S6_Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(lme4)\n",
    "options(rgl.useNULL=TRUE)\n",
    "library(LMERConvenienceFunctions)\n",
    "\n",
    "library(ggplot2)\n",
    "options(jupyter.plot_mimetypes = 'image/png')\n",
    "library(repr)\n",
    "options(repr.plot.width=6, repr.plot.height=6)\n",
    "\n",
    "library(car)\n",
    "library(MASS)\n",
    "\n",
    "library(vcd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Number of answers\n",
    "\n",
    "In this notebook, we document our various steps taken to study the effect of the course of a session on the number of answers a comment receives. Note that we only do this on a sample of 1 mio. data points here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = read.csv(\"/home/psinger/Reddit-depletion/data/sample.csv\", header=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1000000"
      ],
      "text/latex": [
       "1000000"
      ],
      "text/markdown": [
       "1000000"
      ],
      "text/plain": [
       "[1] 1000000"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nrow(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data inspection\n",
    "\n",
    "We start by getting a better feeling of our data. Note that num_answers represents count data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can limit our data to those sessions that have at least two and less than 11 comments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx = data$session_comments > 1 & data$session_comments < 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = data[idx,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "515196"
      ],
      "text/latex": [
       "515196"
      ],
      "text/markdown": [
       "515196"
      ],
      "text/plain": [
       "[1] 515196"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nrow(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6zoAjPFJIoKEUAo2uKWt4vyNZjECja8qV/CNZjECjayLQUAqBhjL6FBQUTJQS4zbxmbRhN0bd9MN2FiXQ6HoGVFVVVUutcZv4zGl1u6L2SDsfLiXQ6JrcNzkulcxPzyTQ6JoINJRCoKGUXsVu3ygk0FAKgUZwZA6+tI/Lx5MINIKi/4wmkfzrSh3PnESgERB9q6WyUPIva6k/3aGKQCMgJslo3dzLcVHr0w5VBBoBsXWlHt5tN8/pS7IEGgHRWBTZD13odAZ/Ao2AKN8QsgKtV6xwqCLQCIhxMrW7EWj9DnnQoYpAIyAy3pSd86W0XNZ1d6gi0AiKrFG1IlJXkO1URKARINmDe7tUEGgEiPvF6wk0AiD5i9cTaARA8hevJ9AIgOQvXk+gEQDJX7yeQCMAkr94PYFGACR/8XoCjQBI/uL1BBoBkPzF6wk0giDpi9cTaASK28XrCTSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAKNAOHi9VACF6+HUrh4PZTCxeuhFC5eD6Vw8XoohYvXQylcvB5K4eL1UAsXr4eauHg9lNHjlBzdrYZAIwj0vInV+4yt6P3Vk853LCTQCIDMWSINFWVzyyrqRYqcPp9EoBEA42XZ5eEYhy4ukzEOlQQaAbBle1b0cfqaTQ6VBBoB0DrbNjGlxaGSQCMAtmyPfWQ0VLnZoZJAIwDGxbahh5bJWIdKAo0AyJgp0lBeOmfB8jqR5zMcKgk0gkDPm1zTJCJNNZPzHA+uEGgEhZ4zgCOF+DdDoBEgWcP7uVQQaARIruS7VBBoBAiBhlIINJTRp6CgYKKUGLeJz2SPfyjqWQKNYBhQVVVVLbXGbeIzuTNnRy2Uds6rRKDRNbHJAaUQaCiFQEMpvYqdv1FIoKEYAo3gyBx8aR+XjycRaARF/xlNIvnXlXLmJKigb7VUFkr+ZS31pztUEWgExCQZrZt7OS5qfdqhikAjILau1MO77ebxJVkooLEosh+6kDP4QwHlG0JWoPWKFQ5VBBoBMU6mdjcCrd8hDzpUEWgERMabsnO+lJbLuu4OVQQaQZE1qlZE6gqynYoINAIke3BvlwoCjUC58wrn5wk0AkWcjqpoBBqBMCxKyowbh0oCjQCQeA6VBBoBcNPHsu7eUSYpN24cKgk0gqDvbCkbYD5gGxpquOGjvXemEWgo4/gSWXQ6gYY6vrWz8ScEGuroUywEGir5+t1fdS4g0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDQCJHvowHTnCgKNABhZYN6eVSoizRNynCoJNAJgiXl579x62Vg0ba2s7eZQSaARAFagC2VcSNP0e2W8QyWBRgBYgd60Xjcf6+vKHSoJNALACnTjc+GJ4kaHSgKNALACvWpZeGLRNodKAo0AWCKP3HnVmEPXm4+vkRKHSgKNAChpFtMeTes55+DeQQ6VBBpBkHbyFSMemLVU03Jl8dlOhQQagdLtJOfnCTQCo8cpObpbDYFGEOh5E6v3GVvR+6snne9YSKARAJmzRBoqyuaWVdSLFDl9PolAIwDGy7LLwzEOXVwmYxwqCTQCYMv2rOjj9DWbHCoJNAKgdbZtYkqLQyWBRgBs2R77yGiocrNDJYFGAIyLbUMPLZOxDpUEGgGQMVOkobx0zoLldSLPZzhUEmj45DbHr1Il0PMm1zSJSFPN5DzHgysEGj6RppKrnX7XfoqeM4AjheiyfrRE5MOJF7lGtGMINHxz6ph1IhvGnJL8ElnD+7lUEGj46byHton88wfHJlmeK/kuFQQafsoaNv2A+V7vj06nJogh0OjCenz7+T0ib/5s0Mj18nRSSxBodFnfmbtfZOnd1gf2M97Z41rfp6CgYKKUGLeJz/R/Y0VUFYGGP0SW/PTEtom5y1zrB1RVVVVLrXGb+Ez3n/0i6jECDX/874nuNYnY5EAXduJXjJsRzt9AiUeg0WVlPCqrjbtaeSyU9DIEGl3WXbJ8uHF3xctyR9LL9Cp2+31OoOGTdVvD30JJ37jSw64EGj5pnBF5MH1vsotkDr60j8tnPwg0fFK1KPLgn+8mt0D/GU0i+deVcuYkdEVPh8+9qF13aIZLZVjfaqkslPzLWupPd6gi0PDJZ2qlbOzt982Tj/onVT9JRuvmXo6LWp0OkxNo+OW056xTis77XHLlW1fq4d128/iSLLqm479w8xVJHy9sLIrshy7kDP5QQPmGkBVovWKFQxWBhl++XfJqRFLl42RqdyPQ+h3yoEMVgYZPRojsqwtLqj7jTdk5X0rLZV13hyoCDZ+8ve9LHfuCbNaoWuM9ZF1BtlMRgYZPmh/v+DLZg3u7VBBo+OS9qUewUEY/Dn2jaxpfe3zyxRkjnpj5k26hCc3ySUlfp0ICDZ+kF1Z996zjeplca3uuMA/BzB0t779aI7VOJz0g0PDJ7t3SxrX2QSkZOvAXsv/Fbpr+U/mDQyWBhk+eiHGtfXu9+a2W5XKOcauvWuVQSaARAPsLzdunxDodzbMc+kbXlMQH9sM2LzRvh0+xJl7Z7lBJoOGXpD6wH/ac3JbW9njIgXkOlQQaPknuA/thJ+6S2metR8Omtxwa4lBJoOGT5D6wH3HCU5vfth4Uy+avORUSaPgkuQ/sx4QvGnTh6c4b3QQaPknuA/sdRaDhk+Q+sN9RBBo+Se4D+x1FoOGT5D6w31EEGn5J6gP7HUWg4SP3D+x3FIGGUgg0fFIc42FXAg2fRD8Nva3aw64EGj5JN2WcMHzNq8d42JVAw2fHbX/Ew24EGn57/H0PmxFo+G1ak4fNCDT8Ffpa0xoP2xFo+GRfWKvIdz3sSqDhk3kR06/xsiuBhlIINJRCoOGTnfE86kqg4ZMpFSI7V9aKbF1i8qgrgYZPPt/ymhmzz7266xwPuxJo+OSF98Of7O+54wUPuxJo+OSDWZEHs2o97Eqg4ZPtb0YeLPvAw64EGj55QW627m8Wp3PVdRSBhk/O3C0vjrx25IvScqGHXQk0/DL0DesLK+/ke9mUQMM3+vk3/fz7l6Z72pNAwz9Jn/A8eQQafunACc+TR6Dhk46c8Dx5BBo+6dAJz5NGoOGTjp7wPDkEGj7hhOdQypGc8Dx76ECXvXwEGj7pyAnPRxaYt2eVikjzhBynSgINn3TkhOdLzMuB59bLxqJpa2VtN4dKAg2/dOCE51agC2VcSNP0e2W8QyWBho+SPeG5FehN662jivq6codKAg2f3NWB88tYgW58LjxRzMXr0QXt2538xzisQK9aFp5YtM2hkkDDJxPkS0nXLpFH7rxqzKHrzcfXSIlDJYGGT9J+VTtyUJ9eJtfakmbro9N7NK3nnIN7BzlUEmj4pK7uYNtFKdyL006+YsQDs5aaxxYXO346j0DDJ0/EdGCpbic5P0+g4YMptx/JUj1OyXF9H0mg4QOZY97eNT3pBfS8idX7jI2T/dWTzncsJNDwQTjQc5LYeA7LnCXSUFE2t6yiXqTI6fNJBBo+6Gigx8uyy8MxDl1cJmMcKgk0fNDRQG/ZnhV9nL5mk0MlgYYPOhro1tm2iSktDpUEGj7o+G/o2EdGQ5VOX9ki0PBBRwM9LrYNPbRMxjpUEmj4QGpnGmplZphrfcZMkYby0jkLlteJPJ/hUEmg4QOJ576Anje5psmobKqZnOd4cIVAwwdD4iW3kJ4zgCOF+DdDoBEgWcP7uVQQaASIdWIaRwQaAUKgoZTDBPqY46K+TqARDH0KCgomSolxm/jMGQft+wAJNAJhQFVVVbXUGreJz+gXXhR1G4FGcLANDaUQaCiFQEMpvYqdv1FIoKEYAo3gSOK6hgQaQZHUdQ0JNAIiuesaEmgERHLXNSTQCIjkrmtIoBEQyV3XkEAjIJK7riGBRkAkd11DAo2ASO66hgQaQZHUdQ0JNALE/bqGBBrBkH1e27WF+p/qUEagEQSffV3k0Nzw9VXecjrTEoFGAJywW5YWrpfaAeYEgUbQFcp/aZo+QRanaQQawbfpDfM27QX5gUagEXyN06273D0f9iLQCL6160LW/Y/lb2kEGoH3kEyzztKovyQPhwg0gq7HWpEtA40Hxy+TmgYCjaDLvHvR+xeYD7r/5n3HM/4TaARM6LQrHZ4l0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgYZSCDSUQqChFAINpRBoKIVAQykEGkoh0FAKgUaAZA8dmO5cQaARACMLzNuzSkWkeUKOUyWBRgAsMa8TlFsvG4umrZW13RwqCTQCwAp0oYwLaZp+r4x3qCTQCAAr0JvW6+ZjfV25QyWBRgBYgW58LjxR3OhQSaARAFagVy0LTyza5lBJoBEAS+SRO68ac+h68/E1UuJQSaARACXNYtqjaT3nHNw7yKGSQCMI0k6+YsQDs5ZqWq4sPtupkEAjULqd5Pw8gUZg9DglR3erIdAIAj1vYvU+Yyt6f/Wk8x0LCTQCIHOWSENF2dyyinqRIqfPJxFoBMB4WXZ5OMahi8tkjEMlgUYAbNmeFX2cvmaTQyWBRgC0zrZNTGlxqCTQCIAt22MfGQ1VbnaoJNAIgHGxbeihZTLWoZJAIwAyZoo0lJfOWbC8TuT5DIdKAo0g0PMm1zSJSFPN5DzHgysEGkGh5wzgSCH+zRBoBEjW8H4uFQQaAZIr+S4VBBoBQqChFAINZfQpKCiYKCXGbeIz+jdujBpLoBEMA6q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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data$num_answers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data$num_answers[data$num_answers<10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression model\n",
    "\n",
    "We use mixed-effects models where in the basic form (that we analyze in this notebook), we are interested in studying num_answers ~ 1 + session_index + session_comments + (1|author)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear mixed-effects regression\n",
    "\n",
    "Even though we cannot expect a simple linear mixed-effects regression to be an appropriate model for our count data, we start with it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer = lmer(num_answers~1+session_index + session_comments+(1|author), data=data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: num_answers ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1823639.9 1823695.6 -911814.9 1823629.9    515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       " -3.054  -0.443  -0.399   0.260 200.394 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.02697  0.1642  \n",
       " Residual             1.99077  1.4109  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error t value\n",
       "(Intercept)       0.619751   0.004167  148.72\n",
       "session_index    -0.042064   0.001489  -28.25\n",
       "session_comments  0.030654   0.001150   26.66\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.174       \n",
       "sssn_cmmnts -0.538 -0.652"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mcp.fnc(m_lmer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we can see in above plot is, that the residuals do not appear to be normally distributed and we can see clear heteroskedasticity. Thus, as expected, a linear model does not provide a good fit here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear mixed-effects regression (log-transform)\n",
    "\n",
    "Next, let us take the log of the response variable and repeat a linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer_log = lmer(log1p(num_answers)~1+session_index+session_comments+(1|author), data=data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log1p(num_answers) ~ 1 + session_index + session_comments + (1 |  \n",
       "    author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       " 641073.8  641129.6 -320531.9  641063.8    515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-1.4921 -0.7955 -0.7139  0.7173 11.6273 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.008545 0.09244 \n",
       " Residual             0.194979 0.44156 \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error t value\n",
       "(Intercept)       0.3557755  0.0013273  268.05\n",
       "session_index    -0.0185186  0.0004719  -39.24\n",
       "session_comments  0.0147068  0.0003657   40.22\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.174       \n",
       "sssn_cmmnts -0.536 -0.649"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer_log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mcp.fnc(m_lmer_log)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That does not look satisfying at all. We should focus on generalized mixed-effects models to better model the count data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson GLMER\n",
    "\n",
    "Let us start with a Poisson GLMER, which is a main choice when working with count data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00539401 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "m_poisson = glmer(num_answers~1+session_index+session_comments+(1|author),data=data,family=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1119602.2 1119646.8 -559797.1 1119594.2    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.708 -0.658 -0.591  0.554 44.510 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.398    0.6308  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.695957   0.004442 -156.69   <2e-16 ***\n",
       "session_index    -0.062017   0.001416  -43.80   <2e-16 ***\n",
       "session_comments  0.045746   0.001078   42.42   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.183       \n",
       "sssn_cmmnts -0.513 -0.605\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00539401 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ds2b+mj139XB7oGAPE1BopIhYI3Rzf7lXl9KGN6W7bJPffl+YoFBopKhYI3T8lNK53peeGm9tOAZQaKSIWCN0/hXUhFpTzemEdmvSu1UpeweBEHs8titdu5zZtV4LL3SVLkPblTafzUYMiIR0KnM+tuzYH6uF7rPnvAHzeWUtVrzIBADli5XNTGYsrNCeqzWaSCrl5/cH9qlXqAOF4X+aaRVIiW9i99mhbCQ31go9DCAzicd8WfsAUv19Dvn4JwNsz9eRKAeFFfpoeHd3UuYfio5OBJ86hTpUACrJR3Pbd7W4FJfdsVboR5kdLF4sfhbcaMdr7PqhD0wzkbOQQnfRNGZe26rPqF4jDc5HVC7MsQLwXYrhl/PoJpFLRvJhrdDq9ZbnDYt81aLodv+5iZyFFHrDUfb15haXl4MJKfHw78IcKwBTbhoSC7xFLhnJh7VCR621PK8256jsNRoTOQsp9Cl2Zbc34D3iN51JjDP1q2ILxj0yJFYfFrlkJB/WCj0ruorFecMiS2SnXQNDTOQspND72D/1H0EJ8uBnJvG5ujDHCkALujG3dQ+ZLHLJSD6sFdpt29OBDStWYDGbd+arOnQrH5huImchhR4f4cHckkG1+hTboeRb87enAnPuZkXm1WVtoti1dyQf1gqdlgZZmM3rvhcg9bb3wbO3kgB2m1pvvpBCl43b5E7cEn+5xj063H20MMcKQdV7savHLryb3FbsgpF8WCv0hleYzyxrsSpUxY6XCl3VwuSzkcI+tvsoLnTj9Lv00+pM+ieK8aq0xY9eBMHz5+PBFxa+LmqZiFFEbymUlXvTeEvh6/dDskksbEthxd8O3NxxVXtyztKb2tGvb44A+ZUvhYgWcTaEELr8O5UEiKTE8JHZ7CxaX45O6654L2r8btL1/q0/X6qdLUBQiLNhtdDl5yYwlYjkBeWFiYfHms5JMv+DXL/srhSOMiyGWCt06afw8vDag7HwRMjOZtYI3YKuzSdOYrtdMcRaoZfCQvbhcoklsFiYgDisEXpwhCHx+w1hgkGcCWuFvnufv8NzeRhoNm9abkzktEboIWGGxBT/FcGalGv9i3wmjvfmHt7/x5sF728y+/D+6XWtKwMRDmuFVmRN+Lkj02ze4f4AYfeyMZHTGqFbUjX4xKn0kPHtvlytzTvHbqGYp7+wYs0t1YiC9s/UX1qx+oZmjDVlIAJirdAPb/Nbmf8D85ndzsLXFp3VqpvCoAMu7PYL+jF3kk46Kzp1DlV8wW6G69ob3z9IxT0dHMSU4YrrMzsC1gq9DiaxdQ7ZJFhnQe4vRRCatJKf7/tWh3kaMMznv92KLkMv/uC3284a3//M8Gxww5NANSQfblD0khBhsFboipEQtHr66iCIrGhB7pqZPS06q3VjChseSAd90GKVof1mxMvf/+iZfz0hS6gFfLcj0lNpdH9VaMonvGBFx8Z9/FJND8RBbI/Vz6FrbtYDgH5zTWHi4bF2kKzsDU/STcGnO6fQ/rcVL3sU5TzvgqEvYRsoYWx/Q+Cbu1tRwI4PdtnzsHjMc+rSe9WZTUOLdpGwMQK0FHo06thI4OGhQoz6rgfvsJv3VQ/PEVJ6maYwk4WVatX7HbZfYMWsxpmBxnvwlTHUrdff55/Z1KQccaZAwal8VXli2f6kF03sHYgRhOnL4VJX2BHXgkxjcOUUe7k8dkn5PfturwWDeA14zJVTaRD9I5O8vJv7xP36v8aznj3K1Wt8I/7j3z8fXvR4nYezj2sxr2XPhgo9p6EAWC10+21NSOVA0K8Q8o+tIEI3SrzaveZ7+sw9nHMd9Bb/zu2K61uClJ+qGc1UNTSrKzAX3iPJdYxnfU++sRIh1RMzDU+qgwt8vichPqDe5rblEobaORIjWCt0Vxo+IqvgfAAI+eWEmWim7nE1U703/KbVBROtI7nooONv7UZmMPe5n0fog0PhfvOCMrcJoZ6F0Ml+/Lsa+rwrJUqRX+8bEtv/s2scRrFWaD9FexeXOH9SIuK6QBGxWCZ041kHD85sQOp/N3nQu0RWr1H+vxEub1TTd2KqukzyI9rSaZ3WneC3rokDmFf39mNGfmiid7XbJ2NGftSa4p7euOx54GJhIc7MnAuGxD+iD6Uwj7VCp+xlnwX8QsiORIEiYrFI6Km6wPUb7ml9qZjLofAsA0C5levGmnss2MVdXtGQfr7T8luWFn4qq1fKtT8sDni6bnnxeWw3KqtzwTFL2h5Exlqh070ImQQtCNmmECYgDkuE7qPpzW7OwFzS5bQGMle93efuk8qd/BSQcS7HXNVDIS3oxCYviupuaeH7s/433Z9oecTfFqOGlVrabty2nuoLO0diBGuFDogq4/ooxoV4PHsiUEQslgj9JOhWsPfUptShG5OpB6nT9Mn3KpW5f0m//fPGPY6ps3/S5TJofVKYUqfTv21p4ZNe8MMd3yxchdil+DR9/53MXktaB5+xdyBGsFbooRB+D+aTTgHMhVI4LBB6GPhPGrg4MepFe5oOAaDlZ+/tZ6KZxO1cGJ813uA03arauE1br6VcW5LvFKWNj9OtlLKBrY1XuH5N3IGJzoPLXFVCYJT+P0f8FbZWaJeZSfpjZcgsOCHkkBXzQr+lhfrMHVvrpPgmQB+Arq2C6GVU9XkwYcE/w6qSEkk/8Nlq0aHc1i34Up5ZjapsjgNd8M/GbuLaJd1fOHZVzAMc9Fogr33167d17B2EUaxvWJGxrYT16gh6NTMv9Orr2i5l97Gt7ulAA5x548AVlbqrL8gvno5VjiFnFvLZBmYE8YnFIbkbVmqEPB787kcz5DuMxV1zwYXgE5NwvmdnxFlbCm9OO370OR28dCWj9MbGkRGJGQOfqkdT+ilrf+80TNvXewGfbUy4pno/5qJdbWramlzHH77J+dpU8aOggSP2xilbCjvte6Z9MlsHy7jpfOlMMiE1Ve5+GLwpeHwkQHdp6bPkgXzOrzNi5emXTsUq79O5hsxW0XfkEysvCRg2Yn+csaVwoW7HisjwVL2Oev4CIIWGwwe1FIxMUNA61QRCat8JhCRDK0rZTLXueOeGbXwg92PodrShO9W3CQKGjdgfJ2wp/FKzXq6KYCrOT9uNGpWZNDgTdOcmjqJ0EAe//cg+tvtRB+OzMt+kZpyQg16R+iLXOT6hDFM69xWyPQixP07YUuh9QzHEXXY8AehyDTbSS8u8hCvsOhcJGZP1PxCuYSURdvmeWVCfzRy1N0MdlARHWkGutSqq6A1jqpZjlUNaOGFLYYpqMPNaYgUNGnh2dQtZAvd//GYlaHr+FccNlKrgEg/HZy/zV/Zj3mi7VOj2y4BGpATkbiU5lHVT+IOAYSP2xwlbCtWZfIPIZpAHPXhMTU3LPBRBa+I+IGPDlQ9D9fHn/cCf3f+rphkhsUP4g+pCw1wnqRHyeFCBj+0Q58UJWwqj4riN+0UAWqNgKhtr2o0NiqxNyFt0hlYZcEcJ1MUtE2sRcnQ3IdsNj59nhucx10TDCuLEOGFL4W6q39DeDclCTRpNs40qGooOWcFONe6SrGj37YJ/zgCc+u+eejw3h1LjzBUlCZEN0gzIf6ICmr4RZ8YJWwqnAx2eBL56OX2o7Me9Gh4+lmjoFfex/hB16+A9AP9lhPyo/boXO9CvY0zc2WPPlOMLPh8iJawRumtXT1LhFQJGZUro4ZrbqRp2xYAbdPXyPy5evDFmzUl+z+jHpOnPa59dgzPX3QhZfHcyN/eNJ9dSKGBwiCNjjdAAdQiA5UtSWI4JocukTSh9WvMwnqlrqP9KTfLxyaC332E+L9Wy97yHzNadUgEFUX1ICwiZJ2BIiHNgjdABATULtySFxZgQuoe8JJEtoSMvQYgW9jO14OmxVABxX6Rhq9OzCdkLf35FP1qoG9YBIoT8o4E4B+IvXm8JJoQe9YSQ1zKYKnF0Mv0koyopHzErPbTHE1ru9f1kLXh10il6daGjqTTmftERp41AbIzjLEmRExNCf58gI2PDXQjZQUFKzLg2gY/2ptJaSPDTeZf7RA++Z7yfqxa4thgsv31F4KAQZ8DplqSoTbf3WH+AENcne5lyaYhOiH4IF6A+afL4BGlJs5/5lmNuBWOodkJGhDgJTrckhUeARk/JfQNUuo36YY+Cj64b00+rf5DK7Hlb35ZEZXqV6RihDril0OGCFMUSZ1uSwtPv5UNtOFC61JW3dadjhzEfLYu+cCeZ3XdzJnmZHOxKPLpN/XM4VZi57BDJIOaSFJZTsNDzI6vLvlNQoerQW4cegOKd6sQ9gBrnDyumzd8Z6tuc9klbxAZU9uJ1p+yk8dq0wze2DXSzdxhOjJhLUlhOgULLYucNnnddfYfWqB/IuafflJ6m6Be0BjK9klL0dKfP029OH7UgKrjWq4NKOuCcgsbpmPRg6R8bU28IfZNdjBB1SQqLKVDoOkDH6SnQZ7BzUjP3fxTQSjUcUURDenQynUFT559eu3Et+PjE7Bq9+x8RNB05XeD5fm1DldTl7EC2aoEOOMWWsyDukhSWUpDQssswXXfmpho0NOhUybcgidYnQ8zT72m/eHYN8QTN3dF/3cro9uoIzysvJ7RoPi7mmjOM4f7jKT8wsxm8letzWasRYzs6xa+k/RF3SQpLKUjor9U6rp6hpFQ0QBqbTGFqHWcpyAyi405cvvxb3F2NPkn9aqLRuVHcmljVIhYKGJ6tOL3MkAgflvPjRncg7Kk+sqPo8TgjzrUkxTGKomdtTgIFOx0HsPUObbJWBfE+FExutcSPbnSHmtzh41Hal2yjd7mhf6/+JX4sf+TIOCe4SfSdYUjc+znHpzVijr9OSPkVylb2iMnZcKolKWQZ8qN0huK2imtS4eG2D5j/6uy/9nSc4hGbb518DSHt4hOO7ngKq/lD34Gq7AlqOfT94XbDHbZ7+jc5Pl13m++3/d818SNyPgToD/32V2P7vCfs9a8AoVvRVDxQr/r3MbeEkKFnXhRJ6ksh8m3+D5Lms/nmBslL1knfwFSbK4GaXyTibahG3jqcAfp7Rnr6Owq9Ffw4sQlpOWeNixnCb5vTr4kekfNhtdAf+XFu3RB06voChB6oAkqnomkd/4yDuz7/BKzRFL1fG/ZNBh3H1uQ9D+2Axhu5B9GymENx3I3W8DhZG8XpPo07LlDmn7XRUZCdjejiRsr/pvtfjg9dacMA9fJQ4DoCSDbWCv1WBpwc/82YYyBvLFBELAUI/S+APFj/6grNDsF6dcHWPgUYQCosfUHBc+ifeGYAW62fEwvsJOTMTaHrk83cST7N04bY+JuhnQrbEaXF8gsXVrY0n6+wlFyvU0fSibmnJ5P35rf1c8/EgBjFWqEPA7fGFBkAh4QIx4BxoRsyLms1mTnqztlmQybodJHz6YstQ555pfmcAb3+QZhmjox4+sLKFs1HhV0r9YnO8Bf7xMYc56x0DOKCNOk/mYuoVK8/p3bLulOYqz8xe9YxvYUPTppsvhd/ZYaRBTGq/rrr+KI8f9mqdf2pTZ71/07v4LeTo53gvtbuWCt0dNaESTejrQ8mG+NCL9dRumyF1YYt+4k2Ac49gejIv7ZQTL1aMaemOkkTO5b0SpvOLlcYS9ORizzJyGDDaab7vTql+80HrZgL4xStmTkbeydk3gpQh3fg3nzHz1z/mdKiOT0GaE6O+W7q87A6eXf0SgvxWnmF+tfcpICf6EZxxclHW1JcccdaoeX7DIl9MdYHk41xoe+BnqLpXJfmrJtD1fR9QM98VC6cffs8SVdrTeQdV/KdogKZEeXCN32PeG44zcwcHaVHJlfltpOTTT7+6KCdwVw2y61ScGMGAhfxn861pHH0TRU3hNfTxy/Pjsbq2ewVt2XqTHOn+Enpv3b5OWqRBaUh1gp9Ipa/IS8VdUCIcAwYFzpan0YHh/IO6/mahqEGnbG8zBka0nT+L+lIABV9hHyXkLinklv6N6O03xmO/oiqwSe8c0yse8qQLqPpbCqeq4a+qKfYX9/SWZMwtQIL6t4LAvhtXfqD3Ds2GyYh+ynd7KPEWtP2HZlXLNYjsh5rhW6ccpldv73B6XhLlwG0BONCBzM1Y23+6zOrd4iWnaKDhnCqY4WqJCGWfBv/fpj8sjxVnf13WnZ3DzerTE/q/VenvD/BkAgbYiKcinRrPvGNnLAr1huWa2kAFszx751V0342MveO54bIytCOOAjOabFWaK8rALEBkTREXWURKCrjQh+C1Dz3gk+yHnJo2Lo0d8Gm9pUgl+CdpZdJid7TlOtyKNcs5drwj4Yd0P2Z45R+hr/3LmnfkIJpDNX5xAdsXK7yXvy77ioL2pMu/2VIBOWZGiT+W0NC2Y0ggmGt0HG5ESgq40J/BrQmbw2avzlU6Shgrt3aGSfhcdQW8is1PoO9y+uuq57z+FpbUtjMIT1efbTgUce32JuyLlR1UjBVwfD3voearfbu9OU6LLte3G/BV9l0kN+WUuRZA+3uVH5bA5pacBrEQoQd9T3f0tVazWBcaDe10frGKzS6SaB5THdtT+tOMtWLDxNW5T7BHOX6O+wlfUPW86/2Qcy79FkejcM25istJ/cN9Ybtp9nX+gnHGjEVjsNJjSz4Kh10fI17UXSeqvKs4BJ8UCH4NE5AhBU6ydR1rhAU0LBykgYjzziyiIdLd3S0bivbIJ6YdmbbbXpz1tAP/sa1KTVXt6l55canaEMHj67ajSNSws5nxGhOmr4x+0bLLnHhMlHH/7Aa3YLkJPC3bOXDtWn/e9P9/XXavItUVojwrsX8/Cfrelt0GsQynErowSYu0XoA5R/UbYBaEQmUynvxsl3TDauqtDuTChkxYedmr7yRMIv9wD2Vv8lzDVtccfi6G3du6xabm4T0Z83zPfsj5dn9QN7u3/8dC7+LbHIyE15Qh3w76vnqXgRlJHxv4XkQi3Aqoesxd4Wm6PYbDfpYSh06ZKU2u8fGCP2/I18mhGv3PNZcz+AvxBdDV7Cb9rqvk+IO7Xqqu22+Mlxr4paNY4vYOci1UQfjc+s1GzKhszMMPHAm7CF02VaNzAwDLUDoao/0RkVm68Vq5hp9cQYFOrZSEv2/jtrP+WPqq4e7Bp32JCujy77Q+vOf3fA9xW5+iuLn2h2sDzUXcs3uI7oL2uMbsRFiCj2SmzyxoTer33KTt4/GhW6bFFpwfYMj4RaA7mj1dyZnbPMyjMv76z75Qs1cIEvLv1lAxXJVi8rqo0fY7QClYTb0C2rT92WuS7Xp99O1S3E0tuMjptBX2QlKqydD8PatQRBUwkROo0KXjVsbaarCwVhN0RRsYrVrrlkVzh+1bx35i2t1fsiOOkyZ4krc9z95yA0NaQSGR9I3oYGxKDrM27VhAjuT+trEvjIi65u41uSXRxwB0YXeBjNd2TslmGUip1GhR8UmmaxB++hV6QrQ8pnVTI1eAAAgAElEQVS9/A19S/avIYvYh2394WbTs7Rc5fPzg7jlmW9w++gHXDHDdGBkVhrXzfTlFdujEtqRZtQXrT/wZNeCez9/NsSxEF3o5w+5P++yB7fz7m7yQTbzjQntVfAdocbwOO/JmFTgnz6MTr7IH/XXo0Fnkpp/uEcP93/x26PUQMyF02pDs+DLl5GLBv5ySvcn1M1f3NyktsxrifWpry9NY86u216VBMzInw1xLEQXWrGLf7Mz7zJw9aicihoR+qCJh9BsJZoO0L/+dcrlM1xNdw41hDvIbRvE+9E0HahPXZFEf1p9VQYVti9r5MeW69MuxQVta7YoOH9pZVX8MzqXu5uVcZ3KVezh/6zibtPNL4gDILrQd2/wby5G5N1dtmI2k4wJHWCywgFaSFxF6kLf9EcHvI7fo9L4M6yMW6bfehQytfTO5clJ+wmZd+7VGeukbivPOD9R9xX/3jVH1/rOGkMlf1pyFLf8YenHS7yFnL8PsQniCr1s1GfTaO7vfQ/YYyKnsTr0ByYaCdlrdCQcdyfk7KM0JZ9Ry/Zmq61bE5w9PjxpKFWTLDuZ45ytozIuno5VcuNVZINuqegXS7Nm/e+XtQj4KHq2gnuMPDxO8ZVlPwbEfggr9KjSpvbu4Rv6Mggpc5CSv2UipzGhvU0LnXoW6jC5etMvt9OJx/TUlBRIvzb/V0XKn53fSaPSAunuVXclZH4puzcr50k9+/wxexCnq8xLPrNTmyGPQg2Pm9vpDA8W10HtwAvsZHOd4b65wSWI3bFaaNe6LQ2Yz+tSq+OwBfuuEVIdfE2uF2FE6DLG21QMaIA6d4/NduEYc/unY9tX7sjTV4WqqScaUIE6PT39VEnXh8o+kxVvGC9ygJJ7hOF53fD82j1hMrctHQMNaj9O3jJ9SzoOUnUCrBX6vefZUhXiqBIFWJWFEaHrm/L5MfNP9/uUuUOn8Jfx594UUHwrzIbhyXGg3Qb6+OApx+Caul8BRV4wjF35hOIHZZFB2vHM7WW9K89ejiKlxmz12XbmXiG+IWInrBX6EvhM/41HoIhYjAhd2ZTQWgBKqwu9lAbQbzzotZ/+EsF+9vws83nszm/l2mC4mfK3r4beWGBF56VhqFYd+mnCzb/ZWsgoRYrfI92t2n++5JpdWsqHCPgNERthrdCZ3rbozWusDh1ksgqto5V7HtL0Brj/ELYsj9x7gpIDNNmsUtDw5ie6W0D3j5q/Tfe44CLj+AEkrZLozQNmBMWyNaLXev8yoq2MuB/PWD9spJd6M/ZbdgKsFfqFTeYhMib0PyaFZi7FwT89Yxu/laCeqLrxRKmj6CqJ7BhxzXGthnvGfStiTsFFnl/JvpaJPsFWOdwPBOcYXSUbeDIi5EhPwb8lYgOsFXr9Q1N9MoqKMaEXmxFaLgeKUh0AwzwH7Ean86Wvg0p7XasNfOfYsaNRJqb8/V7JDrMaGneTuyksl47d7p0Tq1fBuu3bvVEDDoEiYjEm9FIzQgOtggdwUPdqUqX4lFSNVgMxl0MSIf64XPvE1JNC2X9pU9u8eyHF8NjOZ4GAXwcRD2uFblSkpxzmMCZ0D3NCQyC7RiGoQfkClMxbbfSS7fBkG3utDg0edYoa426yTNn4ZzSonxk68R/7R8Cvg4iHtUIfg1tL5/EIFBGLMaHdzArNXprXg1YBas3TvQr2g2eXQa6hTkBG98mqP42Uk4eyNWbeMSRDxwn4dRDxsFbopMtiPeU4ZtJlJVdppkFPJTzUMO8p5jZQ9+/X/2TVP2KHGSkmP2/r+TkOflDXMpMTcUysFTrlb4ECyYURoauabvnOQg609jLtp1v3d2oM0GolyIe3mK+jJln6azcnc1JN2Rt/qicJ/I0QkbBW6A13bDEuyYjQ5h5y8GhTIVV9Rjf21tzDITsHUcdU+rKkXuSynzPNNE1mIxsezZwm1IGn+UdMYq3QJc6caFO1CodAEbEYEfqZRUJDnBb0D1XdRqio5OFkCk1fH7JafraEy/Nfy7f9qoG5yQp46nasLeBXQcTFWqHTMrNdEigiFiNCJ1smNChp+o563kVan9azwy9yXdDjU/9zJWT3Ew2lgKefCxgj4pBYK/SaVwgUEYsRoeVmVWYr2UeoB2vVoI59kZL4WKMPvu7NH+wWL/+yjKzBGn13AYNEHBFh+0MLhRGhM80KzUIlgYratvLMpmGexL0k+TGBb8ccSnGrY5FVoZbVOhCnxVmE9qTM2wwKZdpcCDn16qhyCQtI+zWXfZJ1/LS6r1GtxfsSiD2wRuhleafGqipU81p+oT+wwGeaytD/DuqcT5y7acL0Z/8LAsrwGO5lf4EiRBwUa4TelPHP+6+e78parMgQalR0fqE7WuIzsL3qYnO1cK/UKUDh93y7risXoxz7zEkcq6oc7f3hyYYhbRrVaNRmyMZguNVOqKjyC93Ukis0sPOh++dsQ3GJ+5lUIGTd+c0XuIBNzmuOSADr6tCyNv8lGGxK+E/A6ml+oV3M+6wBnQYU11W9chxWnxs5S97WrWenAan2cIdwMSIOidU3hS5Nf5y8cPKPTQV9fGDkKYcFV2j2In258r4tOY5qBvy0BIO08MfYf5JvFHbJWMTZcJanHLUs8jmtq4zM88lxWKWsdZBnZPg9PjgUpw+VPM4i9FSL+ibpMl5eu5FrjebzR7kqteej5aIFj9gTa4S2zQpYLPmF9rJEaPow/et8/Yuck+K/m+5Vm3m9FFKZfy9768tuQo6tQRwMa4TmViaMBHh5Jwbggm2bvg+aNjmD0sYBRJDzq3bGheda++qDR5CQBhcN3ZvfuweJKXAVZ4yRLNZWOZqlcyvJNrmQ/p4wAXHkF/q0mWszty5F6n9Rmuj3v830zHmkS9MBfbOuyY2S99Yl5O0zUfj0TqpYK/QBw1rfZWJ8zOQsDIUWOltsGkJnw/xKBZz3uA/3MMbjzmYBg0UcCWuFjtlnSOzLtD6YbPILfc0yobOg1BmJaXpl4MGQazlawktpP+MTA5MEDBZxJKwVOvaaIXEj33zPVpBf6L6FEzrXVTs8NTlDrc2Ua/RwddnBBR+R+r2hrIDRIg6EtUIfBX72w/5wUIhwDBS5YSU/WuMfh9at+MX0gKSEM3VLNa3i1nRCj1LEo1TZT3/qY9nysIijYq3Q7yjg0IieIw9DhiULX1tKfqFbFk5jM+NbMjSv0rRhZhq9HigqWQ+p3djyao2a1FjAL4SIhdUNKx3ucVrcFLR9Jr/Q4ZbLHGHYstfm9RS/LCfFrvmWCNwbdRBzgc4y26CzLo0GmkrhP9Ql6rje1ymr/z29vAfbMOPWpHerUsSTHWlbytDGX/NdD4I4Hta3FLq0/uG3/s2FnZ0jv9CWTWLAoXx16QW9YVzAROaf5ir/mfYFu/MxgMotHKIVzEeRI0D/9jzuGPr0UnZSD0pP/zyTgsvLzqiPeZIfoiCNUsXrIeNFFCiufUvcpr5kzuPz6YJzPrPYSOv/c/noxIqt+7Q1MXkeIgrWCN21qyep8AoBo8ovtOU+Z09tRxmS7EsdNsGKHMhcgBVqgISdAG1JT4AfggFqkgzdSPZvQEhPdSSl1gBVp1Q4FX0k9SVpsUr+7LB2anmyXp1x9rOkDNWQzvNVK4+k7tt3P2uU412PLUCnq9ipqPW6i7sD7u1kJ6tx67N496z2tb8a/nkRVwhHioQ1QjOe5BRNwKisElpt2GYYtjrmnxt7pWauqjAZQP468ybtBBvwRAreZWofRKZP9M9k6tVuFeEAbIkFHSFV6MySk2AFde0AUOpe5HNdm6a6AB+PnQ9dSFuK1kXRWi3zK0MdWatk6jb7SpI/VJk0FZ0G9PnJe9U7XBs+SDm6+RxFp95XqP7M9+erzLi9N3ePG7xs13TjfW7xGUyRsUbogICaZMMrBIzKKqGz4FsPeTxiDaYnMHXsfkyFWnWTFXocDW0T2IQ+KuESk5lUhjvUyedAMSUq08jboPmckCT5DHXTnfsJuQDvkdfpVuQ1fWZz5dgS7I3l1riyrqmQSkhtTf/L9P1+2ol0xgLSLH3qs1NM7eNQbPRu4jpUnne9zrrBsf9OP6LXX9p2m96VryreeM9LSD09Z//DG2tftb5W6v7L99gHxQKcpbddEYTOaXYUDdl1kYh05nYxmZG6HekM0Im5GyQkMyZuPbOLfKW6o429DHqmRGU6aQ/sb2lMGDm5L+BXQg4zF24S+SNZoov7/ansPaCVyf1TvycngC5Lxob1Vl5S3lhO/A7oapOJKQnMRfZzbZMP6LcI6avJPW+T+4OzZUi52EN+t13I+1F5+8B8qjzdu1WvCLj288zzmkH8Z7Kpmar7SfSBypb/CKv1nzOhbWHvbFwa9nH2bi7CCO1S1+R6boXGqpvC/ORcQCv7KZ0CqGp32IlpAIYN11H3IpkPBwRt2w/qUNAwDukSyXF2UXtXRSQZEHd7MiGn2XXEoweSx+lx27eQLkz+zJ7n55JD7K/G36c2H1xB6T8jG3dHDScNgbmgkzWnCHk2hjlV1Ihc36VvGnP1/i3Mo5qyGyFddDVy7Swds4J5XRb9p5pRa5SuBffh76qh7oS0Cr5u8bpyv6siLt1R3axfmJ+6bA77N0z9jzA3+CVq2WXKCKuFbr+tCakcCPoVQq7hl19oS2YxiKGzlGXqzZScb1LR6HVGM9PeiYZUCvMmQU+zEz1C8qY4SGaS48mvtHIABSUI+V5D1flcs/kUcQ+HxqQRvEtSY6N3bCbvsetfvOEzj7lCQxfyl+/JxYfV0Jrs3XxlJqkObGeRo8sJ8ZvOJC7OzvVdVhxjXs4sI+T8fMaixO9y7ewjZ64NZVT9SBBbUTm5k/2skoJbGpTUzsidt2AmKvozWtb0DjWyIm+B7KBDJjQdfAPOF+KYguh3RwfyY++azVdy4D87/7RgRUCLsVborjR8RFbB+QAYKlBELPmFNt1SQutBQ1NA01M636B1R9dRbzf2jk4Jj1JA4r4mZFIcBZnh9zf9ek2x65oeKC1k/LXz1SWfVmT9tqgNV+8TAZBOpysgGd6WDcz44+qVn8NaUX1WpFz1Lu3jR0gsRe96JHNRAlwpmfydLAqgNumiPrQ142HckNIJQx+PJ52oA0zM27cRWST7Y7n/S67vsvU/5uXWFEIOrmYSj8bk2jnTl7Bry5Ug6/cyieEh7Gf9kw1XCy9Ty+/mwDON/5vgGV6Itcna0re4AfPboI/lBxXAXPXiTo17H1e1N5OvRWjq6W0BtJfpueiNU/KD3k3zH2et0H6K9i4ucf6kRMR1q86Tm/xClzB9cU4aQeboEzyPhLYjbehL8dn1UsPjAhlfI/L0ezn+o6E7Uu+VYmoSnRdP+apCq0qk9fRdyyb+sW3Ceyf1QbfZR31azm9K+/KZXpuQlPm7rPZzbdDYi7Tmrz5p8uTP283QRU3R6bd/eRmgzeK4qmeYX4JJxCXgiY5uv+L+3oiP4D2X07cUtQkZGV+6l5apPjfKM73NHPZHdZyJMYiR2i3tm1w7Z15mXrqqCFnLdvvqzw2bmBSYtfOKZT+/LmpDD9qFlyw7gGU38I29JbRW/69sTvGLSG8KMW1qxfgd7P+ZD2ILP6GL7Lc05k9q3OC8n1s9PzRzHXkXmCvQjkSrzpOb/EKbWGGFpjN+na/7aR78QEpt0sfc0cLigsYOlpwfQdORC0sa39vsf/MG12W2pfr8/SO3XHKD+dSumoRUP57hE3xh/005RD1PA+rxdOWiz++CPoa1P1UPOv1jSH8ey9RXJq3WacY8PdDwUOpbFx81IaXCrqbNY/7wB+TpWfsBO9BxZFy5TlQTRlll7gf4fdKZ37a3oS65x1Y5Zt1kPxua1fFr5XHLfn4/RBkSo0wsZJeXeypDIiLe8oOMs8pQa6mg6WIy3x/PeOF7aAs9d+3fGcMrk+qTNWPzfG6t0OlezAUEmFuXbQqrzpObfEKXNV4R5nxm6sJjyPi008D+UGr1/fUEbepupGQBNhunT2rG9XvaJ3xd0IW9mrzOvHyeELrXO4Opn3NRhX5Aep4Oub9jjVwXcycBKCX4vkvKH6NfXE4E+cbp2+W38z6c2BTfW1bi0ePU5UTWOy3PM71S0exN4cMNI9TM71almCnsZ/XpVtw+j9BfiEV0UxiujLP8LP+u/mpDIval5QcZ51zW+iT3J5jMd2Ehv3XJ82fKPM30nbntEGXue2qrhQ6IKuP6KMaFeDx7YtV5cpNP6A4mqhtyWkeVdU2MA8OaxptoAdvhy/WcOLpTvvvdcsPW/jflndquxKNj11cX2FLDNp1ZObhLV/4hXfNR8wY1nbTde/PQfE+a3ecrVKFqPR18JVEzN2+wnyoP9mz8i57+jbi1vX+XrzrsflyHeS25Lc7CaRjKKQdyW49nf1l2AMtq4B97v0FfsPwg43hnrSH2wPRSNXcnGhLPhxeyhHm+hkTYyNw7rBV6KITfg/mkUwDMteo8uckn9BBTFWiFFu70S9HDND5vqJCVHxtRvtPQjuVaj5074PX8+94/qwDtw1DI1Oq8DENvyvoo9y/ZEh5l8eOAGamfMK+l9sUWNHbHCG9Swex1veR1urPlBxlnmaGuX0Xb0WS+s4a6s0dmYado250169zpPGuiWCu0y8wk/bEyZBacEHIOl3xC7ylY55ugv8Y+ndDSeq7D5ywwsV6sc+Ba24PI6n3Z4VVXJ1n3f05vGWX5MzjZCvqO18nk0EIN9BxHp3vN2JxMexXmIKO8re/LReH1yPTD3HEx/Ff6UV7Yxv4tuwwJ3zx/g6xvWJGxf1Hr1RG0u10+oRcU6DNFJ/SLBp1W23k4TV+atz4EAnE6GYbm03au+NHTfL6ctH2oASpyiACl/6Zb3fXDfpfSzfxJ8Qy++CZzUeybMbWwBYyK5e+FqqjyzGEvQEuhxzsfVxZ4bbfCNH2za01oH2gjXMlXtBLo5IU4p7kVlBLop9flfDpEe9Uxl+3Nq/qnV5LUMwvtT7mXG9iLv+fRh3keDFotdI3/VABde3k3se40uSmE0Go6MhkgQbuIyRQ4tWRRntAjNsGyClKbcXO+r2E+W/7jEu//9b+5LyLyjiuyVuiqLyBwG3Rtq0kWsldLYa7QtJYGWBvNNg4fWC1gDIhjU3XWueDTU8rl/dhaoVfCFFl16Eo+0P5r1XlyU8jOScqwJTTbDeeSkMszI06JtUKH35ERVmhyMkSgiFgK0TkpXU4/1qerA1deuLBJ003AGBCnxFqhFdsJL7RtWwoLXNWN1tBMpQM0EDdvSTLt9A/sEGuxVujbj105oWX+AQJFxFKIeTl2MzrLafpq+rOM6EPaEcbOhhQjrBV6Jqz1ZISW/Q8WChQRS2EmmqGfMP+ik5Wg8b8ip9DoYo61Qrtfh7hT4H0bHhTyIb5JjAhd8F3hVUoHD//MpPUTySeg/V7AMBDnw+rn0CV/i2akSppncdtl6drlzD5GNyK0skChtTGpoFwfmLpU36EJLIrGdpVijRBjCsu+Y2EXGFmLFS/YJY6VL1Y2M5nRiNAF1TmYK7fuEKWOmkG/v/fwNxlvgJDzVCNOh7VCjxtYiLL2AaT6+xzy8U8G2G6qx4UxoY3XObhPnz5SKU48d5ua4L+daK3uKoY4M9YKnZlmeTP8LLjRjtfY9UOfrM6eRjEmtPEu/mpucq+PaJ3+X3Zmusc94P3CfgVESlgr9HLoYHHesMhXo0Xc7j/Ps7fsso3Z+BoR2tTUHBlAAZ0JmV9v0KcKOfoccTqs7g89I3rkW5Utm9tOuz/HmzWaPHur792fTYCxCckLes6hZuodZwbBzdFJv5KvdMk4KWixxlqhk5KyG6XN5g2LLJGddg001VRurMpBCpi6nKtG05evyqnMEw+o2arPivAtEMlgrdCFmdtu5qs6dCsfmG4ipxGhK74ssMKhS+fmL1eo4G4L8mi0ifO6CDvBE+J4iDm3nftegNTb3gfP3koC2G2q53J+oXuZqEEvpA7GAt2YkA+fectCC57wpvfVTAhbW+gB84gzIepkjbIWq0JVjIGq0FUtTD4cySe0qwmfAfSn9QCJNQipqxxLNy/opDO0K776eNS9sDcKyoBIANFnH5WVe7MILYXPTArNr0KRXJWQfS/9Cjr5J3pu9FnJy+es/g6I4+Ik0+mam3w0zS+VppOG/J6irJ11SM0Ry+f1eXUXSnbu5bdNoFBTciLOhZMIbdJm1vYuuqvRVOblmyeyjvhN/fSod0JE2+xTZM95klzYWXoQJ8JJhDY7PbSC7uV164lH+K+GA4ar2JlnS21Ir5t1iuxZPhP7ivIdELvgJEKbnx5aTvx2a/57WWfRXU30sQ6ucZO542TXNmWd4tB//LY+mJ+1GHFanEToMLNCQzjtT0X2jHg0pmv/zfrlUJ0/cPSLrFN8peFmw5cdFHJoDeJoOInQ5ivRNKQ9fVzmwjnuNrA3TRkednyVln2KLRmTWzbufjEV+5dKGWcR2pI1Vujub4FhqW5fMExeMuZZ9ilkwx9RkLa7jijfALETziK0yozMGr0W4OF3cYbsUzUzua1rwKqcZyltZLJPRFI4i9Bm1nWjE5g6Bw2PIw25J4ZphzCVjtI7EmuKHDpiX5xGaDN1DhoewV5gVznm2L57tDr65GV5WIEN4Yg0cRqhw8zUOQ7MeFFBR0G47P09obpQakC+lkKkWOA0Qpu9LaS2ZQCtgzT9id83qOJSPrBD2Ij9cR6hC57HwIB+mz5hNtCM+NETXP97ihPrFkucR2jzT+4oWDUNghPmsm0qFVVdRY8acQCcSGjTl+jrzL9MV29qz/kXPzVgct/8XfSoEQfAiYQ2f4mmP6RUkJwZTa1xI34rh88fnXd6d0TyOJPQYQWrnEjx03bQaYGzfUnH+LWVNOxEuxBXR+zQEfviTEKb6HNH/8ltdJCoC59DSAcqnKY1FzbfB6qtsRMhksWphDbbRYn5Tw9LPqjaLgPopzWIx8D9oBuEq7wVJ5xLaI0Jn9nLtzKdBjqaSau0dENSMzDtUDKob+A472KEcwlt5r7weXh0FE1TvzQrnaCPIK63/SqRffTFgEsCr6KIODBOJrTJSkeU63qgaQVAaBNa/4D8qOpZjVymr9bVdhI1eMSeOJvQ6aaM3k+rNbSKqUZTQXTmSaDVcFMPW8mV2aIGj9gTZxOa6E0ZTfkApLKt33QSRJ/5z+2rTIr+jBxcVdDJEMnhdEKbqUbr0hTsfKQsmUm3dZl0LCF3TU1FjUgL5xPatNF0PNArGjKVDWAnK6XpS6qSbSjT618gUsIJhTYzeAXCeykhkNlqQ1Kn1a4NQ2I3ixY3YnecUei/TQv9ZcILOgEoUEAUHX4bqA3YkbQY4YxCkxjTRutBnpIE2rOZmYG/nkjCDkrFCqcU2lxnf1qZsYsVm2L+/SVSyIhj4JxCmx2+sjtRBXTCQyVFyXE66GKFkwpt1mgtwFXNy5TdbcBPlIgRB8FZhSZpBdY3DFu/n5Q1Xw4ij6GuuVMhEsJphSb3CzKaesxbrR/XQ1ODHNXdfHp5aR3bx4w4BM4rNLlu1GYaum2O5JP+SX+TqgraZ9y8W4retg8acQScWGjS04jQqRrNX1qNofFbMVh2kaabESJbpKxl86ARR8CZhSZl8gutp+n0R0CnU1n3hsl32ZwugQtsGzHiIDi10Mb7dTAuR9MZfIKpTfPfb94FG4aLOA5OLrSxcbMURdPaOAAdv087nM33+w0bhos4Ds4uNJEbMVoewNQ1KF8/Oo2rS/tXIeS/PUxe10a92pS1YdiI/XF6ockMI7UO7qndUiV1aiawcxuoe9VTfE3Il88hQ69eiet9SxnnF5q4GalIUwqgQ+ik1tpMALZRUXdfRvroFlQhHl+EnnOxXeCIvZGA0Hkq0nTWKxW99LxyWdaHMe/E8KtU1Jb3t0nMiEMgCaHJBWPVjpexu+nH9wBi2GGIGkbwynzmzYdtEDHiIEhDaOJpdFyWFhIZsQ8CfQwUTN1DPYGboGNSoC1CRhwDiQhNyHljRgNkwk0trdHTB2j2sfQddgmWGVdtEDHiIEhGaFLDmM90FChAH/koIXwUu65QQqArkd1YaoOIEQdBOkLnfSSt4m4Pdcz2Lq2nP5oNV+G4Wvv8zHWNoT9pxZHrt/1WX9C4EbsjJaFJ9xyXZjox+3mHEvYFl0yJG8xUOhKjoyllZy5zz5QXe7xu62YKGjhibyQlNCGRWUInXH91m6iD9YHRdK/rkKpPTv6n0ZJ0tibdTD3Lldn0VI4UMnDE3khMaNIo0SB0gsFmw8gW5ZC9NJw5sWcrIS4P5zAZ953kD5gSi+0sUsIeQpdt1cjMJORFF5qQYYaKhgFDo0syRUem67qnsY0qi84xL3E/8NlrA85zICXEFHrkPPa1oTfjl3p5OVM5rRGaVDO6coXaP5UadyeQrWZMu868aLrwuUtAm6IXhTgcYgp9FZiX6skQvH1rEASZWrXYKqEJ+S371jDHpRrklO4qtxT4drbn3ctbT2LPjfcgjeFNa4pCHAzRhd4GM5mrpGwyzDKR00qhCUl69biDu15z00rTG7mWwvrKvoT8QSf9b+CsOP8Kqx5YVxLiWIgu9POHnFWyB7dN5LRaaFL9GXtpTsi6RP9Lc905gj8jbl9GnJKRT/SD4/ZXIlUeBei65Diq1LsNcSI850Z0oRW7+Dc7FSZyWi80Q3D2HSGdcoR5XavXaUGl1W/yJOTAXvLuE+3d60r4X/uhnQ29luqxtXvNOuwv7cyILvRdw1ioixEmcgoiNDmZVY+mprGTRX/BtyRyQ7JChxLi2nnyjG8phTpMoV7GVujrxV/uWPq1/mFXTdXuEQdHXKGXjfpsGv0Nm+4Be0zkFEZo4vKIv0LviWGrHtsArnwTdUYDvxESM4DPMRuWuRDSLXpPeRk5fZ57mFj95VQhykbsg5hC7+Fny8ggpMxBSv5Wnr1vxqRkoxBGaEI8n2TfHV6lgCJk+19OZaUAABYpSURBVJZGNH1hedBibvfrWqjHbJpdA1Ddpj/hj5l+X5iyEXsgasOKS62Owxbsu8ZcBcG3Sd6d7n36ZbNJKKGZq6/hud2zsQDehHgdi1SD736t7j1252gFWwHqqDwY6NV5P4w1HKEUqmxEfOzT9F3CzBy3AlU5eAamAahVKxRAVSAuLzK8/oWDpL5c0b+6Z5unrNeloleS1QfJ+6Dmu971ThWubERspNaXwyg/8JPv3iFkoibK4zjsJ+RjbuxsKPsQ+puM0mTnVuKZGc73vFt7UciyEXGxh9A1jporU2ChCam0SHcKNN036e6srpipY5d5Cx/5XruKbfXMRXnGFVI28SdCVqafYLN2VH8jbNmImNhD6AbQ10wOwYUm5MNzzE2h36eX/r5Da2sz7wN+Je8eTAIqaNAMv5KHX3gyVY8Yzdxe3++gol5cXlDx1YEuDXq1NdnxBHEkio3QhFRIBM2zTBro8cwb16TvOikeaTPUNGj1UeHcI5cg76svYzWRfwyYHhzzbtZRHYMhk9KsKil8PIgtKEZCE7IsgwZ4/gWbHKyoE3de/eNiim1MpM+yN6nD1fVI6Ugvtu27xL7nhtaV7tpVDUiZnhHnXW0RECI4xUpo5sJcx+9ZK0LcflJNHRSfPna6WjlyH3fDGNRzi34E43ky3/BdQd7XtcUPveu4hi/n3tdLH2SbgBCBsYfQrlXMNS7bTGhCyu6mk+6rMieSZTeUrympz45A7ONrauYq7ce2q6zJmoTGe+8LKioJrusr8e/XnLJVQIigFIvHdrlp8N0vPRhNlweGddX5vQv7d10LmqveBlyD95bthky+1FLmTrDxE115/v2YR7YLCBGQYih0VhlJGYMUGzbQlZ+fuzJKvij+Cfvhn3cMe9X8anDfUbP591P8+W3lURu2/lLH5sEhRaX4Cl01Q/+Xfs95xSjl89nz0mb6p7AfNtZ9xe2cCB24bS06hM99aR236ZsevMvrjnayzaNDikjxFZoMoJW6DD9Kfy2xVqSu29OX3IezFKOrkKo/a2jDWPCr+qrsZryW63vSWjuV/byf+gfbh4cUiWIsNOnwkuv8F/uZt+JxNf0Z/sMJySCH9K1gqDuP1iQtG/P7OYPBJ/bzn84KESE8pCgUZ6EJ+ZxdozNKp4lp/pR+z/CZx28JjNL0cQ/u3eF9ww8+8VvRiN+XYWgVfwtwlTgHpXgLTciHvjQonwRq6ElZn4zUTH+DVDhE+bBvftG3zJHZHdryiYrQTKT4kEJS3IUmpPzOSGXipabZb9NGsxvXQ3B99jJ/5fe58iYM5LfN6aqixYcUChQ6D/1TDLM6XXvke2ZBnslJt13l7xX/vSVyVIiloNB5mHLTkFjgnX/nm0nbKxBScpZm7uLFgyqIGhdiGSh0HsZnNQmuOmJkb/MXmjs35RnyyJMnIlJx8SEHBIXOQyuqDrd1fWp08Lf751Om/679namWuP6ma59/P67raWdQ6Lz4XmSllC1Mq1JQjnNe/Hbz5Tw7Gu2Ng5TTH9kqMsQCUOi81Hoau3rswrvpnxeUoYT+Mz7RniqVa0frdJ8fP/p2t7afTeNDTIJC56PUz8eDLywseFx6NTBMKVIfcmUqGb6Jm7Zvsvx1G0aHmAaFLhT1195JuEf/yr/poPfMue/rDP6CLXvI1b4rtG3mIXJ0CApdOHooLvqyE9fQF9hr8c4LuXb+ddmQ2LiLkPcuMdlUq/AeUWxQ6EJQPX32EchcM57SQ6jM/S9N61x7Z2fN57F+L2kuP/hxqWr9nt3EiR9FBoUuBFOefwxJJQnpDzp4kZj6Ze6936cYqhiBs4jfPq46XTVugtgxFndQ6EKwZ+Mp6MgmAvbTynwtheUSZ3HbAdpGb4JhGoTZ2EYuMih0ITi8Mgy4zhyX/0rW5d/9lW5nxwYfL9NNJJ10hvEBfZLEjA9BoQvF31eeAzs/h3vi92lGhCatzipBe6M7IW1pw8Q0P8SIGR+CQheKZtRF6Mlsf09pALFGc7jW5tZoKafqwb0te+pWY5yhRlRQ6MIwVwnKiu8s0X//FCbm3ef+brtK2W82PK1GSKnlGtCAfF9nmahBFm9Q6EIxml2nJS1QDQF5JPVYlMnsuZY1TqDc9cTlQx6pqGjV9SDQn3LQbyNFUOjCIRucTgOo/87js8vxmAE1S7bel9H3u2+5hnH30T7J9OkH/tWZy3ris8PGToXYAhS68JTOv5bhoPQG7KZlCuho0N/nRhzu39ZLXoPNrhqu/1DcCIsxKLQgnOXmdGySHgyaS3sSaHow8+7WlFVHuZ1PR96aZs/gihUotCCE/sS+Hr1OU0zC1S9TX4+Qy3N2b+R2xvxwfJldoytOoNCC8IQdKu6puQGarkyinwI2EbIw6MzTAY0IaQYN70+xd4DFBhRaEHazt311IU5FsbXmpqB9QkoegEwqlt5c/fbxVjRO4yEWKLQgfEz1IaQKpOi5ucLa08pwsjtqpiIlfpdcea975HYjh1Sb73N+6Zsixyl9UGhh+FW/a+SARD23MC1Zeg8utaGak7qrEyATIqjNRjqR/kGBPJWmV4sdqNRBoQWi9Y7HsY909Bom2UN9Wz9k7lXu43dGxB5uYCT7D/TzxoSUOQfTRY1S+qDQQrKUhtCd16koKsA1ey2AfWuzd5du1eeTynwyQc4vFfdEg+trCQoKLShtH7MjtKhdZcjS04aPLs7L2vm/VCpSo1nGNsvUhX/5z4ZDJ/GjlDIotMC4tB3fgb34fqmsyb2vreli2DNePbkMcf82bgeTbgWGoSyfwo/2iFK6oNA2wuXmNbZ28drtK4ZuH68phnHb5rpO7BWaXy6ODKZ72Cc+qYJC24rqd9IOLzuSces1w/tBCYae0afZG8ekeP7dPaqi0aORIoJC2wyPAf/sW/ZddkemGb6GxJIThK07X/EgxHM7vdk+wUkWFFosJt01JDbvYV8X0/qYSB14u9kxJCmCQovFRxTX6EJKRP7MbRvtvP/wcDd7RiRJxBe6dO1yZockSVFo2ZWr7BAt981xOFO6DRFVaFmLFS/YkUrKFytN99aRotCk+oPEVWMXPU1sbT4rUmTEFNpjH0Cqv88hH/9kgO2mKo+SFJqUmnTw9sl5NUzkqDn/fPCJX0qLFpEEEVPoWXCjHa+x64c+YGoQhzSFNkunVP8Zo+ZHvKhj70CcGDGFDot81W/B7f5zEzmLp9AVk/9hJ1wq7X0T5z0oMmIKrd2f480ajYmcxVPoSaH836839O3sHIkTI+4V+lW/YNdAU8tlF0+h9200JAJ/tWscTo2YQs98VYdu5WOyI3DxFDp7KK3vDLvG4dSIKbT7XoDU294Hz95KAtidf3KLVxRPoVcYepy6xGMPvCIj8nPoVaEqdqmG0FUtTN73FE+hP9bz/y/GySuZyYkUiOgthbJybxbPlkIL2J4yqCJ5fbpunL0DcWKwL4cD4T47A+QQM9jecTgzKLRD4dmy9zvY/84aHEdoWbvO2aworkIj1uI4QtdPSskmEzzNH4Ag+RFT6LTcmMj5MeAirEiREFPo4f4AYfeyMZEThUaKiKhVDrez8LVFGVFopIiIW4f+EoVGbIu4QtfM7GlRPhQaKSKO85QjJyg0UkRQaERSoNCIpLCH0DWOmisThUaKiD2EbgB9zeRAoZEigkIjkgKFRiQFCl0cqfT1pJHtXewdhU2wh9CuVYysCpULFNqmDJanXX2gu1vfRBaXN5x0GBg+tit+9NWNdSOk2unwAudaf+OQCiBhljMONUChix0uUbO5bcln8wrIUSf2Vs/X3xqXdMxVvKiEAoUudjSHqnxi6t0Ccpy5yM0x0TB9uEghCQgKXezorjAkvo0znqE63YZPLPUTJSBBQaGLHW3osnxiwhPjGTroDZXnvokWnbBai6oChCUQKHSxo0RWTeLqeuMZ2tKGWa2+f2nB6QZGAkB4f0FCEwAUuvgxNY1dvdb9H3k94/sr6TrziQ3e5k/2s3ZBI/fGf+tGCxaedaDQxQ/ZSvBd6RWe8llBGXbeK89uPtW9UCR49zJ5rjrqQdx2mKqWkCEWHRS6ONJm7s6Nkwqu+FZ+EPHzJ93X0fK/vhqwQbva1Jl+C+a3spAJgkZYZFBoJD9llzzRpCbEcsp30X5lIueGPYbEQZPeiwcKjRingqYrn9h41kSu1QcNiRP/2Dogy0ChEeN8TBt63HxXwONqjp/i+XVzSiX/YPuQLAGFRozTgTI0fH+TbCJX2di1bK89l43RDrIYHQqNGKcm/QGfmHfdVLZ26TfHdBt7O+0jMWKyABQaKYCzp7ge028kjTKZrcHWoOT7/xbwSFt8UGikABonne9Qrc7AqIumVsNxOFBopCDqHtQAJM0paT6nA4FCIwXj/nZte4dQWFBoRFKg0IikQKERSYFCI5IChUYkBQqNSAoUGpEUKDQiKVBoRFKg0IikQKERSeGoQlermI/X6iLFGyNS5KOaQwrdEhCkiLS0t71GkDX/ID8R//0gApNgkhjFeEWLUcoPgadEKYZaIEYpizVGrMhHc3vLazEPx4pRSh2oI0YxYx6JUQo5sUSUYqhOYpTSVSVGKeKBQhceFNqBQaELDwrtwKDQhQeFdmBQ6MKDQjswKHThQaEdGBS68KDQDgwKXXhQaAcGhS48KLQDg0IXHhTagQkcIUYpNaGmGMUML2iNQGE5PF+UYlTtxCilU7oYpYhHLXHmpGokSiklxZmSqFp5UYppKBOjFJcGYpSCIAiCIAiCIAiCIAiCIAiCIAiCIAiCIAiCIAiCIAiCIMLjPj1EEzLDlqtOl1p0X/Fsaw0RCusHX9q8lM+vyF/urWvrYkrPf6B4ML+UTYsZnsZvcxRgexlsjmw3RB2Ihj2260juEQQP/7sGaY1sXthriZzQNi1lMKQdPQ/x1WxbjEcABO0MggAPGxbjdpsXOkcBtpfB9rSAmyVJyVtgu6klJ4KXKyGD4LLNC9sHnNC2LKVsZgjzp2Y4rLFtMRNgnQtx2QDjbFZMje5ngBc6RwG2l8H2rAJ21Fo7WG6zEi5CdXZzjS5r48L6wANOaFuWMgJ6Ma8ux7fbtpj9wA6KagR7bVZMJoBB6BwF2F4G2xOS6sa8uqU+t1kJsWHcZhs0tW1hVRJ8JnNC27IU37TsJT1sWYw3N0K+Dpy1WTE9v/46jBc6RwG2l8HmyFT+3NY/02ZFvM8NjpU9pCvYtrA98jd/Y4W2aSkvA9y6zfqzk8zGxUyGBczrfJhiy2LucULnKEAEGWxOOfDmtj5Q2qbluPwDh2xbWG8YRTihbVmKK3X5JLs4w+HStv0yLuvhwvKLcNDdlsXwQucoQCwZbMmbcJDbHgKbjv6vvh+i37BpYZXjLrrwQtuylBoAod3Kv30C/rbtT042Qs/82mh/ktmyGF7oHAWIJINNKcdW0wj7S1nOdoXIxqSDXx3bFrZTUY9kXaFtV0p1gPeZTalYjYdNf3Kz4HDT0k2PwHRbfpusK3R2AaLIYGNkqlvc1l9hu2ePlU9B/DBX2xb2BYwnBqFt+ZVcqRBuuxvesWUxVbRP2MYNj6fqyjYsJqsOnV2AGDLYnNAkF+bVNemFzUrwvAEnKti6sInZa4+NsulXiuNnztvMXKhtWMzHsMlQTBsbFsMLnbMA28tge1ZDK+b1Q1hpsxLmwFIXmxfW5V+W2+Dzb0ebfqUD2qrMq+yuvoQti6kJp7jtaahpw2IMQucowPYy2J4W4O1K3Ly5qqFNcI0JdROrsN8MLYW2K6UzHCzJNuTtsmkxsgc0+0W+ooNsWcy9rJbC7AJsLoMIyPbCndV3YafNCqgLqTd5ati8MF5oW5bi4g3he25DRHXbFvO+Avy2X4fMZrYsxiB0jgJsLoMYeMwM04ZOt10Hq0+za7d1bF4YL7RNS/GcG6p+tKq8rYupteWp8um/b9i0GIPQOQuwtQwIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiAIgiCITRkWCW91hQBz2a7GcZuNy4pSRgB0tTxzuXhnXqQEsTPV9QkrX+OE/hJ+IFmv+eGFbpfxWlEKKZTQZOpt16IUgiAMbWEaIZ51aloktOz2P0UqpGYdz0LkLiM3HgKCmKcdjDOkLBD6I3GWLPO67cRrsSJ2ZSe7wNZbVWANOcumqvCvhLhPv5kZ+g+7TCZpciQmel9TTuj/nrKmrUkrsT458WjDUuueyy++m/t8cV6NjmdEHWzEpiuue5AZuKQUk9oAFYjLkFtpyVe+YN69SuXMkub2V4TqwVD20y7QUrQfACIt2i+AnUPKs0J3WQGbhpTkX0mJa/BkRyA8r0FIBwVc3x+bHsEI7ZKwgT1mTebpwMVX4PntR0t84Fnu+m7c5eTY/TcgozVTz4gA/+1B8KQ8L/QMiN6+X0G1JzlSObOkbY1euyETvmFOUpqaYY+fBSIFuCoHK3SuKsevsM6VyH6H/4jLPfiWkHKXgRG6KQxhD1kDJ92Y6jT4lSSyc1A31+ni4Eo5QgbCFRnZDL8wte6/YQ4ntCwpvAzz+wPbyKtU7ixPmfvNDrCHPcvdS2L/GBCpYFzo6Dj2Ls7lrsqjNRxmszVlhf4R2rDpNdxmKXRnXqfnqR3EQTN2cwre9tA/YBcpL/kygRPag7rLvHX5qAnJkcqVZSCTlGWeZw/fkyrSt0ckh1Ghy8Kp6izb4J0fYCSX7yUj9GTg6sZrgK1bz+Pe/JZX6FhuMx6+agSrueRhKM9VOY7Dw4nvsP6+SuXO0pBNJv2/vfsHbSIM4zh+pxCVxEpTEO1U/wyV0KG6iCKok4sU6qC7fxBdRMTJwcE2SAcVquBghU4KrQq2Q7HdSmkbq1K7dFJr/1hIHFJaRYKP7/te4ntJwwXaJIXy/Qx3T+C5XA5+vLz33kEGvTNsr/BlY7MqGujY/z9kPnZLzpq+CRXouOzVZae+a1SBPugUCbT3hKZVrp+UO6Z8LDET6Eh8QWThYZ1jq/yWWl16gW6T+spfOTalooGOysAZT915uWz65vwjdECgZ8zumpzLDb89EjWBVrOMIzcn5MMWW61uYYTGOhWfQ6e8leDjLW6z9OrqUN4cOiDQfw/o3RtpCmUm9Xdsm0uZOfT+u6fVJ3dI9tmqoEUfmGQOjXXxB/qik9vekysqaod/DzjumF7liAzmrXIEBFr61e3kBRnVqxw31FjcIXGT1gZJhFR232citipo0cd7gWaVA2tlA31KJtsj2e3OKRnvevvnZ0yN0ksy8nI2PeRbhw4K9PfFby9GZEkN5fUzMtb9ObcO7fbJ9LPur/LIsVVBiz7eBDqcYR0aa2QDHer9lYxmt86O+x9XvnSZ6UPjq9nld02dvieFQYEebuiZn3/dqOvaJ1PLnzrCjpfWXe3TK6nRS1sdX1XQ4mQDzZNCVMdRaS7R8WO4DKd5nuBdDlSDO/6gREc5Ah1O87YdquNEendwQzkCfTvB+9CokqerX4i+mrTayhDomsVS8xqggsJ7rJqN/jEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADYEP8AYj4S17M8rpwAAAAASUVORK5CYII="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(fitted(m_poisson),resid(m_poisson))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The convergence message shows low magnitude and for such large data this might be a false positive as emphasized in the lme4 docu. \n",
    "\n",
    "The residual plots for generalized linear models are generally quite difficult to interpret as the residuals do not necessarily need to follow a normal distribution any longer. However, the fitted vs. residual plots shows a typical pattern for Poisson regression with curvilinear traces. What we can do though as a first step here, is to look at overdispersion (see http://glmm.wikidot.com/faq)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "overdisp_fun <- function(model) {\n",
    "  ## number of variance parameters in \n",
    "  ##   an n-by-n variance-covariance matrix\n",
    "  vpars <- function(m) {\n",
    "    nrow(m)*(nrow(m)+1)/2\n",
    "  }\n",
    "  model.df <- sum(sapply(VarCorr(model),vpars))+length(fixef(model))\n",
    "  rdf <- nrow(model.frame(model))-model.df\n",
    "  rp <- residuals(model,type=\"pearson\")\n",
    "  Pearson.chisq <- sum(rp^2)\n",
    "  prat <- Pearson.chisq/rdf\n",
    "  pval <- pchisq(Pearson.chisq, df=rdf, lower.tail=FALSE)\n",
    "  c(chisq=Pearson.chisq,ratio=prat,rdf=rdf,p=pval)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>chisq</dt>\n",
       "\t\t<dd>408930.369865232</dd>\n",
       "\t<dt>ratio</dt>\n",
       "\t\t<dd>0.793743633179926</dd>\n",
       "\t<dt>rdf</dt>\n",
       "\t\t<dd>515192</dd>\n",
       "\t<dt>p</dt>\n",
       "\t\t<dd>1</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[chisq] 408930.369865232\n",
       "\\item[ratio] 0.793743633179926\n",
       "\\item[rdf] 515192\n",
       "\\item[p] 1\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "chisq\n",
       ":   408930.369865232ratio\n",
       ":   0.793743633179926rdf\n",
       ":   515192p\n",
       ":   1\n",
       "\n"
      ],
      "text/plain": [
       "       chisq        ratio          rdf            p \n",
       "4.089304e+05 7.937436e-01 5.151920e+05 1.000000e+00 "
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "overdisp_fun(m_poisson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It does not seem that we have any problem with overdispersion here.\n",
    "\n",
    "Let us be sure and check it with the dispersion_glmer function from the blmeco packages. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.00794778266311"
      ],
      "text/latex": [
       "1.00794778266311"
      ],
      "text/markdown": [
       "1.00794778266311"
      ],
      "text/plain": [
       "[1] 1.007948"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "library(\"blmeco\") \n",
    "dispersion_glmer(m_poisson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value is between 0.75 and 1.4 which gives an indicator that there is no overdispersion problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What might be an issue for our model though, is the vast presence of zeros in our data. In order to tackle this issue, one can look at zero-inflated Poisson models. Unfortunately, these are only implemented in the MCMCglmm and glmmADMB packages which both utilize complex fitting methods that do not scale to large data and are thus, not useful for our large data case. \n",
    "\n",
    "To that end, we use a generic \"implementation of the EM algorithm that alternates between fitting a GLMM with data that are weighted according to their zero probability, and fitting a binary FLM for the probability that a data point is zero\"---for detailed reference please refer to https://groups.nceas.ucsb.edu/non-linear-modeling/projects/owls/WRITEUP/owls.pdf. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "source(\"../owls_R_funs.R\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 1 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 2 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 3 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00320821 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 4 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 5 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0010158 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 6 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00337835 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 7 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0018187 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 8 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.0019164 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "m_poisson_zi = zipme(cformula=num_answers~1+session_index+session_comments+(1|author), zformula=z~1,data=data,cfamily=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Length Class    Mode   \n",
       "zfit          30 glm      list   \n",
       "cfit           1 glmerMod S4     \n",
       "itr            1 -none-   numeric\n",
       "deltainfo     20 -none-   numeric\n",
       "z         515196 -none-   numeric"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson_zi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: bydataw\n",
       "Weights: (1 - z)\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1086528.5 1086573.1 -543260.2 1086520.5    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "     Min       1Q   Median       3Q      Max \n",
       "-11.7907  -0.6490  -0.5860   0.5147  21.4109 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.3912   0.6254  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.651175   0.004437 -146.76   <2e-16 ***\n",
       "session_index    -0.060732   0.001419  -42.80   <2e-16 ***\n",
       "session_comments  0.044971   0.001082   41.57   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.183       \n",
       "sssn_cmmnts -0.514 -0.607\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00108068 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson_zi$cfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though we see some convergence warnings (low magnitude, for each iteration), we can see is that the coefficients are very similar to the model fitted without zero-inflation. Comparing the BIC thoughs reveals a better fit in general for the ZIP.\n",
    "\n",
    "Again, for completeness, we fit a negative binomial regression with quasi likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#just for initialization\n",
    "init = glm.nb(num_answers~1+session_index+session_comments,data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.63717013177077"
      ],
      "text/latex": [
       "1.63717013177077"
      ],
      "text/markdown": [
       "1.63717013177077"
      ],
      "text/plain": [
       "[1] 1.63717"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init$theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iteration 1\n",
      "iteration 2\n",
      "iteration 3\n",
      "iteration 4\n",
      "iteration 5\n",
      "iteration 6\n",
      "iteration 7\n",
      "iteration 8\n",
      "iteration 9\n",
      "iteration 10\n"
     ]
    }
   ],
   "source": [
    "m_pql_nb = glmmPQL(num_answers~1+session_index+session_comments, random = list(~1 | author), data = data, family = negative.binomial(theta=init$theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed-effects model fit by maximum likelihood\n",
       " Data: data \n",
       "  AIC BIC logLik\n",
       "   NA  NA     NA\n",
       "\n",
       "Random effects:\n",
       " Formula: ~1 | author\n",
       "        (Intercept)  Residual\n",
       "StdDev:   0.5794954 0.8185763\n",
       "\n",
       "Variance function:\n",
       " Structure: fixed weights\n",
       " Formula: ~invwt \n",
       "Fixed effects: num_answers ~ 1 + session_index + session_comments \n",
       "                      Value   Std.Error     DF    t-value p-value\n",
       "(Intercept)      -0.6119775 0.004101172 288628 -149.22014       0\n",
       "session_index    -0.0575931 0.001397287 226565  -41.21776       0\n",
       "session_comments  0.0434079 0.001071905 226565   40.49599       0\n",
       " Correlation: \n",
       "                 (Intr) sssn_n\n",
       "session_index    -0.185       \n",
       "session_comments -0.536 -0.618\n",
       "\n",
       "Standardized Within-Group Residuals:\n",
       "       Min         Q1        Med         Q3        Max \n",
       "-4.0031806 -0.7304668 -0.6600525  0.5278735 23.7386414 \n",
       "\n",
       "Number of Observations: 515196\n",
       "Number of Groups: 288629 "
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_pql_nb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, very similar results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Final model choice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given our extensive analysis regarding the appropriate model for our data, we can conclude that all have very similar conclusions, namely that the session_index has a negative effect on num_answers. Probably, the most appropriate model would be the zero-inflated Poisson regression. However, as the simple Poisson regression scales much better for larger data, we will continue to use it from this point on. Also, we do not use quasi likelihood, as it is difficult to compare the significance of fixed and random effects as no likelihood can be given."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Significance of effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have decided on a model, we want to extend our inference. First, we want to study the significance of the fixed effects as well as potential additional random effects. \n",
    "\n",
    "There are several options for determining the significance of a fixed effect on the model. For example, a common approach is to use the ratio of the slope to its standard error and then use a t-test for determining its significance. Alternatively, one can also use F-tests for contrasting simpler to more complex models. Both methods require a specification of the degrees of freedom though which is not trivial in mixed models; methods such as the Satterthwaite approximation or Kenward-Roger approximation can be used for that task. \n",
    "As stated in Baayen 2008, we can also directly use the t-statistics given to derive statistical significance. Because we have a huge dataset, a t-statistic above 2 can be regarded as significant at the 5\\% level in a two-tailed test. You can derive this directly from the results above.\n",
    "\n",
    "However, here, we follow an approach used for comparing models: the Bayesian Information Criterion (alternatively we could also work with AIC or LRT). Basically, the idea is to specify different (in this case nested) models that successively incorporate additional fixed or random effects and then compare their BIC scores. The lower the BIC, the better a model is (above a small threshold).\n",
    "\n",
    "The baseline model we start with is:\n",
    "\n",
    "num_answers = 1 + (1|author)\n",
    "\n",
    "The reason why we incorporate the random effect for author from the beginning is that this is necessary based on the design of the experiment. Also, as pointed out in http://glmm.wikidot.com/faq, you should not compare the fit of a (g)lmer with one from a (g)lm.\n",
    "\n",
    "Okay, so let us get the BIC for the baseline model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1121866.2 1121888.5 -560931.1 1121862.2    515194 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.647 -0.657 -0.584  0.512 41.656 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4012   0.6334  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "             Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -0.666373   0.002642  -252.3   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1 = glmer(num_answers~1+(1|author), data = data, family=poisson())\n",
    "summary(m1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let us incorporate the index and session length individually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1121353.7 1121387.1 -560673.8 1121347.7    515193 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.588 -0.664 -0.592  0.524 41.917 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.3994   0.632   \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "               Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -0.603266   0.003816 -158.07   <2e-16 ***\n",
       "session_index -0.025455   0.001130  -22.52   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "session_ndx -0.722\n",
       "convergence code: 0\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2 = glmer(num_answers~1+session_index+(1|author), data = data, family=poisson())\n",
    "summary(m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1121525.0 1121558.4 -560759.5 1121519.0    515193 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.719 -0.657 -0.598  0.539 42.410 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4018   0.6339  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.730513   0.004365 -167.34   <2e-16 ***\n",
       "session_comments  0.015978   0.000858   18.62   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.796\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00474022 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3 = glmer(num_answers~1+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the lower BIC we can clearly see that the incorporation of the session_index and session_comments (separately) improve our model, thus, we make inference on it (also the t-value indicates high significance)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1119602.2 1119646.8 -559797.1 1119594.2    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.708 -0.658 -0.591  0.554 44.510 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.398    0.6308  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.695957   0.004442 -156.69   <2e-16 ***\n",
       "session_index    -0.062017   0.001416  -43.80   <2e-16 ***\n",
       "session_comments  0.045746   0.001078   42.42   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.183       \n",
       "sssn_cmmnts -0.513 -0.605\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00539401 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4 = glmer(num_answers~1+session_index+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected based on our initial empirical analysis in the paper, both the session index and session length are important effect to incorporate.\n",
    "\n",
    "We stop at this point as our scope of interest is covered. However, one can arbitrarily extend the existing model.\n",
    "For example, one might also argue that it is necessary to incorporate a random effect for the intercept based on different subreddits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index + session_comments + (1 | author) +  \n",
       "    (1 | subreddit)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1117926.1 1117981.9 -558958.1 1117916.1    515191 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.817 -0.691 -0.600  0.497 45.886 \n",
       "\n",
       "Random effects:\n",
       " Groups    Name        Variance Std.Dev.\n",
       " author    (Intercept) 0.36087  0.6007  \n",
       " subreddit (Intercept) 0.01945  0.1395  \n",
       "Number of obs: 515196, groups:  author, 288629; subreddit, 12041\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.725504   0.005606 -129.41   <2e-16 ***\n",
       "session_index    -0.061710   0.001411  -43.73   <2e-16 ***\n",
       "session_comments  0.044560   0.001078   41.35   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.145       \n",
       "sssn_cmmnts -0.384 -0.602\n",
       "convergence code: 0\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m5 = glmer(num_answers~1+session_index+session_comments+(1|author)+(1|subreddit), data = data, family=poisson())\n",
    "summary(m5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the BIC shows an improvement in the model. Yet, the inference on the fixed effects does not change. For complexity reasons, we neglect the random effect for the subreddit for the complete data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Collinearity\n",
    "\n",
    "We also want to check for multicollinearity in our model; some explanations and code for checking that in lme4 is provided in https://hlplab.wordpress.com/2011/02/24/diagnosing-collinearity-in-lme4/."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.48954996169921"
      ],
      "text/latex": [
       "4.48954996169921"
      ],
      "text/markdown": [
       "4.48954996169921"
      ],
      "text/plain": [
       "[1] 4.48955"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "1.57796040588551"
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      "text/latex": [
       "1.57796040588551"
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       "1.57796040588551"
      ],
      "text/plain": [
       "[1] 1.57796"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "source(\"../mer-utils.R\")\n",
    "kappa.mer(m4)\n",
    "max(vif.mer(m4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both the condition number and VIF show no reasons to be concerned about collinearity in this model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Length as random effect\n",
    "\n",
    "We have decided to incorporate the variation between different session lengths as a controlling covariate, however we might also incorporate it as a controlling random effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index + (1 | session_comments) + (1 |  \n",
       "    author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1121355.8 1121400.4 -560673.9 1121347.8    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.588 -0.664 -0.592  0.524 41.917 \n",
       "\n",
       "Random effects:\n",
       " Groups           Name        Variance Std.Dev.\n",
       " author           (Intercept) 0.3994   0.632   \n",
       " session_comments (Intercept) 0.0000   0.000   \n",
       "Number of obs: 515196, groups:  author, 288629; session_comments, 9\n",
       "\n",
       "Fixed effects:\n",
       "               Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -0.603261   0.003817 -158.03   <2e-16 ***\n",
       "session_index -0.025456   0.001130  -22.52   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "session_ndx -0.722\n",
       "convergence code: 0\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_control = glmer(num_answers~1+session_index+(1|session_comments)+(1|author), data = data, family=poisson())\n",
    "summary(m4_control)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficient also indicates a negative effect (but lower effect size)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence problems\n",
    "\n",
    "Convergence warnings (which we partly also see for experiments on the complete data) are most likely false positives and do not effect the results. The gold standard approach to investigate this is to utilize different optimizers and compare the coefficients. If they are not similar, our inference is stable which is the case here. The code is based on Ben Bolkers code presented online: http://stackoverflow.com/questions/21344555/convergence-error-for-development-version-of-lme4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00283729 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.105164 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00586488 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "g0.bobyqa <- glmer(num_answers~1+session_index+session_comments+(1|author),\n",
    "      family = poisson, data = data,\n",
    "                   control=glmerControl(optimizer=\"bobyqa\"))\n",
    "g0.NM <- update(g0.bobyqa,control=glmerControl(optimizer=\"Nelder_Mead\"))\n",
    "library(optimx)\n",
    "g0.nlminb <- update(g0.bobyqa,control=glmerControl(optimizer=\"optimx\",\n",
    "                              optCtrl=list(method=\"nlminb\")))\n",
    "g0.LBFGSB <- update(g0.bobyqa,control=glmerControl(optimizer=\"optimx\",\n",
    "                              optCtrl=list(method=\"L-BFGS-B\")))\n",
    "\n",
    "library(nloptr)\n",
    "## from https://github.com/lme4/lme4/issues/98:\n",
    "defaultControl <- list(algorithm=\"NLOPT_LN_BOBYQA\",xtol_rel=1e-6,maxeval=1e5)\n",
    "nloptwrap2 <- function(fn,par,lower,upper,control=list(),...) {\n",
    "    for (n in names(defaultControl)) \n",
    "      if (is.null(control[[n]])) control[[n]] <- defaultControl[[n]]\n",
    "    res <- nloptr(x0=par,eval_f=fn,lb=lower,ub=upper,opts=control,...)\n",
    "    with(res,list(par=solution,\n",
    "                  fval=objective,\n",
    "                  feval=iterations,\n",
    "                  conv=if (status>0) 0 else status,\n",
    "                  message=message))\n",
    "}\n",
    "g0.bobyqa2 <- update(g0.bobyqa,control=glmerControl(optimizer=nloptwrap2))\n",
    "g0.NM2 <- update(g0.bobyqa,control=glmerControl(optimizer=nloptwrap2,\n",
    "                           optCtrl=list(algorithm=\"NLOPT_LN_NELDERMEAD\")))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "getpar <- function(x) c(getME(x,c(\"theta\")),fixef(x))\n",
    "modList <- list(bobyqa=g0.bobyqa,NM=g0.NM,nlminb=g0.nlminb,\n",
    "                bobyqa2=g0.bobyqa2,NM2=g0.NM2,LBFGSB=g0.LBFGSB)\n",
    "ctab <- sapply(modList,getpar)\n",
    "library(reshape2)\n",
    "mtab <- melt(ctab)\n",
    "library(ggplot2)\n",
    "theme_set(theme_bw())\n",
    "ggplot(mtab,aes(x=Var2,y=value,colour=Var2))+\n",
    "    geom_point()+facet_wrap(~Var1,scale=\"free\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Randomized baseline data\n",
    "\n",
    "In order to finally confirm our intuition and inference on the negative effect of the session index on the number of responses, we also study our randomized baseline data. We basically have two different randomized datasets: (i) new sessions based on randomized time differences and (ii) randomized positions inside existing sessions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx = data$session_comments_random > 1\n",
    "data_random = data[idx,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       " 846628.8  846650.5 -423312.4  846624.8    388336 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-9.559 -0.657 -0.584  0.511 41.652 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4025   0.6344  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "             Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -0.664973   0.003042  -218.6   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1_random = glmer(num_answers~1+(1|author), data = data_random, family=poisson())\n",
    "summary(m1_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index_random + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       " 846630.0  846662.6 -423312.0  846624.0    388335 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-9.561 -0.657 -0.584  0.512 41.531 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4026   0.6345  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                       Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)          -0.6667287  0.0035875 -185.85   <2e-16 ***\n",
       "session_index_random  0.0005890  0.0006369    0.92    0.355    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_ndx_rn -0.529\n",
       "convergence code: 0\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2_random = glmer(num_answers~1+session_index_random+(1|author), data = data_random, family=poisson())\n",
    "summary(m2_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_comments_random + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       " 846612.7  846645.3 -423303.3  846606.7    388335 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-9.565 -0.657 -0.587  0.515 41.162 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4029   0.6347  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)             -0.6736861  0.0036617  -184.0  < 2e-16 ***\n",
       "session_comments_random  0.0017494  0.0004071     4.3 1.73e-05 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnt_ -0.557\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00176358 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3_random = glmer(num_answers~1+session_comments_random+(1|author), data = data_random, family=poisson())\n",
    "summary(m3_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index_random + session_comments_random +  \n",
       "    (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       " 846604.1  846647.6 -423298.1  846596.1    388334 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-9.560 -0.657 -0.587  0.516 41.382 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4028   0.6347  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)             -0.6717834  0.0037117 -180.99  < 2e-16 ***\n",
       "session_index_random    -0.0030156  0.0009276   -3.25  0.00115 ** \n",
       "session_comments_random  0.0031729  0.0005920    5.36 8.34e-08 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n_\n",
       "sssn_ndx_rn -0.165        \n",
       "sssn_cmmnt_ -0.256 -0.728 \n",
       "convergence code: 0\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_random = glmer(num_answers~1+session_index_random+session_comments_random+(1|author), data = data_random, family=poisson())\n",
    "summary(m4_random)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When comparing m3_random and m4_random, we can see now is that the incorporation of the session index is not improving the model in terms of the BIC score  and is thus, not significant (also has a low t-value < 2). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Randomized indexes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1121525.0 1121558.4 -560759.5 1121519.0    515193 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.719 -0.657 -0.598  0.539 42.410 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4018   0.6339  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.730513   0.004365 -167.34   <2e-16 ***\n",
       "session_comments  0.015978   0.000858   18.62   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.796\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00474022 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3_random_2 = glmer(num_answers~1+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m3_random_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: poisson  ( log )\n",
       "Formula: num_answers ~ 1 + session_index_random_2 + session_comments +  \n",
       "    (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1121526.5 1121571.1 -560759.2 1121518.5    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-8.724 -0.657 -0.598  0.539 42.410 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4018   0.6339  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                         Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)            -0.7309949  0.0044251 -165.19   <2e-16 ***\n",
       "session_index_random_2  0.0009546  0.0014135    0.68    0.499    \n",
       "session_comments        0.0155018  0.0011117   13.94   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) ss___2\n",
       "sssn_ndx__2 -0.161       \n",
       "sssn_cmmnts -0.505 -0.636\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00790221 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_random_2 = glmer(num_answers~1+session_index_random_2+session_comments+(1|author), data = data, family=poisson())\n",
    "summary(m4_random_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we see similar behavior, the incorporation of the random session index does not improve the model compared to one that already includes the session length."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overall, the analyses presented in this notebook have demonstrated that the course of a session has a (negative) effect on the number of answers a post receives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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