{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " \n", "
\n", "\n", "# Beetle Mortality Data\n", "Author(s): Paul Miles | Date Created: June 18, 2018\n", "\n", "This is a binomial logistic regression example with dose-response data.\n", "\n", "A. Dobson, \"An Introduction to Generalized Linear Models\", Chapman & Hall/CRC, 2002." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.9.0\n" ] } ], "source": [ "# import required packages\n", "import numpy as np\n", "import math\n", "from pymcmcstat.MCMC import MCMC\n", "import matplotlib.pyplot as plt\n", "import pymcmcstat\n", "print(pymcmcstat.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Define mortality data" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Beetle mortality data\n", "dose = np.array([1.6907, 1.7242, 1.7552, 1.7842,\n", " 1.8113, 1.8369, 1.8610, 1.8839])\n", "number_of_beetles = np.array([59, 60, 62, 56, 63, 59, 62, 60])\n", "number_of_beetles_killed = np.array([6, 13, 18, 28, 52, 53, 61, 60])\n", "\n", "x = np.array([dose, number_of_beetles]).T\n", "y = number_of_beetles_killed" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Define model options\n", "The user is given several modeling options. The user chooses the desired options by defining the appropriate keywork to beetle_link.\n", "\n", "- logitmodelfun: \n", "$$y(d,\\theta) = \\frac{1}{1 + \\exp(\\theta_0 + \\theta_1d)}$$\n", "- loglogmodelfun:\n", "$$y(d,\\theta) = 1 - \\exp(-\\exp(\\theta_0 + \\theta_1d))$$\n", "- probitmodelfun:\n", "$$y(d,\\theta) = \\frac{1}{2}\\Big[1 + \\text{erf}\\Big(\\frac{\\theta_0 + \\theta_1d -\\mu}{\\sigma\\sqrt{2}}\\Big)\\Big], \\quad \\mu = 0, \\quad \\sigma^2 = 1$$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def logitmodelfun(d, t):\n", " return 1/(1+np.exp(t[0]+t[1]*d))\n", "def loglogmodelfun(d, t):\n", " return 1 - np.exp(-np.exp(t[0] + t[1]*d))\n", "def nordf(x, mu = 0, sigma2 = 1):\n", " # NORDF the standard normal (Gaussian) cumulative distribution.\n", " # NORPF(x,mu,sigma2) x quantile, mu mean, sigma2 variance\n", " # Marko Laine \n", " # $Revision: 1.5$ $Date: 2007/12/04 08:57:00$\n", " # adapted for Python by Paul Miles, November 8, 2017\n", " return 0.5 + 0.5*math.erf((x-mu)/math.sqrt(sigma2)/math.sqrt(2))\n", "def probitmodelfun(d, t):\n", " tmp = np.vectorize(nordf)\n", " return tmp(t[0] + t[1]*d)\n", "\n", "beetle_link_dictionary = dict(\n", " logit={'theta0': [60, -35], 'modelfun': logitmodelfun, \n", " 'label': 'Beetle data with logit link'},\n", " loglog={'theta0': [-40, 22], 'modelfun': loglogmodelfun, \n", " 'label': 'Beetle data with loglog link'},\n", " probit={'theta0': [-35, 20], 'modelfun': probitmodelfun, \n", " 'label': 'Beetle data with loglog link'},\n", ")\n", "# specify model type\n", "beetle_link = 'loglog' \n", "beetle_model_object = beetle_link_dictionary[beetle_link]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Setup MCMC Simulation\n", "Note, $\\theta_0 = b_0$ and $\\theta_1 = b_1$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Initialize MCMC object\n", "mcstat = MCMC()\n", "# initialize data structure \n", "mcstat.data.add_data_set(\n", " x, y, user_defined_object=beetle_model_object)\n", "# initialize parameter array\n", "theta0 = beetle_model_object['theta0']\n", "mcstat.parameters.add_model_parameter(name='$b_0$',\n", " theta0=theta0[0])\n", "mcstat.parameters.add_model_parameter(name='$b_1$',\n", " theta0=theta0[1])\n", "# Generate options\n", "mcstat.simulation_options.define_simulation_options(nsimu=5.0e3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sum-of-squares function is somewhat involved as you must make sure the data component are the appropriate sizes." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# define sum-of-squares model function\n", "def ssfun(theta,data):\n", " # unpack data\n", " ss = np.zeros([1])\n", " y = data.ydata[0]\n", " ndp = len(y)\n", " dose = data.xdata[0][:,0].reshape(ndp, 1)\n", " n = data.xdata[0][:,1].reshape(ndp, 1)\n", " obj = data.user_defined_object[0]\n", " model = obj['modelfun']\n", " # evaluate model\n", " p = model(dose, theta)\n", " # calculate loglikelihood\n", " ss = -2*(y*np.log(p) + (n-y)*np.log(1-p)).sum()\n", " return ss\n", "\n", "# Define model object:\n", "mcstat.model_settings.define_model_settings(sos_function = ssfun)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Run simulation\n", "We observe several error messages associated with numerical overflow. This is acceptable in light of those points being rejected during the simulation." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Sampling these parameters:\n", " name start [ min, max] N( mu, sigma^2)\n", " $b_0$: -40.00 [ -inf, inf] N( 0.00e+00, inf)\n", " $b_1$: 22.00 [ -inf, inf] N( 0.00e+00, inf)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/envs/pymcmcstat_190/lib/python3.6/site-packages/ipykernel_launcher.py:14: RuntimeWarning: divide by zero encountered in log\n", " \n", "/anaconda3/envs/pymcmcstat_190/lib/python3.6/site-packages/ipykernel_launcher.py:14: RuntimeWarning: invalid value encountered in multiply\n", " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 5000 of 5000 complete in 0.9 sec" ] } ], "source": [ "# Run mcmcrun\n", "mcstat.run_simulation()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Extract results and display chain statistics" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "------------------------------\n", "name : mean std MC_err tau geweke\n", "$b_0$ : -39.9298 3.1084 0.1059 6.8859 0.9892\n", "$b_1$ : 22.2399 1.7278 0.0592 6.9157 0.9890\n", "------------------------------\n", "==============================\n", "Acceptance rate information\n", "---------------\n", "Results dictionary:\n", "Stage 1: 37.82%\n", "Stage 2: 48.14%\n", "Net : 85.96% -> 4298/5000\n", "---------------\n", "Chain provided:\n", "Net : 85.96% -> 4298/5000\n", "---------------\n", "Note, the net acceptance rate from the results dictionary\n", "may be different if you only provided a subset of the chain,\n", "e.g., removed the first part for burnin-in.\n", "------------------------------\n" ] } ], "source": [ "# Extract results\n", "results = mcstat.simulation_results.results\n", "names = results['names']\n", "chain = results['chain']\n", "s2chain = results['s2chain']\n", "names = results['names'] # parameter names\n", "# display chain stats\n", "mcstat.chainstats(chain, results)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plot the chain and pairwise correlation panel" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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