S2_Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 42,
   "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": [
    "# Num answers\n",
    "\n",
    "In this notebook, we document our various steps taken to study the effect of the overall length of a session on the number of answers to the very first comment. Note that we only do this on a sample of 1 mio. data points here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = read.csv(\"/home/psinger/Reddit-depletion/data/sample.csv\", header=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1000000"
      ],
      "text/latex": [
       "1000000"
      ],
      "text/markdown": [
       "1000000"
      ],
      "text/plain": [
       "[1] 1000000"
      ]
     },
     "execution_count": 44,
     "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 limit the data to only consider the first comment of each session and limit for session lengths as stated in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx = data$session_index==1 & data$session_comments<11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data_first = data[idx,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "494483"
      ],
      "text/latex": [
       "494483"
      ],
      "text/markdown": [
       "494483"
      ],
      "text/plain": [
       "[1] 494483"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nrow(data_first)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data_first$num_answers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(data_first$num_answers[data_first$num_answers<10])"
   ]
  },
  {
   "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 num_answers ~ 1 + session_comments + (1|author) where num_answers is the number of answers the first comment receives, session_comments refers to the session length and author represents the redditor username."
   ]
  },
  {
   "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": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer = lmer(num_answers~1+session_comments+(1|author), data=data_first, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: num_answers ~ 1 + session_comments + (1 | author)\n",
       "   Data: data_first\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1789598.4 1789642.8 -894795.2 1789590.4    494479 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       " -3.889  -0.382  -0.379   0.285 271.813 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.0603   0.2456  \n",
       " Residual             2.1245   1.4576  \n",
       "Number of obs: 494483, groups:  author, 368403\n",
       "\n",
       "Fixed effects:\n",
       "                 Estimate Std. Error t value\n",
       "(Intercept)      0.525314   0.003298  159.28\n",
       "session_comments 0.047161   0.001477   31.92\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.765"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "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": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_lmer_log = lmer(log1p(num_answers)~1+session_comments+(1|author), data=data_first, REML=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed model fit by maximum likelihood  ['lmerMod']\n",
       "Formula: log1p(num_answers) ~ 1 + session_comments + (1 | author)\n",
       "   Data: data_first\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       " 619376.4  619420.8 -309684.2  619368.4    494479 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-1.6434 -0.7107 -0.7098  0.7904 12.3128 \n",
       "\n",
       "Random effects:\n",
       " Groups   Name        Variance Std.Dev.\n",
       " author   (Intercept) 0.007913 0.08895 \n",
       " Residual             0.197079 0.44394 \n",
       "Number of obs: 494483, groups:  author, 368403\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error t value\n",
       "(Intercept)      0.3049251  0.0010112  301.55\n",
       "session_comments 0.0232390  0.0004527   51.33\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "sssn_cmmnts -0.764"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_lmer_log)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "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": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00156296 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "m_poisson = glmer(num_answers~1+session_comments+(1|author),data=data_first,family=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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_first\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 1037430  1037463  -518712  1037424   494480 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.0286 -0.5835 -0.5563  0.6138 15.6626 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.5952   0.7715  \n",
       "Number of obs: 494483, groups:  author, 368403\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.944834   0.003839 -246.11   <2e-16 ***\n",
       "session_comments  0.070186   0.001378   50.95   <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 -0.647\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00156296 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "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": 59,
   "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": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>chisq</dt>\n",
       "\t\t<dd>309799.206213001</dd>\n",
       "\t<dt>ratio</dt>\n",
       "\t\t<dd>0.626515139566821</dd>\n",
       "\t<dt>rdf</dt>\n",
       "\t\t<dd>494480</dd>\n",
       "\t<dt>p</dt>\n",
       "\t\t<dd>1</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[chisq] 309799.206213001\n",
       "\\item[ratio] 0.626515139566821\n",
       "\\item[rdf] 494480\n",
       "\\item[p] 1\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "chisq\n",
       ":   309799.206213001ratio\n",
       ":   0.626515139566821rdf\n",
       ":   494480p\n",
       ":   1\n",
       "\n"
      ],
      "text/plain": [
       "       chisq        ratio          rdf            p \n",
       "3.097992e+05 6.265151e-01 4.944800e+05 1.000000e+00 "
      ]
     },
     "execution_count": 60,
     "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": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.971810619282066"
      ],
      "text/latex": [
       "0.971810619282066"
      ],
      "text/markdown": [
       "0.971810619282066"
      ],
      "text/plain": [
       "[1] 0.9718106"
      ]
     },
     "execution_count": 61,
     "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": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "source(\"../owls_R_funs.R\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "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$checkConv, : Model failed to converge with max|grad| = 0.00135615 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 3 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 4 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00137264 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 5 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 6 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00135065 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$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$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 8 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00117913 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 9 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 10 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 11 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 12 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00144662 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 13 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00244959 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 14 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 15 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00102558 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 16 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00174901 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 17 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 18 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 19 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00192292 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "itr: 20 \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00153061 (tol = 0.001, component 1)Warning message:\n",
      "In checkConv(attr(opt, \"derivs\"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue\n",
      " - Rescale variables?"
     ]
    }
   ],
   "source": [
    "m_poisson_zi = zipme(cformula=num_answers~1+session_comments+(1|author), zformula=z~1,data=data_first,cfamily=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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         494483 -none-   numeric"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m_poisson_zi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "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: bydataw\n",
       "Weights: (1 - z)\n",
       "\n",
       "      AIC       BIC    logLik  deviance  df.resid \n",
       "1015027.6 1015060.9 -507510.8 1015021.6    494480 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-7.2612 -0.5806 -0.5553  0.5877 15.6814 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.5753   0.7585  \n",
       "Number of obs: 494483, groups:  author, 368403\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.902693   0.003826 -235.93   <2e-16 ***\n",
       "session_comments  0.070039   0.001380   50.75   <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 -0.652\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00153061 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 65,
     "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": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#just for initialization\n",
    "init = glm.nb(num_answers~1+session_comments,data=data_first)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.22525038734232"
      ],
      "text/latex": [
       "1.22525038734232"
      ],
      "text/markdown": [
       "1.22525038734232"
      ],
      "text/plain": [
       "[1] 1.22525"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init$theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iteration 1\n",
      "iteration 2\n",
      "iteration 3\n",
      "iteration 4\n",
      "iteration 5\n",
      "iteration 6\n",
      "iteration 7\n",
      "iteration 8\n",
      "iteration 9\n",
      "iteration 10\n"
     ]
    }
   ],
   "source": [
    "m_pql_nb = glmmPQL(num_answers~1+session_comments, random = list(~1 | author), data = data_first, family = negative.binomial(theta=init$theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Linear mixed-effects model fit by maximum likelihood\n",
       " Data: data_first \n",
       "  AIC BIC logLik\n",
       "   NA  NA     NA\n",
       "\n",
       "Random effects:\n",
       " Formula: ~1 | author\n",
       "        (Intercept)  Residual\n",
       "StdDev:   0.7943736 0.6988311\n",
       "\n",
       "Variance function:\n",
       " Structure: fixed weights\n",
       " Formula: ~invwt \n",
       "Fixed effects: num_answers ~ 1 + session_comments \n",
       "                      Value   Std.Error     DF    t-value p-value\n",
       "(Intercept)      -0.9019146 0.003185255 368402 -283.15304       0\n",
       "session_comments  0.0702522 0.001310569 126079   53.60434       0\n",
       " Correlation: \n",
       "                 (Intr)\n",
       "session_comments -0.715\n",
       "\n",
       "Standardized Within-Group Residuals:\n",
       "       Min         Q1        Med         Q3        Max \n",
       "-2.6602585 -0.7120744 -0.6625956  0.5889095  9.8148781 \n",
       "\n",
       "Number of Observations: 494483\n",
       "Number of Groups: 368403 "
      ]
     },
     "execution_count": 69,
     "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 length has a positive effect on num_answers of the first comment in the session. 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; yet, it is reassuring that the coefficients are very similar to the Poisson models."
   ]
  },
  {
   "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": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m1 = glmer(num_answers~1+(1|author), data = data_first, 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: num_answers ~ 1 + (1 | author)\n",
       "   Data: data_first\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 1039904  1039926  -519950  1039900   494481 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.5417 -0.5954 -0.5518  0.5735 15.2965 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.5988   0.7738  \n",
       "Number of obs: 494483, groups:  author, 368403\n",
       "\n",
       "Fixed effects:\n",
       "             Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -0.824676   0.002934  -281.1   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let us incorporate the session length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "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| = 0.00156296 (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": [
    "m2 = glmer(num_answers~1+session_comments+(1|author), data = data_first, family=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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_first\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 1037430  1037463  -518712  1037424   494480 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.0286 -0.5835 -0.5563  0.6138 15.6626 \n",
       "\n",
       "Random effects:\n",
       " Groups Name        Variance Std.Dev.\n",
       " author (Intercept) 0.5952   0.7715  \n",
       "Number of obs: 494483, groups:  author, 368403\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.944834   0.003839 -246.11   <2e-16 ***\n",
       "session_comments  0.070186   0.001378   50.95   <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 -0.647\n",
       "convergence code: 0\n",
       "Model failed to converge with max|grad| = 0.00156296 (tol = 0.001, component 1)\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the lower BIC we can clearly see that the incorporation of the session_comments improves our model, thus, we make inference on it (also the t-value indicates high significance)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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": false
   },
   "outputs": [],
   "source": [
    "m3 = glmer(num_answers~1+session_comments+(1|author)+(1|subreddit), data = data_first, family=poisson())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "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) + (1 | subreddit)\n",
       "   Data: data_first\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 1037216  1037260  -518604  1037208   494479 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-7.6744 -0.6316 -0.5779  0.5274 14.5395 \n",
       "\n",
       "Random effects:\n",
       " Groups    Name        Variance Std.Dev.\n",
       " author    (Intercept) 0.542151 0.73631 \n",
       " subreddit (Intercept) 0.008722 0.09339 \n",
       "Number of obs: 494483, groups:  author, 368403; subreddit, 14040\n",
       "\n",
       "Fixed effects:\n",
       "                  Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)      -0.934665   0.004608 -202.84   <2e-16 ***\n",
       "session_comments  0.068017   0.001373   49.54   <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 -0.513\n",
       "convergence code: 0\n",
       "Model is nearly unidentifiable: very large eigenvalue\n",
       " - Rescale variables?\n"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(m3)"
   ]
  },
  {
   "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": [
    "## 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 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": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "g0.bobyqa <- glmer(num_answers~1+session_comments+(1|author),\n",
    "      family = poisson, data = data_first,\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": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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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": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.2.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}