [
							"array([1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0,\n",
							"       0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0,\n",
							"       0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1,\n",
							"       0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1,\n",
							"       0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0,\n",
							"       0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0,\n",
							"       0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1,\n",
							"       1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,\n",
							"       0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,\n",
							"       1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,\n",
							"       0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0])"
						]
					},
					"execution_count": 3,
					"metadata": {
					},
					"output_type": "execute_result"
				}
			],
			"source": [
				"# Latent truth\n",
				"Zi = np.random.binomial(n=1, p=p_interest, size=nobs)\n",
				"Zi"
			]
		},
		{
			"cell_type": "markdown",
			"metadata": {
			},
			"source": [
				"The next step is to transform $Z_i$ into fake observations using the known randomizer probabilities:"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 4,
			"metadata": {
				"collapsed": false
			},
			"outputs": [
				{
					"data": {
						"text/plain": [
							"array([ 1,  0,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0,  0,  0, -1,  1,  0,\n",
							"        0,  0,  0, -1,  1,  0,  0,  0,  0,  0, -1,  0,  0,  0,  0, -1,  0,\n",
							"        0,  0, -1, -1, -1,  0,  0,  0, -1,  0,  1,  1,  0,  0,  0,  0,  0,\n",
							"        0, -1, -1, -1, -1,  0,  0,  0,  0,  0,  0,  0, -1, -1,  0,  0,  1,\n",
							"        0,  0,  0,  0,  0,  0,  0, -1,  0, -1,  0,  0,  0,  1, -1,  1, -1,\n",
							"        1,  1,  0,  0, -1,  0,  0,  1,  1,  0,  0,  0,  0,  0,  0,  0,  0,\n",
							"        0,  0,  1,  1, -1,  0,  0, -1,  0,  1,  1,  0,  1, -1,  0,  0,  0,\n",
							"        1, -1,  0,  0,  0, -1,  1,  0,  1,  1,  1,  0,  0,  0, -1, -1,  0,\n",
							"        0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,\n",
							"        0,  0,  0,  0, -1, -1,  0,  0,  0,  1,  0, -1,  0,  0,  0,  0,  0,\n",
							"        1,  0,  0,  0,  0,  0, -1,  0,  0,  0,  0,  1,  0,  1,  0,  1,  0,\n",
							"        0,  0,  1,  0,  0,  0,  0,  0,  0, -1,  0,  1,  1,  0,  0,  0,  0,\n",
							"        1,  1,  0,  0,  0,  0,  0,  0,  0, -1,  1,  0, -1,  0,  0,  0,  1,\n",
							"        1, -1,  0,  0,  0, -1,  0,  1,  0,  0,  0,  0,  0,  0,  0, -1,  0,\n",
							"        0,  0, -1,  0, -1,  0,  0, -1, -1,  0, -1,  0])"
						]
					},
					"execution_count": 4,
					"metadata": {
					},
					"output_type": "execute_result"
				}
			],
			"source": [
				"# Create forced no and yes array\n",
				"randp = np.random.multinomial(1, randomizer, size=nobs)\n",
				"Ri = np.array([np.array([1,-1,0])[x==1] for x in randp]).reshape(1,nobs)[0]\n",
				"Ri"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 5,
			"metadata": {
				"collapsed": false
			},
			"outputs": [
				{
					"data": {
						"text/plain": [
							"array([1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,\n",
							"       0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1,\n",
							"       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1,\n",
							"       0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1,\n",
							"       1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1,\n",
							"       0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0,\n",
							"       0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1,\n",
							"       1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1,\n",
							"       0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0,\n",
							"       1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0,\n",
							"       0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0])"
						]
					},
					"execution_count": 5,
					"metadata": {
					},
					"output_type": "execute_result"
				}
			],
			"source": [
				"# Observed data\n",
				"Yobs = 1*((Zi+Ri)>0)\n",
				"Yobs"
			]
		},
		{
			"cell_type": "markdown",
			"metadata": {
			},
			"source": [
				"Now that we have known data with 1/6 probabilities of false yes and no responses, we can build a statistical model to see if we can recover the true probability of yes."
			]
		},
		{
			"cell_type": "code",
			"execution_count": 6,
			"metadata": {
				"collapsed": false
			},
			"outputs": [

			],
			"source": [
				"# True probability of yes\n",
				"P_yes = pm.Beta('P_yes',alpha=1,beta=1)\n",
				"\n",
				"# Mean model\n",
				"p_mu = pm.Lambda('p_mu', lambda p=P_yes: p_truth*P_yes+p_fyes)\n",
				"\n",
				"# Likelihood\n",
				"Yi = pm.Bernoulli('Yi', p=p_mu, value=Yobs, observed=True)"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 7,
			"metadata": {
				"collapsed": false
			},
			"outputs": [

			],
			"source": [
				"M = pm.MCMC(locals())"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 8,
			"metadata": {
				"collapsed": false
			},
			"outputs": [
				{
					"name": "stdout",
					"output_type": "stream",
					"text": [
						" [-----------------100%-----------------] 10000 of 10000 complete in 3.5 sec"
					]
				}
			],
			"source": [
				"M.sample(10000,9000)\n",
				"M.sample(10000,9000)"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 9,
			"metadata": {
				"collapsed": false
			},
			"outputs": [
				{
					"name": "stdout",
					"output_type": "stream",
					"text": [
						"Plotting P_yes\n"
					]
				},
				{
					"data": {
						"image/png": 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N2FlE+gILgZHAKcETVHWD3UBEJgJPqOpkEemU61qjcJqaYOed4YADisuqvu++Lino/ffn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\nWQ3+H0IC7ODgzaO1AAAAAElFTkSuQmCC\n",
						"text/plain": [
							"<matplotlib.figure.Figure at 0x10374cc50>"
						]
					},
					"metadata": {
					},
					"output_type": "display_data"
				}
			],
			"source": [
				"pm.Matplot.plot(P_yes)"
			]
		},
		{
			"cell_type": "code",
			"execution_count": 10,
			"metadata": {
				"collapsed": false
			},
			"outputs": [
				{
					"data": {
						"image/png": 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						"text/plain": [
							"<matplotlib.figure.Figure at 0x12dfe4438>"
						]
					},
					"metadata": {
					},
					"output_type": "display_data"
				}
			],
			"source": [
				"pm.Matplot.summary_plot(P_yes, vline_pos=p_interest)"
			]
		},
		{
			"cell_type": "markdown",
			"metadata": {
			},
			"source": [
				"So from this we have a model framwork for analyzing a forced response design - covariates in a linear model can be readily added to 'P_yes' using a logit link."
			]
		}
	],
	"metadata": {
		"kernelspec": {
			"display_name": "Python 3",
			"language": "python",
			"name": "python3"
		},
		"language_info": {
			"codemirror_mode": {
				"name": "ipython",
				"version": 3
			},
			"file_extension": ".py",
			"mimetype": "text/x-python",
			"name": "python",
			"nbconvert_exporter": "python",
			"pygments_lexer": "ipython3",
			"version": "3.5.1"
		}
	},
	"nbformat": 4,
	"nbformat_minor": 0
}