S5_Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 52,
   "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": [
    "# Body length\n",
    "\n",
    "In this notebook, we document our various steps taken to study the effect of the course of a session on the body length (number of characters). Note that we only do this on a sample of 1 mio. data points here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#no zeros in the outcome variable\n",
    "data = read.csv(\"/home/psinger/Reddit-depletion/data/sample.csv\", header=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1000000"
      ],
      "text/latex": [
       "1000000"
      ],
      "text/markdown": [
       "1000000"
      ],
      "text/plain": [
       "[1] 1000000"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nrow(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": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx = data$session_comments > 1 & data$session_comments < 11\n",
    "data = data[idx,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "515196"
      ],
      "text/latex": [
       "515196"
      ],
      "text/markdown": [
       "515196"
      ],
      "text/plain": [
       "[1] 515196"
      ]
     },
     "execution_count": 56,
     "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 body_length represents count data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data$body_length)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data$body_length[data$body_length<1000])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression model\n",
    "\n",
    "We use mixed-effects models where in the most basic form (that we analyze in this notebook), we are interested in studying body_length ~ 1 + session_index + (1|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": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer = lmer(body_length~1+session_index+session_comments+(1|author), data=data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: body_length ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 7246789  7246845 -3623390  7246779   515191 \n",
       "\n",
       "Scaled residuals: \n",
       "   Min     1Q Median     3Q    Max \n",
       "-6.372 -0.412 -0.247  0.084 35.261 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 12897    113.6   \n",
       " Residual             63957    252.9   \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                 Estimate Std. Error t value\n",
       "(Intercept)      170.9110     0.8158  209.50\n",
       "session_index     -5.2595     0.2833  -18.57\n",
       "session_comments   3.6147     0.2222   16.27\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.169       \n",
       "sssn_cmmnts -0.530 -0.642"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zng08kVw3FdicSLCnEUc2JeWvluOZRKeQNqH6IzEd0l1NrnsNcCGwYo9iUm85jZ1UbQuAT9T9fBvRYvdqYnnv+3OI6UpgR+Aw4CiWnp1pMXAJUSmfmW1oktoweU6pXUJ1UHKp+TkxLVK9IWBD4mxqFZM90NLgWUCsIJunmcllCpHQr51sf5CYC3r+BG9/BrB1iv2G6u5bknqiXUL1IKO9aa8D/grMa7Jf7RCdiskKtFRtac6az6OqtAyxCNdmxGIul7D0uTNbAq8FTh/H7X+adCes/5KY2k+SeqZdQjU9uUCcFHgYUTVQuViBlqrt/Q0/1yquewDLEm0SWVuVWKH29XXbZhOLutxbt20n4GuML4G+MeV+I7Q+6V1ScPnuLqVNqN7Y1yjUT55EKFXbGS22H0ccHXwz8OvMoglHEYWXvYg2ju2BU4lpULfFhFZSybVLqC4nWjg+SwzEnXy2JxGp15zGThpMI0RyfSLw+YzvezfifeOC5OcLiLbAmcBHgG9nHI+k1vJePKWU2iXQO9ddv0eK2zKBLiYr0NLgWo84gS9raxHLiNf7PXAy8EXgbOCxrIOS1JLtG11ql1DV/zFdKaq86ivQQ8R0UovzC0dSjx3WYvvawIeBqzKMpeYOYBdikZd6XwDeCZwFvD3roCSpV7qpSK4MvJA4m3qYOHFlC6LV45e9D009Un8SIcT/3ARaqo5WR/8WM9oykbVvAacRlejpRMV5HrGYyoHEjBwXMrq4iqR82L7RZ28AHgd+lPz8n8Qf/eHk6545xVUUS4Aj8w6ihTcQ/6Pa15XyDUfK3aeBa/MOouKGicT9PmLcaTyK+VbgnuS6fr+BF3l8lvJWtAS6NONz2gr0V4E7gS8nP38I+D6x0MrZxCHEC5r/at8NAZsQvX5rES0KDxCD8xyK9+TIWn0PNHgioVRFqwAvI8bD2cDcuuuWY+lFsPptCdHvfDKwGvB0w/WXEYtwbQNsnG1okpSdeUQvHcAaRFL6puTn9wFP5REUsC8wi9EqRuPlJuDfM4ijyBWO7Ym/xcuTry/MNxwpd6WpcKSwDbGYVePYdx3wKuAFwC3Au/IKsACKPD5LecriCFC3SjM+p61AP0dMyA8xO8dC4Jrk55XJ5x+wP3AmUcn4KvEm8RhRgVkN2BTYm5gHdRg4J4cYi6B2EmGtArVsqx0llcpHge8Q08MdRVSeFxLnpryfGKPnEOc/eJ6KpGacfaPPLgRuBt5BJKq1FQo3Ij4p/D6HmK4jEuhO//wTGU32+6XIFY4diPheTHzQ2SDXaKT8labC0cbmwLNE69zKTa5fAfgd8ZrfLcO4iqjI47OUp6JVn6FE4/Nw510A+AyxNOsvgHWB/0m2X0G0Bnyp55F1tinwKzo/AWYw2NPwDRF/o9osHFagpfI7HHiIqDTPa3L9q4DXAI8A+2QYl6RyKGLyXCppWzhuJarNLwXuZbTn+VCiz/ju3ofW0SximdifMJocNppEvHnclFVQBTRMVGA8iVCqjq2Aixh7smC9p4BPAtOI+ZglqZHtGxPQzTzQzwP3EwnYGsm2WuvGGsCjPYwrjaOJVpLriT7n2YzOKTqVOMS5F/EGsmvGsRWJFWipejYBvtfm+r8kl48CB2QRkCQNkrQJ9NbAeUQVupWsP8lcCexITKF3FFFtrreYmKz/UGIxgUHVWIE2gZbK7w7aj8c1GyT7SpJ6KG0C/R1iLtEPEmd8F8XM5DIFWIdYuhYixgeA+TnFVSS2cEjVcxNxcuDngGda7DOZWLDkL1kFJakU7H/ugbQJ9DRi+dVz+xjLRMwnpmuak3cgBVRr4VhMJNJWoKXy+zrwbmKhkg8TM3LUmwQcSyyuclC2oUkqAfufJ6ibkwgbB+iyeAmxfPXscfzujsRqWZ0MUdzEtFaBhuiDtgItld9NwOeJOfC3JY4Szibme98C+AAxC8dX6P80npI0cNIm0N8GDiGmhGtckrXoTgPezPg+bX2QdH2GECt+FVGtAg3RxlHURF9Sd74G/Bk4iZjvvt6DxCqs52cdlCQNgrQJ9KrEIcE7gMuJ+Ucbe2g+28O4eulnjK/6DOnnT11CzLdaRFagper6FTHP/bpEu8byxHh3J6Ove0mqsf+5R9Im0AcnX58EtmmxT1ET6JPyDiBnVqClahsh5ue/N+9AJJWC/c89kDaBHuSV/MquvgJtAi1JkjRB3SykAjEbx+uB1YFTienj7sJDAkVmC4ckSTJX66G0CfRk4AzgvXXbLgCOI1b9253R5b1VLLZwSJIksH2jZ9Im0EcAexO90D8BHk62/w+x2t8XiVk6snR1l/u/sS9RFN8QVqAlSRpkVp97bDjlfgcQUyadAsyt234z8F1gz96Glcr3gBcSc6CuTpzg2O4yqCZhD7Q0CKYRRY7PE2PjS7DaJGmU40EPpa1Arw7ManHd7cAavQmnKz8ALgXuJpLp43OIoQzsgZaqrcgtdkPAJsB6wFrEB/oHgHuIlWOtikn95+usD9JWoG8Bdm1x3RuAv/YmnK49BFyb032XRX0C/RywXI6xSOq9+ha7FxCvc4gWuw2JFrs87EusmHgbsQjXj4GzgF8m224kFnuR1H9Wn3ssbQX6eOC85PsfEEnZ5sC7gI8BB/U+tNQOwRMY2zGBlqrtAEZb7OrVWuw+RPbnqOwPnAlcRiw3fgvwGPEmvhqwKZH0n0uMUedkHJ80KKw+90naBPqnRHXjf4mBEWKFv7nEAipn9T601K7P8b7LoD6BfpZYqUxSdRSxxe7jxPvCASz9Bn4PUZk+l1iC/FOYQEv9ZPW5D9K2cEBUN9YDtgb2AF5LLB97An7CKTIr0FK1FbHFblNimfFO7w0zcKEuqV/Mzfqo24VUngf+QvSuqRxMoKVqK2KL3SxgL2La0+db7DMJ2IeoRkvqD6vPfZImgX4d8BlgS+DFyba7iAHyK8B1fYlMvdLYwrFijrFI6r0ittgdDUwnWuzOBWYDTyTXTSUS/L2IqfdaVc8ljZ/V5z7rlEB/nehPe4Q4HHd+sn19YEdi/ucTgMP6FaAmrLECvVqOsUjqj1OIRHkzYny+H/gbMD+neK4k3iMOA44iqs31FhOLcB0KzMw2NGlgWH3uo3YJ9HuI5PkEYjqkZxquX5GoMhxKTCV3HioiWzikwbCAaK8rSovdzOQyBVgHWDvZ/iAxF/REk/s3ARun2G8I57/XYLH6nIF2CfQHiOWyD2c0Aav3DPBpYJtkXxPoYppEVHvABFqqii/1ef9emk8smjKnx7d7KOlPQJza4/uWis7qc5+1S6C3JqYYapY81ywhDtV9opdBqacaK9BOYyeV3wFd7v+lPsSQt7S900uAh/sZiFQgVp8z0i6Bngrcm+I27sG+2iJrPInQCrRUfhvkHYCkwrL6nIFOJxGm+STjp51iswdaqr5hYHdifv71iB7ja4nZONodReyXq7vc/419iUIaLCOYPGemUwI9KeU+Ki5bOKRqW5VYkORVxIxJ9wI7Eeeo/Bl4M/BkxjF9j5hC76XArcAdGd+/NGgsZmasU3J8enJReVmBlqrtROJkut2JuZdrVajdiCWyTyBO9M7SD4BLgbuJZPr4jO9fGkRWnzPULoH+38yiUD/ZAy1V21uA44CL67aNJD9/BfhQHkEBDxFtJJL6y+pzDtol0EdkFoX6qT6BXgCskGMsknpviDiZu5k7ybfN7hDgqRzvXxoUVp8zNpx3AOq7+gT6GVzKW6qaS4D/YOmCyDDwbuDyzCMadT29n/9Z0iirzznp1AOt8mtMoJcl/u+LcotIUi+dDvwQuI5YzvteYE1gX+AVRAvHbg2/Mz3LACX1RS15tvqcAxPo6htibAINUYWem084knrsmrrvX9nk+rObbPMNVyo3k+ecVS2BHiambJpGJIh/Am7ONaL8NVagwQRaqpJ18g5AUi5MnnNU1gR6PeJw5fuBy5JtU4mzzrdt2Pc04CPA4syiK5ZJNE+gJVXDg3kHIClT9j0XQFkT6EnAWoydku0rxOHLA4CLiCfYHsDJwF+Bb2QbYmEMM/rhwQRaqp4VgYOAl9F6xo2DsgtHUh/ZulEQZU2gm3kHcCxwZt22M4gFBt7HYCfQVqCl6voeMdvG7cRKhJKqyeS5QKqSQC8DvJBYtrbRjcAnsg2nUBrngR7BBFqqkl2Bo4Av5h2IpL4zeS6IqswDvQj4CzFlU6MtgIezDadQ6hPoESKJNoGWquMJ4A95ByGpr+x7LpiyJ9DnALcAFxKJ4ZeAlyfXLQ98EPg08JM8giuI+gQaTKClqjkX+AD5rjgoqX9s3SigsrZw3E9MV7dRctkQmAw8TyTQs4EdgVOBnwLH5BNmITQm0POAlXOKRVLvfQG4g5iy8/fAwib7fCzTiCT1islzQZU1gV4I/Dq51BtitKo+iziB8LYM4yqixgR6LrBKTrFI6r1vAOsSrWxb5xyLpN4xeS6wsibQrYwwOmXbP/MMpECsQEvVtidwHPA57JOUqqD+dWzyXFBVS6CbeQmwEtHW0a0pwJq9DSdzzSrQJtBSdcwDfoPJs1QFVp1LYhAS6NOIfunxPBmvJpYFT6Ooy+nawiFV2xnA/sAMxr7WJZWLyXOJDEIC/TPGV30GeAvpqrV3UNzldE2gpWqbD2xHzIP/B5qfRPjJTCOS1C2T55IZhAT6pAn87iOkW9lrhOIePp3E0j3QRa2WS+reB4jX9TLA9jnHIqk79juXVBUS6CFgE2A9YC0iYXwAuAeYQ3ET26wMM3piJXgSoVQ1L++8i6QCsupcYmVPoPcFDge2bHH9LOBY4LzMIiqeYcYe0n0CmJpTLJKy9U7gE8AOeQci6f9Yda6AMifQ+wNnApcBXyVWJHyMeDKuBmwK7E2s0jVMrFo4iBp7oE2gpWpZHfg6sBVLry77EuAfmUckqRWrzhVR5qW8Pw6cBewK/Bi4iZj7+Z7k+3OBvYhFBj6VU4xFYAItVdvXiUrz1cByRMvWlcBzwALgrfmFJilRf66UyXMFlLkCvSnwbTr3OM8ADux/OIXVLIGewujS55LKbWfgROCLREHhkOQyGbgK2J2JnUwtafxs16gzEh/yV00uL6j7flVg6qWw8yWwehkGrDIn0LOICvNPaJ0ITgL2ISrSg6pZAg3xZE0zw4ikYlsN+Gvy/R+BVxGv++eJOaI/jAm0lKXGwl5lEucRWJaxSe+YBJjmiXH9ZYW6m1sCPJlcngCefBGsMTVyt8IrcwJ9NDAduJ5o15jNaHI4FdicSLCnEVWZQdUqgZ6KCbRUBQ8R/c/nAo8DTwGvAa4BFgGb5ReaNFAKXW0eiZxvTeL9v/GyPJHcNruufp+6m+NBok3sWSK3qL/c3mTb/12G4vea+TRx/lrhlTmBvhLYETgMOIqlP7EsBi4BDgVmZhtaoTQm0I8nX1fLIRZJvXc+8F/Aw0Q/9A3EuPdlYD/gzvxCc5pRVV5m1eaReP2sRW8SYGie+NYu/2hzXbsEeGCUOYGGSIxnEj296wBrJ9sfJAbp+TnFVSSNCfSzRIVqrXzCkdRjnyPeWF+V/PzfRPV5b2IKy31yistpRlVFzT70pUqa2yTAaZJfE+CCKXsCXTOfqGbMyTuQAmpMoCFaN9bMIRZJvbeAmOu55jaioPBq4A7g/hxicppRVcX/Jcy17Pe+WLyoPrH9EONLgJ8jjgp3mwAvAJ41Cc5XVRJotdYsgX4YE2ipqlYn3uBvJ47E5aE2zegBLF2xq59q9ERimlETaPVduwrwJ+GUVlnvFvE6qk+AZydfFxIfDNMmwGP6hU2Ay80EuvpaJdAvzCEWSb0zDfgC8BfgyGTb24jEdEry84nESTmLM44ti2lGzwZel2K/IeJDhUquRQLcsf3hAdii2eIHzwOPEtns3sC2MTFBy4pv43YT4MFmAl19k2ieQK/dZF9J5fAK4E/EDByXJtuWJ6q+c4g5oV9P9EP/EfhpxvFlMc3o2cBvU+z3HeDacd6Hemi8CTAw9dloSxpjEdGP2LLRl9HM98yYD33M1SVTyOkAACAASURBVMuaAGsCTKCrb5ilq0//JA7xSiqnzwN3E9PVzUu27URUWvcgViW8GNgCOJjsE+gsphmdnnK/ExidfUjjMwLxZrI24zv7rVkFuF0C3KzkexFsV79pchcJ8FldPFgpDRPo6mvWwvFPYlopSeX0OmJxlHl123YAbgV+X7dtJtFjnDWnGS2gERheFxaPJ/ldJ/LZxpPgFhNHNFO1PDReukmAoYATK2ugmUBX3zBL9yHeSxQSJpF9b6SkiVuH+CBc71+BKxj7ep9Hfuc7OM1oj40sXQReKgf+FnyxXQX4vrE3uYRoA+oq8a1d7AHWIDOBrr5mFeh7gMnAusn3ksrlAeL1W/Mi4JWMnkxY82KWypky5zSjiTQJcIfL8g23x4OMzXw3BHaDH2ICLPWVCXT1NUug7yYqzxtiAi2V0Z+ADwPfJ5KhjxItpVfV7bMcsRKhJ9D1SEMC3G3y22weYIj/X7Oq75hp0HaHM5v1SWBng5QLE+jqW5GlqwwLiTaOjUl3FrukYjkGuI5YNOU2YFtiVoonGZ3d4uPA+sCeOcVYOCORbK5DbxPgVi0PbVeCI10FOLNloiV1xwS6+lYEnm6yfQ6wUcaxSOqNW4hp6j4LvBQ4FfhMct1k4MdE68auwA15BFgUP4Tld4Nvrwr/D1gVWKXJbnOJDx/1l8eJJLj281NN9nkCeHKo83zX3TBplkrABLr6ptA8gZ5F9ExKKqdZwHuabF9I9ETfT28Tu1KaCYvXhl/vCH+gSfJLJMCNbW5ZM2mWSsYEuvpWonkCPZvmb76Sym0J+Z84WBinwfOnwc9JP290luoTZ5NmqUSG8w5AfTeF5tNF3QD8C2PP5Jck9ddI3QUicTZ5lkrGBLraliWOMjSrQP+NOIFl60wjkqTB1CxpNnGWSsoEutpWSr42S6AXEVNhbZtdOJI0cKw2SxVUhR7oIWATYmnqtYgpnB4g5jeew2CfRNMugYZY8vdNGcUiSYPE/mapwsqeQO8LHA5s2eL6WcCxwHmZRVQsU5KvrRLoGcQ0WKsSZ6NLkiauvuIsqYLK3MKxP/Aj4mzz/YCtiEUDXpx8/27g78C5yfeD6AXJ17ktrv8j8CjwvmzCkaTKM3mWVGjXAWfSeZA6Ebimz7EsAY7s832Mx97AYx32OYL4oFHmD1NSNz6Ny1sPknnAbhncT+PsGpK6V5rxucxJ06bAr+g8WM0ANut/OIW0AXBXh31OIXrH9+l3MJJUUZ4kKA2YMifQs4C9iGVrW5lEJIY3ZRJR8WxA5wT6EeAk4H+JXmhJUnojmDhLA6fMJxEeTawsdT3R5zybWJoVYCqwOZFgTwN2zSPAAphGVOk7OQZ4O/B9YE88BClJadSSZ0kqle2Bi4g5jUcaLouAC5N9+q2IPdDLAs+Q/sPDy4hewa/jG4KqrTQ9duqJfvRA2+ss9UdpxucyV6ABZiaXKcA6wNrJ9geJuaCbLWE9KN5EtLD8LuX+twDvBH5O9Ix/gji5UJIGXX2Ps1VnSaXuga43n1g05XfJZQ6DnTwPE/NjX0zrKeyamQFsA6xM/A3/BnwM2JjqPFckKY3GhVCG6r6XNODKXoFO4yXEinyz8w4kA8sBbwQ+RcyFvc04buMWou1lK+BdwOeAbxP95X8mpsW7FbgdWEgswDKfOEz6OLAguZ0lwFPjfBySlDcTZUktDUICfRrwZsY3GJ4OvLLTTpMnTx6aOnXq2hdccMHUZtefcsopq19yySVnjYyMrDCOGFoaGRlZEVh2ZGRkleTrFGDJ5MmTf/mKV7xip2OOOeZh4oTK8bgTOAE44cgjj9xgzpw52z777LMbL168eM1Fixa9dWRk5P0jIyMr12LocFvPDg0NPZt8v2RoaGgBkWAvIUUf4dDQ0NPA8yMjI6sMDQ11U1HXABoeHn7o7LPPfu9KK63U9Lm1zz77rPDwww8PLVq0KOvQVFy2ZUjqyiAk0D9j/NXnXxOtDG09//zz0x5++OFrt9tuuyda7LIgiWPSOONoNB94vu7nucnP/yTifeKqq65iu+2269Hd8QRwY5vrJxNtH6sS/ei1qQVXJp5jKxLV8WZWBha3ub5b4/3AoOp4apdddnm8zfUL8AQwjWXyLKkrg5BAnzSB3z075X5HAA+1uf5Z4PgJxFF0zxPtG+2SFkmSpEqoQgI9BGwCrEesqDeJmIHjHqIaa6VJkiRJPVP2BHpfYraJLVtcPws4Fjgvs4gkSZJUaWVOoPcHzgQuA75KzB7xGFGRXg3YFNibWKVwGDgnnzAlSZJUJWVOoD8OnAUcwNJtGvcANxHJ84nEtG79TqBfSfQ6F9kU4FXElHNltRIxe8eCTjsW2GrE9H9L8g5kAlYAfp93EOO0cd4BKHNZjM8bAWsCz/X5fnptZWJK0rLFPYVYcbjo77uNyhr3SsT0te3O9+qF0ozPZU6gNyXmJ+7U4zwDOLDPsTwGHN3n+5DUO5fnHYAy4/gslYvjc5/9DriI0SnTmplEVKmvyiSi4vtPyr+gzHnAd/IOYoIeJtqLymoL4oPrmnkHIhXI5cQ5N2VzKXBc3kGMw8XA1/IOYhwuJNZYKJufE0f0lShzBfpoYDpwPdGqMZuYrxhiLuDNgb2AacCueQQoSZKk6ilzAn0lsCNwGHAUSy9Sshi4BDgUmJltaJIkSaqqMifQEInxTKIpfx1g7WT7g8Rc0PNzikuSJEkVVfYEumY+sWhKx2W3JUmSpIkYzjsASZIkqUxMoCVJkqQumEBLkiRJXTCBliRJkrpQlZMIlc6DxDLnZXYf8EjeQUzQXcRiKmX1FHAv8EzegUgFci8x+1PZGHe2yhr3fcD9eQchSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkqeB2AmYCc4FrgP3yDSe19wNXt7iuyI9pGDgQmAU8DdwBfBNYtWG/oj6GFYBjgNuBBcnXI4DlGvYravxS3r4C3Jt3ECmkHauKooxjTtn+xq2U5Tkt9cz2wELgYuB9wA+BEeC9eQaVwprArTRPoIv+mA4m4vk+sDeRfM4Ffg9MSvYp8mM4GXgG+B9gT2LgXAKcULdPkeOX8rQ98XopQ7KRZqwqirKOOWX6G7dSpue01DMXEp98Jyc/DwGXJduG8gqqjVcBvwWeJQadZgl00R/TvcQgX29P4vHskvxc1MewArCYSJ7rnQU8ymhsRY1fytMqwJ1EglSGZCPNWFUUZR1zyvQ3bqZsz+lMDOcdgPpuCrArcC7wfLJtBPgxsCWwSU5xtTMXmE58Sr+1yfVFf0yrAesSj6HezOTr5hT7MawJ/A64omH7XcQb1zDFjl/K0zeAh4Gz8w4khTRjVVGUdcwp09+4lTI9pzOzTN4BqO/WIQ4R3dKwfXbydT2iv7VI5gDHJ9//G0v3iRX9MT1NDIr3NWzfPvn6D4r9GO4m/u4QMb4AmAbsD5xHVKeLHL+Ulz2AdwNbAR/POZY00oxVRVHWMadMf+NmyvaczowV6OpbO/n6eMP2x5Kva2UYS68U/TE9R1TO59Vt2xY4lRjsL6H4j6HmnURMvyYqEP+VbC9L/FJW1gJOAw4Hbss5lrTSjFVFUdYxp0x/40ZlfE5nxgR6cNX6xcpyAkMaRXxMU4FvE4fr/gG8DVjUZv+iPYZfE4P9B4kK0G8Z7T9spmjxS700RBy5rV0m1W0/nejFPSmf0NpqFXe9bseqoijTmFOmv3HRn9O5s4Wj+h5Mvk5t2L5a8vWBDGPplbI8pp2AHxBTv30S+C6jvXtleQyPA39ILvcBlwJvYvSwY9Hjl3ppW+L8gJoriJPA9iNeF9sQJ1xBvO6HiRa0hcSsNnlpFXdNu7GqKMoyZrZShr9xvaI/p6W+m0L0rH6mYfs+xAkYL808ou5MZ+lZOMrwmHYhKguXAqs3ub7Ij2Ev4pDjKg3bNyFi24dixy/1yxTglXWXjZLtxxHP+1aXM7IOtEGruKHzWFUUZR5zyvI3rlf057SUiYuAaxnbsnM+xZ/6B5on0FDsxzSJOBFvOu3bpIr6GF5FDJD/3rC9NpfpFsnPRY1fytqGxIm39ZefA48k32+WS1SdpR2riqKMY07Z/sY1ZX1OZ8YWjsFwPDCD+MR4DrAjMQflu4mEqIyK/JheD6wPXAUc0uT6K4GbKe5j+DMR16lE1XkOUbX6JPAT4K/JfkWNX8raP1h6NoW9iBPIfpt5NOmlHauKooxjTtn+xjVlfU5LPbcT0QM3l/gE/558w0mtVQUaivuYDqD9oa+D6vYt6mNYDfh/xNzPC4ipoz5P86W8ixi/lLfvUPxFJw4g/VhVFGUbcw6gfH/jVsrwnJYkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkDY6hvANQR8sC/9Jk+2LgnzncjlQEPp8lSSqwGcAIsGOb6y/v4/2/Kbn/xsuDLfZ/P3B1H29nMvBpYDYwH7gW+FCT/V4GnAc8kNzH94A1WtxXt37B0o/jaeAG4D96dB9pbJbc9zbj/P0ROj93Gu9jN+Cghn1uBY4bZwwTsRMwE5gLXAPs16PfGwYOBGYR/9c7gG8Cq9bt0+n5vDywQZtL7bmY9vks9cs5NH8u119uTfbN67XerWbjVJrxrlt3AV9Kue92wE+J96SFwP3AT4gxNk9p/lZ3kf5xKiPL5B1AiZwKvIJ4Q8/SRsBzwLsbtj/XZN81gc8Aj/bxdk4C9ge+DvwZ2DbZthJwYrLPi4HfAbcARwDrA58AXkIkPr3wCHB48v0QsDrwLuCsZNsPe3Q//fQr4KYuf2c34JXA6b0PpyvbA9OBK4CPEx8wfwgsAc6e4O99CDgZ+AFwDLAp8b9+dfL7i+n8fH418Rxs5UzgANI9n6V+OpmxydLHiA95h9VteyrLgHqg2Tg1nvGuV74EfBH4B3A+MIdInHcDbgQOJV73eSja30rqmRnEi+054IQW1/ezAn0ckYi28yrgt8CzxCfXZpXjXtzOxsn2TzVs/x+i8rds8vPxyX0tX7fPfsD1wIs6xJDGL4C/N9m+LHAPcGUP7iONiVagx3Mf3wX+1LBPHlWpC4kK8eTk5yHgsmRbu9awNL93L3Bxw+/tSfwddkl+7vR8Xh3Yo8nlo0QC/k7SP5+lLJ1PVBybKUsFutk41Q930bkyWzta9UPig3G9FwAXEB/gX9fj2NJK87e6CyvQhTOcdwAlcQdRCfsk8JqM73tDRpPFVkcM5hJVvSMYPdTXj9vZMvn6y4btlwBrEQPQJKKydzqRiC9DPM9+RFQF721x372wEHgceLhu2wpEdfEe4kPQ/cAZwGp1+9xK/G/fRyT584HfA1s3uZ07iMr8z4C1666/Griq7uepxKB8Z9224SS+WqWh8c0wzX18mPg7N0vcPwL8hThK0hh/L00BdgXOBZ5Pto0APyaeI5tM4PdWA9Ylnof1ZiZfN0++dno+P0Z80Kq/XAzsRbSD/Jx0z2epiDq91vcC/kiMZXcSydfkuuuHiaOCNyX73Ax8lhi/a24lquEfIcbtvVLefqtxqnG8Gyaq7LXHcTPw3rrr04zdnQwRFf47gA+y9BHkp4j3q4eA79Rtf5SxRwBI9hvpMr5O7y1p/1bNdPofb0qMc48Q7+0zgdd3uE2pp2oV5mWJF/rNjK1M9bsCfQPx6fQmIiF7ADiFSNCamU7zCnQvbueNxIv87Q3b90m27wOsk3z/AeLv8gwxSP2IqAr2wi+IT+RrJ5d1gC2Ao4B5RK9bzbeABcBXiMP9Ryf7nFG3z63EY51JVCnfQ5yIVl/lnk4kfccR1fTzgCcYHfSOIAbRFZL9d2O0f3H9ZNu05Oc96+63fpDsdB/rEMnmjcQh3uXqbuefRAL/DuJN6D7g9qX+cr2xSRLTOxq2vzLZ/uYJ/N5yRNV95YZ9ahXo2u92+3yGaEuqr36neT5LWetUge70Wv8QoxXXfYAvE+PKj+r2+XKyz7eAfwe+RhyZObnhvq4kjsacSpzXkub2241T9ePdiUTR4ygiGfxhcrtvTa5PM3bfRfvK7LrJbX6yzT4ARyb71cadNAl0L95b0v6t7mLs4+z0P5gM3E3kLJ8ADiZa1B4jChlSJuoT5NcRb9ZHtLi+14aAJ4kk9DPEwHIE8Sn6apofQWiW+PbqdpYHbiNaWrYnqnS7EwP4CPFC3Tr5fgHRw7pHsv1xIuHpxVGPZicR1i7HM7Yi+WOiv63eScQHoZpbiTeJ+sN7ByW3tyrwhuT7g+uuHyI+3deS21czNnk8jujBfY7RExs/ASwiDhvW7rc2SKa5D2jdwvEAsGLdtoMZ+4bQS9slt71dw/b1ku3vXeo3JvZ72xID/1+I/+14ns/rJtfX9+CneT5LWeuUQLd7ra9AVBzPavi92j7TiOf5c0TiV++/ifFpg7r7egJ4Yd0+aW4fOreavZhI+OoT2yHgOuIIFaQbu++ifQK9M+0nAajZO9mvVqFNk0D34r0F0rXl3cXo40zzP3hZ8v0edde/jEiwN0Q94UmE3bmGOPz7BWKQa9Uu0eg2YsBo5jss/UKtGSZeFLOTC0S/6L1Ecvpmlj783M/beZboHT2L0XaFp4DPJ4/jcUYHhYuImTxq7iP+Zmnvq5MHG25/GWAr4jDkBowOiPvW7TOVSFTfwtInT17O2MN7tdkclgFeS3xwOqPu+hFGPyBAfLp/FNiBOAFku+Q2R4B/JSoF/0ocvmt2QlCa+2jnCiKhbIx/UpN9a8b7vGyl1sPc7j67+b2pRHXqo8Tf913EG/wkun8+f5n4v/y6blua57NUNO1e6xsTM8z8oOF3ziaqy68n2hmWZWxFurbPsUQR5K5k28VEslazWYrbn5XiMbyWGFvrTziuVZ9rR3jTjt3t1M7D6fQ7C5Ov3Uzt24v3lvFI8z84hxjL/pf4sHUFcc5I2pmSlIIJdPe+QLzpnk5UrdJ4G2N7k+o90eb3FhMvhEYXJV+nkS4Z7dXtAPyV6ANfl0iWbyUSV4gesNrMHY09rLXb7+a+2nmapSv/04l+sK8TbQE3Ai8lPslvTQxyNxBvPo3J2kNt7mtt4nE927C9vp97CTFI7UAM2q8mqqKTicN2Q8TzpdmJqGnvo5128bcy3udl7Q2gsV2i1vv3QA9+byfiDWI5okr1XUb7prt9Pm9IvHHs0OR3Oj2fpaJp91qvtYtdQYxJjVZndIxpfJ3Wfl6vzX2luf001idex480bK+f+Snt2N1O7QP25rSflWeLhv2baUyue/HeMh5p/gdPEoWEo4lxdFnig80pyaXZ76lLJtDdm080/V9OnFyRxh3jvK/1iGRgBmMTq9qTf27Gt7Ms8Sn7diKxqyV3r09u61ZGP8kv1/C7tURtXsr7Gq8/J1/XS+K5lkim3pN8v5hIsHdq+L0RWvsn8Yl/ecb+/dZp2O9yYrDagaj6X5N8/QJxCHENolI6kftopV38rYz3efkA8f/enNGkFeKkFYiTaibye7sQH4auJNpfHmu4nW6fz/9JPGdnNmxP83yWiqbda732oW8f4G9Nrn+MKC7A6Id26n6uvw2I8bLb20/jQSLRnMrYIz1rJdvuJv3Y3c6dRAL7AWItgvrH8wqine4G4mjmDbR/L6w/oXuFLuIbz9jcTtr/wQ1EkWQlov10P6LFZCHxt9AEOQvH+FxBHPY9jqhcdXIb8Ubf7HJ8m99biTiE1rg4SO1EqmtSxtur21lEnNh2St225YnB6VJGK9B/IPpZ6z+x7518vTblfY3XG5KvtxHT8r2AOCz5R2KAm0z6Iwc1tUS4vmVkiOiJq3cl8aH0s8QZ188k9/s8kUTfz9j+uPHcR217L4z3eTmfmKliT8aOIXsTj2/OBH5vEvH8upw4EbPZG3I3z+dliUVZaico1UvzfJbK5FaiSLF58n3tsizxfjWFeK0tZGwLAsnPSxgtQoz39mvajVPX0/xE3TOIo029GruXEOcyvJZo46o/4rYt8SH8CuIo1YfrrltMJPM1Q4w9+blX8dXfflpp/gfvIE5U3Ig4WvtrYlx7hNGTQTVBVqDH7xCiX2sz4tNyO+M9VH4r0Tf8TSJR/ytRPfgU0UKSptesl7ezhDhz+ljiBJS/EYtQbM7Yk9+OI070u5A4IWRzYrW3s4i2il5YhbHJ5STiMR2c3O/txCCzkGib+BGjU+xtQFQQ3kmcpNfJ9cltfiv53ZuJ6di2atjvYeJT//aMJqDPEB8atgO+T+tqRNr7WEwM9m8hTrh5MkX8rYz3eQnx+GYQb3jnEBX2PYmz0WuP8aNE3/IHGZ3Or9PvvZ44RHkV8RprdCXxt0n7fN6OaM34VZPbSvt8lspiHnHewJeJQ/l/JFoNPkIsInIX8To7kTgBdwWi4PEa4vV2Ku2PTKW5feg8Tt1GjIffICq7s4iWg12IGTn+QW/GbojVB19NnNOxM3EU8G6iAj2XGCP+xthZl64nxoDa0akDGHtUtZfxdTump/0fr0ustHhm8js7EyeE9nPWMGmMdrNs1Ka76ucTciXizf1uYmaLWcRA16oPrNU0dr26nUnA55LbeTzZ79+a7Pf25PfnEoPTEfTuA1urWTjuJA6h1Z/x/E7i5IlniMrKfxKLucwGfpPs02zOzdo0dLUln5dndI7mx4jB8UUsPR/zMcm23Ztsq59Htdn9prmP7ZPYnyGqIK3i34OxZ3r3w05EX+Fc4kPCexqu/0YSw8u7+L0DaL+kcW3J27TP5xOJynerDwppn89SVrpdSKXxtT7EaEvC08Rz+0TGjgXDxLkFs5J9ZhMJdeM80M3mIk5z+2nGqWWI1QH/ltzOTYydiSfN2H0X6RcY2Yb40H4LMWbcTSS/bydm+JnNaJK8PnG0bB6RRB/L6IIs3cSX5r0lzd+q8XGm+R+8hUiu5zI61u6NJEmS1AMrMzo/vyRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkipnKO8AKuIWYIu8g5CU2gXAXnkHIUkqp2XyDqAi1ge+APwp70AkdbQ3sFXeQUiSyssEunduAmbkHYSkjrbCBFqSNAHDeQcgSZIklYkJtCRJktQFE2hJkiSpCybQkiRJUhdMoKXeG8k7AEmS1D8m0FLvNZtf3aRakqSKMIGWsuGiRZIkVYQJtJQ/q9OSJJWICbSUP6vTkiSViAm0VB1WsiVJyoAJtFQdVrIlScqACbQkSZLUBRNoSZIkqQsm0JK6YZ+1JGngmUBL6oZ91pKkgWcCLUmSJHXBBFoaHFVov6jCY5AklZwJtDQ4yt5+MUL5H4MkqQJMoCWVhcmzJKkQTKAlSZKkLphAS5IkSV0wgZZUFJ4gKEkqBRNoSUVhj7MkqRRMoCVJkqQuLJN3AD0wBGwCrAesBUwCHgDuAebgYWEpjTymiHNaOklSKZU9gd4XOBzYssX1s4BjgfMyi0gqpzwSWZNnSVIplbmFY3/gR8B9wH7AVsD6wIuT798N/B04N/leGg+PYEiSpMq4DjiTzlWsE4Fr+hzLPGC3Pt+HpN74NHBt3kFIksqrzBXoTYFf0blCOAPYrP/hSKkMWkV70B6vJGkAlDmBngXsBUxus88kYB/gpkwikjobtL7fQXu8kqQBUOaTCI8GpgPXE33Os4EnkuumApsTCfY0YNc8ApQkSZKKZnvgImARcai4/rIIuDDZp9/sgZbKwx5oSdKElLkCDTAzuUwB1gHWTrY/SMwFPX+Ct/8+opLdyfLEHNSSJEmquLIn0BA9lguIRVPmED3RbwK2Bm4G/jaB294G2DjFfssQrSKSJElSYS0HnAA8CjwFnAqsRExvV9/KcXaybz8tAY7s831I6g1bOCRJE1LmWTgOBz4FXAp8E9gZ+A3RxvE24KXAR4F3AofkFKMkSZJUGHOAr9T9/Cai4nxgw35fBv7S51isQBeP8w+rFSvQkqQJKXMF+kWMXWFwVvK1sef5JmCjTCJSkTj/sCRJ6osyJ9D3AVvU/fwksDdwW8N+mxCzckiSJEkTVuZZOM4DPkdUGq8kqtHn112/CvBW4nDtWZlHpyyNYMVZkiSpoxWB7wKLgd82uf5WIrG6Elitz7HYA62iG09PeFX7yO2BliRNSJkr0M8ABxMzcazZ5PojgDuBP1PdREBKazwVeqv6kiQ1UeYEumYBcHeT7ec32Sap+mzpkST1VbsEepsub+tPEwlEmoAqJUxFeSxFiWM8yhq3JKkk2iXQf+zytnzTUl6q9NwrymMpShySJBVOuwR687rv1wZ+Tpys9wPgXmAd4ABgK+Df+hKd1D9lrrBKkqQS+Blwn7gRmgAAH6pJREFULksnHEPAT4jkepA5C4fKwhNqnYVDkjRBaRdS2R64iKXffEeAS5LrJUmSpMpLm0DPA17e4rotgcd7E46kPrNtRZKkCUqbQF8IHEbMu7xcsm154KPEPMy/6H1oUq5sdZAkSROyAtGqMUKs/PdQ8nWE6H9ervWvDgR7oAdH2RLrssWbBXugJUkTknYhlQXArsAbgNcSs3L8E7gGuL4/oUmF1MsWiCxmArFlQ5KkHut2JcK/Abc3bFsj+froxMORBorJrSRJJZQ2gd4aOA/YqM0+JgMqkkGb53nQHq8kSblJm0B/h+hz/iDwYP/CkZqqJYfdJIllSCZ7mfSW4fFKklQJaRPoacCBxGIqUtaGGr5WRS8ej5VnSZIylnYau1uBZ/sZiKRxMXmWJCljaRPobwOHACv1MRapF8Y7bVse0705xZwkSSWUtoVjVWAScAdwOTEPdOOb/2d7GJc0XuOtyOZRybV6LElSCaVNoA9Ovj4JbNNiHxNoaeLsaZYkqeDSJtCb9TUKqXu9TDR7nbRO5PZMniVJKrhuF1Jp5p3AJ4AdenBb/7+9ew+epSwPPP79ncM1wVUuyYFdEbwCuwaigLCGolIGggQqmoiQLJRixF1jsmoQg1plFcYqI66BlJi4xmS9RESMK+GSIgm4sfAsyG3lJKAQriJyEzAIeLicw9k/3h5Pn/e83fP2TPd0z8z3U/Wr+U13T8/TM1TxnOf39PNOYgV4KbAnsIbQanIfcDdwK/aZLqo2E80m5xpqhXiocUmStHByE+hdgbOAV7D1jYcvBO5oM6gGTgT+ENi/Yv864COERWCkNuQkqdMmspMkwybPkiTNSO4UjrMIlea1hAVVNgL/CDwFrAeO7iS6em8Cvgj8ADiJkNy/ANir+P23gNsIs6t/q4f4pCbKfykxGZYkaQHcD3yo+P0Y4OvF79sCVwLv6CGma4HPMz7ZOBu4uuNYnmXz5yM1tYnZthote1vTe4Fr+g5CkjS/civQuwDfKX6/CjiweO0zwOeAt7Ye2Xj7EBL5ccnA5XgT5DxbhmRvhdlWna1wS5I0hdwE+gFCWwTAI8CjwMHF8w30k6CuA44jVMGrrAZOAG6YSUTqgsmeJEkalNybCL8KvAt4kNAPfT3wHuCPCf3Hd3YSXb0PA5cA1xH6nG8EflTs2xnYj5BgH0BoO9Fw9D0xYtL3H1XDTeolSdJYOwKfAM4tnu9DWFRlE+FGwtf3FNfhwEWEKvim6GcDcGFxTNfsge7PLFo82nqPZWhHmQf2QEuSppJbgV5PmPU8cguwB3AQYXnve1uOK9cVxc9ORTy7F9vvJ8yCfnzK818OvDLjuJXSe6s7qcrxLKrBbb2HlWtJkhZAbgJ9KPBtQrV5ZD3wTeB5hJsKr283tCzbAEcSerDvAP6OUHku2x94FfCXE5z/vYQZ2ONcBjw0wfnVTFUC2ndLSJ0hxzZrfhaSpKWyCdi7Yt+RwE9mF8pPPY8wQq/ctvEvwPOj406j+z+d28LRTNPvo+vvr4vzb4oeNRy2cEiSplJXgT6l+Bm5gC0r0BCqSS8iLFgya38EvJxwo+AVhF7nvwD+N/BLbF2J1nB0scpeubrZtNLZZVXUiqskSQumLoG+n83j3w4hzIF+LHHcaArGrB0LfJSQMFM83k9Ipn8XOKeHmDS5cUlv3QSM+LW5SWsbLQXxOUbPTZwlSVpyawk36Q3JE4Tqc+yThH7kUe+yLRztsiVh689g1isJajq2cEiSppK7kMphhIkWLyq97q3AnxB6oPtwO/DaxPYPElpNvkD+9SnfpJXVRUowy60i8TZJkiQAXk1YgfCLxfPfIyQPDxaPb+ghplOK974Y+G/Ac0r7jiL0QF9MSKStQA/bNN/PEBLzIcSgfFagJUkzsZYwpu4/Fc/XAX9FqLqdB1zVQ0yrCL3OPyAkMPFy4kcDdzObP6+bQPcv5ztu878Dk+b5ZQItSZqJxwhVXoDdCMnDa4rnbwYe7SOokl2A7RPbtyG0n5zc8fubQHerrbF3bYyWs995/plAS5KmkruQylPAdsXvRwFPA1cXz59D/wnFIxXbNxCq52tnGIvaN8nYu9RYu5WK/TnqpoBIkqQlkptA/1/gbYSWiA8QVt57Angx8Cbgpk6i0zzoa3W5qvctJ8t1I+UmiTlnhN7Q+Q8BSZJmZF829xP/G/DKYvtthFUI+5rEMRS2cHRv1n/lSLVq9P2XFrXDFg5J0lRyK9A3E6rNLwPuYXPP83sIi618r/3Q1LGhVk6r4hq3yMqkqxDWic8zxM9LkiTNWG4CfRzwXbZu1biw3XA0Q7Ncra+JaeOaJtbyOePzDPUfHJIkacZyFxr5U+C/dxmIOjVN68FQk8aqpbsnudZRu0bdtQ71c5AkSTOWm0B/BHgd8HMdxqLumPwFbYyxkyRJSy63hWMV8C/ALcAlwAPAxuiY97UYl4ZllktWjyrBk7ZM5FSR7W2ePVtgJEkLIzeB/v3i8UHgVRXHmEAvrkn7kseNmst9r9Tx4xKyaferXX7WkqSFkZtAx8tkSym5ld2cJLmux7lqtnPOe+e+fihM9CVJGphxCfQqYC/gXsJqhAA/A7wBOAD4PnAeoTItweSV35wkcZKKdvmYJsc30WWSa/IsSdLA1N1EuCfwLeAONt88uD1wEfC/gCOAMwgzon+huxA1ZyatDOeeO3UD4LiEvbz6Xm71ucmNhia5w+ENopKkztUl0J8CngYOAe4rtr0O+BXg9cAvEpLsa4GPdRij5ldOMlO32l9qNcAm56+6+TEnLpPi+eT3JknqzXOAZ4CXE9o8Rj+XAtcB25a2vRp4qPR8GbmUd75U8lqV0E4zdi5OxHNj0eJzKW9J0lSqEt5RQnw9W/75ezvC+LrHSseOtj9O6JN+bieRaiiqls3OGT9XlbCmJmzE+zdFxzbpO560b1qSJGkrVS0c/w54kjCybofi5zeLfQeVtu0AHAX8sPjd5HnxjZusEbdKxG0UTZLWeBJH1WSO8vvV7a86tyRJUraqBPopws2CnwYOBg4FPk64qfCG4pgVYL9i+5XdhqmBGldpLie94/qZ49eWXxO3cqT6puvaPXLaOXLY8iFJkmpvInwXobf3GuAqYEfglNL+rwPfAXYDTusqQA3CtEln3H5Rd/5y0h1PzYgfcydsjKtcV8VSdx5JkrSk6m76ux84jDAHegfCMt7PlvZ/BvgEcBnwRFcBZlgBXkqYCLIGWE2YGnI3cCtWDdvQdGntuGe5XB3OSWBHiXBd3/O4pDxH7sqJkiRJrfoN4J96eu8TgXVs+af+8s8NwPEziGMZpnA0bYNIHZ/TnpFz3k2J36vee1xsWj5O4ZAkTSV37NyuwFnAK9i67eOFhMVWZu1NwOcJo/U+BtwEPEyoIO4C7AO8ETifEPOXe4hxXuRUXnPaIFI38ZXPnapk51S34/OOqz57A6EkSerd54EfA39OaItYR0ioryeMvHt+DzFdW8Q1Lhk6G7i641gWsQI9bZW5al9cNa5bSKW8Lee1Ug4r0JKkqdTdRFh2FCERfQfwbkLSfCphOse/Ar/eSXT19iHcyDguiboc2Lf7cBZKqtc4/j0W9zqnXpsacRf/A6hqDF7qJsGqpb0lSZI6k5tA70KYuAFhIseBxWufAT4HvLX1yMZbBxxHWBWxymrgBDaP3tNmdYlxXbtGqu+4bopG1TnjEXfx+VNtGqlkeVbtGLlj+IZs3uOXJGkQcnugHyD0P58PPAI8SpgPfTWwgX4qvB8GLiEsLX4+cCPwo2LfzoQZ1ccBBwDH9BDfPJlkRb9UtTnuZ66qQKcS7rrkuK6HelYWoW96Ea5BkqS5cTawntC2AfA14CuEpPr/EJLXPhxOWPBlA1v3yW4ALiyO6dpQeqAnqTA2mWJR18sc7yc6puo18b6649rUZOqHFos90JKkqeRWoD9AaIc4sHj+fkL1+Y3A04Q2iT5cUfzsBOwB7F5sv58wC/rxKc//GuAlGcetUN9KMitVy1vXVR7rFh5JTdVI7Y/bLVIV5XhbVVyTVplTFfA6k1Td2+K8aUmS5lhuAr0eeGfp+S2EhPUg4Hbg3pbjaupxwnSQW1s+73vIb0/ZueX3nrW4xaIqGU71JqduIIyPSW2rqkanWkFSv5efp/quhyo3RhNtSZIGKDeBPhT4NvBUadt64JvA8wiV6evbDW0QcnunnwUe7DKQKeSstFd3E2F8TKr6nFodMHUjYKqyXfWedTcgVh2Xk3DWJeNtGTenOpfJsyRJA5Q7heMqQsU55WBCIq3FkKogpyZm1LVr1FWh65Ln3JF5qWp36r1SchaEmVY8bk+SJC2Qugr0KcXPyAVsWYGGkCS8CLit5bhyrG14/GGdRDFscTtEqn2ibtJFqp2iqqWjfI64El3VE52KNXWuupimqSK3UYG2zUKSpCVTl0Dfz+b5yYcQ5kA/ljhuNEZu1v4KeB/wMuBmQi+2tpRqnai7ma9uIkfOzYjlRD2ewJEb67j9VY918dXdsDgt+5klSVLSWqpbOPq0BngSOK3nOIYyxm6ceERcagGTqmNT26tGz6VG16X2pWKoirkpx8+pimPsJElTye2BPowwFi7lN4B/aiecxh7A/xHWSbVNpFonqm4QrDquStU0jvK++JicynNOH/Uk/dCTaiM5N8GXJGlO5U7h2BU4i7BwSpx0vxC4o82gGjqVsDLiMkslouOmTaRaN+J+5pwWjKZJc7y9/LqcpDdVEa9Kspsk0eM+o7JZtn5IkqSBya1An0WoNK8Ftgc2Av9IuKlwPXB0J9HluY725z/Pm7okry5Rrasq51ZIc4+Le6Pj+FI3Gtadp/y86rgmukqUJUnSgslNoI8iLOf9DuDdwEOEyu+hwL8Cv95JdJpWVZV5Fu0O42Y/p3qflyVhtX1DkqQ5lptA70KYwgFhJvSBxWufAT4HvLX1yDSNcWPm4t+7SmCrbiAsV5FTUztS51kky/IPBUmSFlJuAv0Aof8Z4BFCz/HBxfMN5C93remNSzKr5inHr825Ea+pqjaIcTcvVvUx15139Lo2VE0ckSRJ2kpuAv1V4F2Etg0Iy3a/h5BUnwTc2X5oqpCa45yabhHvH3fOaWOK3zd+/1Svc91CKJPMjh73D4Sqfakk32R6Pvm9SZI6lzuF4wPAakLrBsD7gauBNwJPAye0H5pqVC2MkjMRI2XapGPczYlxYhrHHO+re824xVxSv0+i7vVNJ3zk6OKcy8rPUpLUqdwEej3wztLzWwgLqxxEWAHw3pbjUr66JDo+blaxlE1aXa5KpruKqYkub7rUdPwcJUmdq0ugD814/TPAC4qfb7USkVLq5hHXTbfoQ90NiVWV5NybGCdJjiZ5jRVMSZJUqS6BvqrhuUw4ulPV5lB3fF+JdKpHO2f1waq50KnH+NxVz2O5x9cl/5IkacnVJdD7lX7fHbgA+AbwWeAeQgvHyYQbCX+5k+gUSyWU0F8VOnXzYF2iWbc9FXNd0pybDKdaQcatXthF24e6t2zzxCVJA/c14HzSScV5hOR6mT0LfGgG75OaqzzLn7r3zIkxPqb8fFJNpm208X6af+8Fruk7CEnS/ModY3c4cBHpSuffFfs1W30kgVVV4tG+nApgqvrbZFZ13b7U5JEmTKwlSdJYuQn0Y8DLK/btT1hcRcspbncY1wIRrzpYN/Kubs5zVVtGjqYtJpIkST+Vm0BfCJwGvB3Yvti2A/AO4A+Av20/NJXESeZQxAujQHUVuK5CXZUoN6koN0l+22ofafMcQ7Jo1yNJUi92JLRqbAI2Epb23lg8v4DNSfWy6qoHuq9e59we6KoYq+KvO25cv3Ib/cxNeq+HkkQOJY5FYg+0JGkqTRZSOQZ4NfAqwlSO7xNWI7yum9BEeuJGn8oV5CZV3HLbRk77RPm4cYupVM2TrmsjqXqeu2+WhhLHvGjSyiNJ0kRyE+iRK4sfdSvu9R1C8lyWUxWO2zuqbhSM96We18VQ1TM97hwmWovJ71SS1LncHmj1Z0jJc9M+4zhJTW2r+wdCXaKemuPchInWbA3pv2NJkqZiAq0mqqZl5Lymrr2ibiGV+L1S/ddVMebEpdnwHyySpIXh/9RacD1semXfQUjKdhE8/DrYre84JEnzqWkPtBLeBpsOhXP/DD4/zXmOhMvaiqkLl8GR08ZYPsdlcORo+5FwWfl5Sup1dcdWHZfzXlpcp8LxX4dD+45DkqRl18YYu75H1M1i5B2J31Oj7lKfTer3SdS9z7jXDdnQ4xsSx9hJkqZiD3S/UgnmvCsvnJJ6Tun5pKsI5iTUVZ9rVTw57ztkQ49PkqSFYQKttqUS59SKhVWJcOomwdSYu7oEPU7OY3XJZpvV6ZzquiRJmjOL0AO9ArwU2BNYA6wG7gPuBm5luInLKMkbanxNxUlt+fpS1eeqc4z2pxLi8vmrkuryvqoK96bo+FQMTYxb5GWRvmdJkpbevCfQJwJ/COxfsX8d8BHgKzOLqJlFSqqqqsmQTiDjpDOnUpxKyOsWa6laxXDc6oZdyF0cxlYMSZIGbp4T6DcRpl5cCnwMuAl4mJCA7ALsA7wROJ/QqvLlfsJMWqTEuamcHuaqanHq9anXpJ7PyjRJsMmzJEnq1LWEBHpc0nE2cHXHseRO4eh7MsYQfogex20fl2x3Kbf1ZJYxaHpO4ZAkTWWeK9D7AOcwPsG4HPidCd/jS8AhGcetALuOOWaZE6Fy1biqQptq8Ui1gozTZhtE3MvdR4XYqrQkSQMzzwn0OuA44DzgmYpjVgMnADdM+B5fAr6RcdwnsaJVlmrTiJPR1HEkno+Oi88Vi28g7II9ypIkaa4T6A8DlwDXEfqcbwR+VOzbGdiPkGAfABwz4XtcknncnwCPjDkmTgIXWer64uQzNdYuJTUOr+58OdXiJolw6obDeUuk5y1eSZLUocOBi4ANbN03uwG4sDima48Bx7Z4vr77lPvoia7qh059LvG21HHjjDtm2v0aLnugJUlTmecKNMAVxc9OwB7A7sX2+wmzoB/vKa5pjasWzmvyltOyUXftOePwytviymv5+bQV5Vn2RVtBliRpQOY9gR55nLBoyq19BzIjba+kNyt1NwqWj0klwOUWjqoe6qpjx819Ts2kzklYZ9VvbfIsSdKALEoCrc1yJ1UMQXxTYWp7fDNi1XGzWFmw/J6TSr2+rbglSdIMmEAvpyFVsJu0ZMSvG7fSYNM4ql6Xk6jnyr2+OCbbOCRJGggTaMVm2X+dO8auqlJd3gfNq+/xFI+q4+Pzt5XIjkuKc+KTJEkz5v+UW3AOPP0GuGkPeKjvWPp0ORzR9jmPgMvj8x4RFsf56fuNjik/jouvfI7U68rP6845TxblOqZ1G+x1Lmx/BuzVdyySpPlkAt2C98KTx8PFB8HtfccyZGfC6W2d63Q4s3ze0+HM0WNOHKnjy9vj92jyPrlxzMrQ4unbpXDIxfCCT8GL+45FkqRl1vYc6GUVz4AeNy86vsGwapb0uBsRU/OlU8fXnbfudXXb2jCUm0LnhXOgJUlTsQdaQzKu1zg1u7kueYxv+IuT4dylv6t6lXP6pquOb/OmwJy+9VnOrZYkaaGt6jsAaULlJLtqcZR4WzzRoq7yHL8mfs/c15RV3cCY2t8m50lLktQiE2gtijihrls0pSrhTrWEjI4bN5O6ats445JqSZI0MCbQWnapSnZqpcOcWdOpVpHc95ckSXPCBFraWlWVOtUiUvX6sqokPOdcTXgzoSRJM2ACLU2myWqO5cp0KsmtSrjbjGma80qSpBITaKl9Of3XsVQvdJOEN+dY20UkSWqBCbQ0DE3G5OW+vikr1JIkZTCBlpZHk5F9kiSpggm0tPhSU0UW0SJfmyRpQEygpcUXTxLJWUBmHpNRK+iSpJkwgZaWT84S5k2mjEiStFRMoCU1ZaVXkrTUTKAldc2KtSRpoZhAS+qaFWtJ0kIxgZYkSZIaMIGWJEmSGjCBliRJkhowgZYkSZIa2KbvABbILwJPAr8ErO85llnZCdjIclzvCrAL8HDfgczIc4FvsZjf7Uv6DkCSNN+8O74ddwF79R2EpGx/DxzddxCSJAl2J8y83bfvQGbkAuDsvoOYkdeymNXYKncCJ/cdhCRJQ2QPtCRJktSACbQkSZLUgAm0JEmS1IAJtCRJktSACbQkSZLUgAm0JEmS1IAJtCRJktSACbQkSZLUgAl0u54A7gEe7TuQGfkBcG/fQczIDwmLiyyL7wEP9B2EJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJA3RSt8BaFC2A/59YvtG4PszjkXd8/uWJEm9+lXgCuDHwNXASf2GM5HXAJsSP/dHx+Vc65A/j7cAayv2tXVtQ7r+qutdlu9bkiQN0OHA08DFwJuBvyYkIv+lz6Am8DbgSeD10c/RpWNyrnXIn8fPAzeTTijburYhXX/d9S7D9y1JkgbqQmAdsG3xfAW4tNg2T20yHwVuGnNMzrUO8fM4EPgGIWHcRDqhbOvahnD9Ode7yN+3JEkasJ2ADcAHou0nERKXl808osl9hZAMAWyT2J9zrUP9PF4KnFb8fJetE8q2rm0o1z/uemGxv29Jkjqzqu8AFsAewGq2ruTdWDzuOdtwpvJiYA1wA+FP8vcBnwZ2LvbnXOtQP49bgY8XP7cn9rd1bUO5/nHXC4v9fUuS1BkT6OntXjw+Em1/uHhcM8NYprFCSKj2B84DjgH+jFBJvJjw30rOtc7r59HWtc3L9S/79y1J0sRSf7ZVO0a9n6t7jSLfKuDthMrhqHp4KXAP8FngVwj9tCk51zpvn8dIW9c2tOv3+5YkaUJWoKc3Gvm1c7R9l+LxvhnGMo2NwJfZnEyNXFQ8HkDetc7r59HWtc3L9S/79y1J0sRMoKd3H/AssF+0fZ/i8e7ZhjOxPYFjgR2i7c8Wjz8m71rn9fNo69rm5fqX/fuWJEk9uwi4hi3/QfJV5muM176EqQlvi7a/udh+QPE851qH/nlcQnoqRVvXNrTrT13vMn3fkiRpgEYLSXwB+DXgLEISckKfQU3gb4CfAGcAxwMfAdYDnykdk3OtQ/88qhLotq5taNdfdb3L8n1LkqSB+lXgm4Q/fV8D/Ha/4UzkZ4Ezge8REql1wKlsfSNYzrUO+fOoSiihvWsb0vVXXe+yfN+SJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEnq2F7ANcAG4LXA7wObgGOL/ccCp0SvSW2b1L7F+x0abT8FOKel95hEVVx17gLOKH5/CbAO2K7VqCRJUqVVfQegpfE7wC8AxwNXA/cAXwceKvZ3nUCn/BzwIeCPO3yPrt0GXAec2ncgkiQtCxNozcrPAt8Dvgb8CPhb4AjgWz3G9HvAN4B7e4yhDZ8ETgN27DsQSZIkteMSQpvC6Oe1hOR5E7A3sDbaf2jFtpHjgKuAx4E7Ce0M25b27wicBdxOqHB/Dfjl6DzbAvcBvxbFeiPwB8AHCdXdB4A/J7RIfLR4v0eBL7FlwroKeCdwQxHXPwPvA1Y3jCvn+u5icwsHwApwE3AykiRJWghrgM8QEse9CYlkOYHeAzgX+HbxfPuKbQD/tXjdXwMnENovngG+WHq/S4ptHwVOAr5CqHqXE9XDCP3YPxPFeiOhUn4ucFRx/k2ElpO/IST/Hy62vbP0utFxnyC0qfwPYCPwqYZx5VzfXWyZQAOcTajqS5IkaUF8HLi59LycQAP8T7Zu54i37Qj8EPhCdNzbi3MdALy6+P3tpf0rwAVsmah+kJCcx24kVJFH7U0rhIT6O2yuJq8AtwCfLp6vAZ4CzozO9X5Ckr53Zlw51wfpBPq3gX9jy4q3JEnqgD3Qmif7ArsBn422f6l4/M/Aq4Bngc+V9m9KvOY/Elo0Uq4szjF67Q8JLSUbo22jZHV/QotHuUo8ims18MrMuHKur8rtwHMJlXtJktShbfoOQGrgBcXjP7A5wS3bFXgOob/4yWjfPdHzNcCtFe/zdOa2kf9QPN4XbR893xPYPSOunOur8nDxuIatr1WSJLXIBFrzZDQt4wTgu4n9DxP6j3cDdmDLZDWuzG5qMa4fFI+jJJnScwhxb8iIK+f6qoyux78qSZLUMf9nqyFZGbPtZuAxYL/i99HPaELGToQZ06uAt0TnODk674PUV3Sb+GdChfrEaPuJhEry/8uMK+f6qoyuJa6CS5KkllmB1lBsBF4EHAlcS7ghLrXtjwiTKXYljHp7GfC7wB2Em+vuBC4kTMPYm5DcHgO8Inq/7wC/2VLsDxCmYJxOuBHwSuBgwuImf0HoTyYjrscyrq/Ki4EfYwItSZK0MMZN4TicMAHjJ8CBNdtWCFXc64EnCBMyzgaeVzr3Dmyet/wwYdLF88kfY/en0bbrCIuVlK0F/rL0fBXwbsKy2k8U5zmdLadi5MSVc313kR5jdyGSJElSR0YLqRzTdyAtWCEk7G8Zd6AkSZI0jTMIC6bMuwMIFW2X8pYkSVKnfp4wQWPeZyd/hrBoiyRJktS5U4Bz+g5iCi8h9F1v13cgkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkjQ8/x9qzxKEYn+35gAAAABJRU5ErkJggg=="
     },
     "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": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer_log = lmer(log(body_length)~1+session_index+session_comments+(1|author), data=data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index + session_comments + (1 |  \n",
       "    author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1649931.4 1649987.2 -824960.7 1649921.4    515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7413 -0.5556  0.0374  0.6037  4.0714 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3303   0.5747  \n",
       " Residual             1.1621   1.0780  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error t value\n",
       "(Intercept)       4.4384597  0.0035791  1240.1\n",
       "session_index    -0.0209770  0.0012290   -17.1\n",
       "session_comments  0.0181105  0.0009679    18.7\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.167       \n",
       "sssn_cmmnts -0.526 -0.639"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer_log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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 looks pretty good already. For completeness, we proceed by looking at generalized linear mixed-effects models though as they usually capture count data quite well."
   ]
  },
  {
   "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": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00407952 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "m_poisson = glmer(body_length~1+session_index+session_comments+(1|author),data=data,family=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "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: body_length ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       " 38014403  38014447 -19007197  38014395    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-69.779  -3.179  -0.045   0.908 196.933 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 1.195    1.093   \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       4.568e+00  2.065e-03  2211.5   <2e-16 ***\n",
       "session_index    -2.563e-02  1.084e-04  -236.4   <2e-16 ***\n",
       "session_comments  1.853e-02  9.025e-05   205.3   <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 -0.027       \n",
       "sssn_cmmnts -0.091 -0.594\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00407952 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "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": 68,
   "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": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>chisq</dt>\n",
       "\t\t<dd>34358623.4865417</dd>\n",
       "\t<dt>ratio</dt>\n",
       "\t\t<dd>66.6909103529202</dd>\n",
       "\t<dt>rdf</dt>\n",
       "\t\t<dd>515192</dd>\n",
       "\t<dt>p</dt>\n",
       "\t\t<dd>0</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[chisq] 34358623.4865417\n",
       "\\item[ratio] 66.6909103529202\n",
       "\\item[rdf] 515192\n",
       "\\item[p] 0\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "chisq\n",
       ":   34358623.4865417ratio\n",
       ":   66.6909103529202rdf\n",
       ":   515192p\n",
       ":   0\n",
       "\n"
      ],
      "text/plain": [
       "       chisq        ratio          rdf            p \n",
       "3.435862e+07 6.669091e+01 5.151920e+05 0.000000e+00 "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "overdisp_fun(m_poisson)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, we have to deal with overdispersion. There are generally some ways of doing so: (i) adding an individual-level random effect or (ii) using a negative binomial model or (iii) using quasi likelihood. Let us start with the first option."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "data$obs<-factor(seq.int(nrow(data)))\n",
    "m_poisson2 = glmer(body_length~1+session_index+session_comments+(1|author)+(1|obs),data=data,family=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "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: body_length ~ 1 + session_index + session_comments + (1 | author) +  \n",
       "    (1 | obs)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 6237919  6237975 -3118954  6237909   515191 \n",
       "\n",
       "Scaled residuals: \n",
       "     Min       1Q   Median       3Q      Max \n",
       "-1.64115 -0.08574  0.00234  0.04149  0.15658 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " obs    (Intercept) 1.0735   1.036   \n",
       " author (Intercept) 0.3237   0.569   \n",
       "Number of obs: 515196, groups:  obs, 515196; author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       4.4548812  0.0034859  1278.0   <2e-16 ***\n",
       "session_index    -0.0206626  0.0011955   -17.3   <2e-16 ***\n",
       "session_comments  0.0179436  0.0009419    19.1   <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 -0.167       \n",
       "sssn_cmmnts -0.526 -0.639\n",
       "convergence code: 0\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>chisq</dt>\n",
       "\t\t<dd>19332.9050753099</dd>\n",
       "\t<dt>ratio</dt>\n",
       "\t\t<dd>0.0375257042054498</dd>\n",
       "\t<dt>rdf</dt>\n",
       "\t\t<dd>515191</dd>\n",
       "\t<dt>p</dt>\n",
       "\t\t<dd>1</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[chisq] 19332.9050753099\n",
       "\\item[ratio] 0.0375257042054498\n",
       "\\item[rdf] 515191\n",
       "\\item[p] 1\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "chisq\n",
       ":   19332.9050753099ratio\n",
       ":   0.0375257042054498rdf\n",
       ":   515191p\n",
       ":   1\n",
       "\n"
      ],
      "text/plain": [
       "       chisq        ratio          rdf            p \n",
       "1.933291e+04 3.752570e-02 5.151910e+05 1.000000e+00 "
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "overdisp_fun(m_poisson2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great, the overdispersion problem is gone. The results (coefficients) are very similar to the previous models though (specifically to the log-normal)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For completeness, we also want to utilize a negative binomial family though by first using the nb functionality provided in lme4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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| = 0.00407952 (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| = 0.366738 (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| = 0.00397176 (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| = 0.0115897 (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| = 0.0276036 (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_nb = glmer.nb(body_length~1+session_index+session_comments+(1|author),data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: Negative Binomial(1.2607)  ( log )\n",
       "Formula: body_length ~ 1 + session_index + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 6256424  6256480 -3128207  6256414   515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-1.1206 -0.6550 -0.2316  0.4070 13.3236 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.4134   0.643   \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)       4.7722006  0.0034437  1385.8   <2e-16 ***\n",
       "session_index    -0.0227814  0.0011235   -20.3   <2e-16 ***\n",
       "session_comments  0.0221241  0.0008964    24.7   <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 -0.153       \n",
       "sssn_cmmnts -0.512 -0.638\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00430912 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_nb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We end up with multiple convergence warnings (not shown); the coefficients are quite similar to our previous observations though. Note that this model also takes a very long time to fit for this sample of 1 mio. data points; it does not really scale for larger data which in our case consists of more than 50 mio. data points.\n",
    "\n",
    "As a consequence, let us next also fit a negative binomial regression, but this time we use quasi likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#just for initialization\n",
    "init = glm.nb(body_length~1+session_index+session_comments,data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.86141910645522"
      ],
      "text/latex": [
       "0.86141910645522"
      ],
      "text/markdown": [
       "0.86141910645522"
      ],
      "text/plain": [
       "[1] 0.8614191"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init$theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_pql_nb = glmmPQL(body_length~1+session_index+session_comments, random = list(~1 | author), data = data, family = negative.binomial(theta=init$theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "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:   0.5674362 0.8578411\n",
       "\n",
       "Variance function:\n",
       " Structure: fixed weights\n",
       " Formula: ~invwt \n",
       "Fixed effects: body_length ~ 1 + session_index + session_comments \n",
       "                     Value   Std.Error     DF   t-value p-value\n",
       "(Intercept)       4.793046 0.003166117 288628 1513.8561       0\n",
       "session_index    -0.022682 0.001074639 226565  -21.1065       0\n",
       "session_comments  0.022100 0.000849586 226565   26.0122       0\n",
       " Correlation: \n",
       "                 (Intr) sssn_n\n",
       "session_index    -0.165       \n",
       "session_comments -0.523 -0.637\n",
       "\n",
       "Standardized Within-Group Residuals:\n",
       "       Min         Q1        Med         Q3        Max \n",
       "-2.7901396 -0.6490876 -0.2448333  0.3938080 15.4216657 \n",
       "\n",
       "Number of Observations: 515196\n",
       "Number of Groups: 288629 "
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_pql_nb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, similar results (even though we receive some convergence warnings)."
   ]
  },
  {
   "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 conclude that regardless of our model choice, the coefficients and subsequent inference are very similar. Nonetheless, we will proceed with a linear model on the log-transformed body_length due to the appropriate diagnostic plots, the simplicity of the model and the high mean of body_length."
   ]
  },
  {
   "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",
    "body_length = 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": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m1 = lmer(log(body_length)~1+(1|author), data = data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1650321.4 1650354.9 -825157.7 1650315.4    515193 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7292 -0.5556  0.0381  0.6032  4.0935 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.330    0.5745  \n",
       " Residual             1.163    1.0786  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error t value\n",
       "(Intercept) 4.458131   0.001941    2296"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let us incorporate the index and session length individually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m2 = lmer(log(body_length)~1+session_index+(1|author), data = data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1650279.3 1650324.0 -825135.7 1650271.3    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7159 -0.5578  0.0370  0.6037  4.0808 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.330    0.5745  \n",
       " Residual             1.163    1.0785  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                Estimate Std. Error t value\n",
       "(Intercept)    4.4737038  0.0030443  1469.5\n",
       "session_index -0.0062794  0.0009456    -6.6\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "session_ndx -0.770"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1650220.6 1650265.3 -825106.3 1650212.6    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7530 -0.5562  0.0372  0.6030  4.1022 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3302   0.5746  \n",
       " Residual             1.1629   1.0784  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error t value\n",
       "(Intercept)      4.4282411  0.0035296  1254.6\n",
       "session_comments 0.0075506  0.0007446    10.1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.835"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3 = lmer(log(body_length)~1+session_comments+(1|author), data = data, REML=FALSE)\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": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m4 = lmer(log(body_length)~1+session_index+session_comments+(1|author), data = data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index + session_comments + (1 |  \n",
       "    author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1649931.4 1649987.2 -824960.7 1649921.4    515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7413 -0.5556  0.0374  0.6037  4.0714 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3303   0.5747  \n",
       " Residual             1.1621   1.0780  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error t value\n",
       "(Intercept)       4.4384597  0.0035791  1240.1\n",
       "session_index    -0.0209770  0.0012290   -17.1\n",
       "session_comments  0.0181105  0.0009679    18.7\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.167       \n",
       "sssn_cmmnts -0.526 -0.639"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "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 effects 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": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m5 = lmer(log(body_length)~1+session_index+session_comments+(1|author)+(1|subreddit), data = data, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index + session_comments + (1 |  \n",
       "    author) + (1 | subreddit)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1608475.2 1608542.1 -804231.6 1608463.2    515190 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-5.2603 -0.5574  0.0443  0.6101  5.0959 \n",
       "\n",
       "Random effects:\n",
       " Groups    Name        Variance Std.Dev.\n",
       " author    (Intercept) 0.2067   0.4546  \n",
       " subreddit (Intercept) 0.2532   0.5032  \n",
       " Residual              1.1192   1.0579  \n",
       "Number of obs: 515196, groups:  author, 288629; subreddit, 12041\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error t value\n",
       "(Intercept)       4.4609224  0.0074568   598.2\n",
       "session_index    -0.0205173  0.0011854   -17.3\n",
       "session_comments  0.0208530  0.0009335    22.3\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.077       \n",
       "sssn_cmmnts -0.222 -0.639"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the BIC shows an improvement in the model. Yet, the inference on the fixed index effect does not change. For complexity reasons, we neglect the random effect for the subreddit for the complete data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Outliers\n",
    "\n",
    "We also want to check for robustness when removing outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data_limit <- romr.fnc(m3, data, trim = 2.5)$data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m4_limit = lmer(log(body_length)~1+session_index+session_comments+(1|author),data=data_limit, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index + session_comments + (1 |  \n",
       "    author)\n",
       "   Data: data_limit\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1534980.4 1535036.0 -767485.2 1534970.4    506076 \n",
       "\n",
       "Scaled residuals: \n",
       "     Min       1Q   Median       3Q      Max \n",
       "-3.02984 -0.59809  0.02065  0.61528  2.81522 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3415   0.5844  \n",
       " Residual             0.9360   0.9675  \n",
       "Number of obs: 506081, groups:  author, 285915\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error t value\n",
       "(Intercept)       4.4695738  0.0033227  1345.2\n",
       "session_index    -0.0174504  0.0011308   -15.4\n",
       "session_comments  0.0171682  0.0008932    19.2\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.166       \n",
       "sssn_cmmnts -0.523 -0.637"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m4_limit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not much changed."
   ]
  },
  {
   "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": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.48954996169921"
      ],
      "text/latex": [
       "4.48954996169921"
      ],
      "text/markdown": [
       "4.48954996169921"
      ],
      "text/plain": [
       "[1] 4.48955"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/html": [
       "1.69068454529362"
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      "text/latex": [
       "1.69068454529362"
      ],
      "text/markdown": [
       "1.69068454529362"
      ],
      "text/plain": [
       "[1] 1.690685"
      ]
     },
     "execution_count": 113,
     "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": {
    "collapsed": true
   },
   "source": [
    "### REML\n",
    "\n",
    "Until now, we have fitted the models using ML as this allowed us to compare models with each other. To be sure regarding the consistency of our coefficient estimations, we will now also quickly fit the model with REML."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m4_reml = lmer(log(body_length)~1+session_index+session_comments+(1|author), data = data, REML=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index + session_comments + (1 |  \n",
       "    author)\n",
       "   Data: data\n",
       "\n",
       "REML criterion at convergence: 1649956\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7413 -0.5556  0.0374  0.6037  4.0714 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3303   0.5747  \n",
       " Residual             1.1621   1.0780  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                   Estimate Std. Error t value\n",
       "(Intercept)       4.4384597  0.0035791  1240.1\n",
       "session_index    -0.0209770  0.0012290   -17.1\n",
       "session_comments  0.0181105  0.0009679    18.7\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n\n",
       "session_ndx -0.167       \n",
       "sssn_cmmnts -0.526 -0.639"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m4_reml)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are exactly the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "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": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m4_control = lmer(log(body_length)~1+session_index+(1|session_comments)+(1|author), data = data, REML=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by REML ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index + (1 | session_comments) +  \n",
       "    (1 | author)\n",
       "   Data: data\n",
       "\n",
       "REML criterion at convergence: 1649885\n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7123 -0.5570  0.0369  0.6038  4.0592 \n",
       "\n",
       "Random effects:\n",
       " Groups           Name        Variance Std.Dev.\n",
       " author           (Intercept) 0.3300   0.57443 \n",
       " session_comments (Intercept) 0.0017   0.04123 \n",
       " Residual                     1.1620   1.07798 \n",
       "Number of obs: 515196, groups:  author, 288629; session_comments, 9\n",
       "\n",
       "Fixed effects:\n",
       "               Estimate Std. Error t value\n",
       "(Intercept)    4.543408   0.014597  311.25\n",
       "session_index -0.020563   0.001221  -16.84\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "session_ndx -0.292"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m4_control)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are similar."
   ]
  },
  {
   "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": 117,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in control$optimizer == \"none\": comparison (1) is possible only for atomic and list types\n",
     "output_type": "error",
     "traceback": [
      "Error in control$optimizer == \"none\": comparison (1) is possible only for atomic and list types\n"
     ]
    },
    {
     "ename": "ERROR",
     "evalue": "Error in control$optimizer == \"none\": comparison (1) is possible only for atomic and list types\n",
     "output_type": "error",
     "traceback": [
      "Error in control$optimizer == \"none\": comparison (1) is possible only for atomic and list types\n"
     ]
    }
   ],
   "source": [
    "g0.bobyqa <- lmer(log(body_length)~1+session_index+session_comments+(1|author),\n",
    "      data = data,\n",
    "                   control=lmerControl(optimizer=\"bobyqa\"))\n",
    "g0.NM <- update(g0.bobyqa,control=lmerControl(optimizer=\"Nelder_Mead\"))\n",
    "library(optimx)\n",
    "g0.nlminb <- update(g0.bobyqa,control=lmerControl(optimizer=\"optimx\",\n",
    "                              optCtrl=list(method=\"nlminb\")))\n",
    "g0.LBFGSB <- update(g0.bobyqa,control=lmerControl(optimizer=\"optimx\",\n",
    "                              optCtrl=list(method=\"L-BFGS-B\")))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "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",
    "                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": {},
   "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 text length, 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": "markdown",
   "metadata": {},
   "source": [
    "### Randomized sessions (time differences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx = data$session_comments_random > 1\n",
    "data_random = data[idx,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1243363.3 1243395.9 -621678.6 1243357.3    388335 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7249 -0.5587  0.0364  0.6030  3.8770 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3258   0.5708  \n",
       " Residual             1.1647   1.0792  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error t value\n",
       "(Intercept) 4.460537   0.002235    1996"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1_random = lmer(log(body_length)~1+(1|author), data = data_random, REML=FALSE)\n",
    "summary(m1_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index_random + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1243329.8 1243373.2 -621660.9 1243321.8    388334 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7616 -0.5606  0.0366  0.6034  3.8746 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3251   0.5702  \n",
       " Residual             1.1651   1.0794  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                       Estimate Std. Error t value\n",
       "(Intercept)           4.4701134  0.0027516    1625\n",
       "session_index_random -0.0032723  0.0005486      -6\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_ndx_rn -0.584"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2_random = lmer(log(body_length)~1+session_index_random+(1|author), data = data_random, REML=FALSE)\n",
    "summary(m2_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_comments_random + (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1243301.7 1243345.2 -621646.9 1243293.7    388334 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7622 -0.5602  0.0367  0.6035  3.8751 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3247   0.5698  \n",
       " Residual             1.1653   1.0795  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error t value\n",
       "(Intercept)              4.4744779  0.0028363    1578\n",
       "session_comments_random -0.0028653  0.0003591      -8\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnt_ -0.616"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3_random = lmer(log(body_length)~1+session_comments_random+(1|author), data = data_random, REML=FALSE)\n",
    "summary(m3_random)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: \n",
       "log(body_length) ~ 1 + session_index_random + session_comments_random +  \n",
       "    (1 | author)\n",
       "   Data: data_random\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1243303.7 1243358.0 -621646.9 1243293.7    388333 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7626 -0.5602  0.0367  0.6035  3.8751 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3247   0.5698  \n",
       " Residual             1.1653   1.0795  \n",
       "Number of obs: 388338, groups:  author, 216454\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error t value\n",
       "(Intercept)              4.475e+00  2.874e-03  1556.9\n",
       "session_index_random    -7.055e-05  8.165e-04    -0.1\n",
       "session_comments_random -2.831e-03  5.345e-04    -5.3\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) sssn_n_\n",
       "sssn_ndx_rn -0.161        \n",
       "sssn_cmmnt_ -0.289 -0.741 "
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_random = lmer(log(body_length)~1+session_index_random+session_comments_random+(1|author), data = data_random, REML=FALSE)\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). \n",
    "\n",
    "The reason why the session length itself is still significant can be explained by our very conservative randomization method that just randomizes the time differences between comments before sessionizing and thus, still keeps many sessions intact."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Randomized indexes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_comments + (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1650220.6 1650265.3 -825106.3 1650212.6    515192 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7530 -0.5562  0.0372  0.6030  4.1022 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3302   0.5746  \n",
       " Residual             1.1629   1.0784  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error t value\n",
       "(Intercept)      4.4282411  0.0035296  1254.6\n",
       "session_comments 0.0075506  0.0007446    10.1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.835"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m3_random_2 = lmer(log(body_length)~1+session_comments+(1|author), data = data, REML=FALSE)\n",
    "summary(m3_random_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log(body_length) ~ 1 + session_index_random_2 + session_comments +  \n",
       "    (1 | author)\n",
       "   Data: data\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1650222.6 1650278.4 -825106.3 1650212.6    515191 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.7531 -0.5562  0.0372  0.6030  4.1022 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.3302   0.5746  \n",
       " Residual             1.1629   1.0784  \n",
       "Number of obs: 515196, groups:  author, 288629\n",
       "\n",
       "Fixed effects:\n",
       "                         Estimate Std. Error t value\n",
       "(Intercept)             4.428e+00  3.584e-03  1235.7\n",
       "session_index_random_2 -7.037e-05  1.231e-03    -0.1\n",
       "session_comments        7.586e-03  9.652e-04     7.9\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) ss___2\n",
       "sssn_ndx__2 -0.173       \n",
       "sssn_cmmnts -0.524 -0.636"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m4_random_2 = lmer(log(body_length)~1+session_index_random_2+session_comments+(1|author), data = data, REML=FALSE)\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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