T264831_navigations_clicks_regressions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variant C/D Task Navigations and Clicks – Regression models\n",
    "\n",
    "The approach for fitting regression models to predict whether users are likely to navigate to another task, or make a task click, is the same as we've used in the previous analyses. Because the outcome is binary, either a user did something or they did not, we use a logistic regression model. We add predictors iteratively until we find the most likely model. Like before, we have predictors for which variant the user had, whether they registered on desktop or mobile, and when they registered (in time since the start of the experiment)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
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    "# https://stackoverflow.com/a/35018739/1091835\n",
    "library(IRdisplay)\n",
    "\n",
    "display_html(\n",
    "'<script>  \n",
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    ")"
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   "execution_count": 2,
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   "source": [
    "## libraries\n",
    "library(tidyverse)\n",
    "library(data.table)\n",
    "library(ggplot2)\n",
    "\n",
    "library(lme4)\n",
    "\n",
    "library(caret)\n",
    "\n",
    "library(interactions)\n",
    "library(multcomp)\n",
    "library(emmeans)\n",
    "\n",
    "require(gridExtra)\n",
    "\n",
    "## library(ROCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Configuration variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Set BLAS threads to 1 so glmer doesn't use all cores\n",
    "library(RhpcBLASctl)\n",
    "blas_set_num_threads(1)\n",
    "\n",
    "## parallelization\n",
    "options(mc.cores = 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Function that takes in a model, the validation set, the name of the predicted column,\n",
    "## and returns a plot of the ROC curve\n",
    "plot_ROC = function(mod, val_data, col_name, plot_title, cutoff_steps = 0.1) {\n",
    "  preds = predict(mod, val_data, type = \"response\")\n",
    "  ROCR_pred = prediction(preds, val_data[[col_name]])\n",
    "  ROCR_perf = performance(ROCR_pred, \"tpr\", \"fpr\")\n",
    "  plot(ROCR_perf, colorize = TRUE, print.cutoffs.at = seq(0, 1, by = cutoff_steps),\n",
    "       text.adj = c(-0.2, 1.7), main = plot_title)\n",
    "}\n",
    "\n",
    "## Function to output a confusion matrix\n",
    "confusion_matrix = function(model_predictions, threshold, reference, levels = c(\"yes\", \"no\")) {\n",
    "  pred = factor(ifelse(model_predictions >= threshold, levels[1], levels[2]), levels = levels)\n",
    "  truth = factor(ifelse(reference, levels[1], levels[2]), levels = levels)\n",
    "  confusionMatrix(pred, truth, mode = 'prec_recall')\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data import and setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "navigation_click_counts = fread('datasets/variant-test-2-navigation-click-counts.tsv',\n",
    "                     colClasses = c(wiki_db = 'factor', user_registration = 'character'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this analysis, we're only interested in users in the Homepage group, with a valid variant assigned, who visited the Homepage. Here's how many of them we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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      "text/html": [
       "32615"
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       "32615"
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      "text/plain": [
       "[1] 32615"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length(navigation_click_counts[hp_enabled == 1 & hp_variant %in% c('C', 'D') & visited_homepage == 1]$wiki)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the dataset does not include known test accounts, users who were in the control group (meaning they didn't have the Homepage enabled upon registration), or users who turned the Homepage on/off during the experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Configuration variables for this experiment.\n",
    "start_ts = as.POSIXct('2020-10-28 18:40:02', tz = 'UTC')\n",
    "end_ts = as.POSIXct('2020-11-25 18:40:02', tz = 'UTC')\n",
    "\n",
    "## Convert user_registration into a timestamp\n",
    "navigation_click_counts[, user_reg_ts := as.POSIXct(user_registration, format = '%Y%m%d%H%M%S', tz = 'UTC')]\n",
    "\n",
    "## Calculate time since start of experiment in weeks\n",
    "navigation_click_counts[, exp_days := 0]\n",
    "navigation_click_counts[, exp_days := difftime(user_reg_ts, start_ts, units = \"days\")]\n",
    "navigation_click_counts[, ln_exp_days := log(1 + as.numeric(exp_days))]\n",
    "navigation_click_counts[, ln_exp_weeks := log(1 + as.numeric(exp_days)/7)]\n",
    "\n",
    "## Convert all NAs to 0, from\n",
    "## https://stackoverflow.com/questions/7235657/fastest-way-to-replace-nas-in-a-large-data-table\n",
    "na_to_zero = function(DT) {\n",
    "  # or by number (slightly faster than by name) :\n",
    "  for (j in seq_len(ncol(DT)))\n",
    "    set(DT,which(is.na(DT[[j]])),j,0)\n",
    "}\n",
    "\n",
    "na_to_zero(navigation_click_counts)\n",
    "\n",
    "## Create boolean column for whether the user navigated, or clicked\n",
    "navigation_click_counts[, did_navigate := num_task_navigations > 0]\n",
    "navigation_click_counts[, did_click := num_task_clicks > 0]\n",
    "\n",
    "## set the random seed so train/test/validation splits can be reproduced\n",
    "set.seed(42)\n",
    "\n",
    "## Remove all control group users, users with an incorrect variant assignment,\n",
    "## and users that didn't visit the Homepage.\n",
    "exp_users = navigation_click_counts[hp_enabled == 1 & hp_variant %in% c('C', 'D') & visited_homepage == 1]\n",
    "\n",
    "## Split the experiment users into training, testing, and validation datasets\n",
    "trainIndex <- createDataPartition(exp_users$hp_variant,\n",
    "                                  p = .8, \n",
    "                                  list = FALSE, \n",
    "                                  times = 1)\n",
    "exp_users_train = exp_users[trainIndex,]\n",
    "exp_users_second = exp_users[-trainIndex,]\n",
    "\n",
    "testIndex = createDataPartition(exp_users_second$hp_variant, p = .5, list = FALSE, times = 1)\n",
    "\n",
    "exp_users_test = exp_users_second[testIndex,]\n",
    "exp_users_validate = exp_users_second[-testIndex,]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task navigations\n",
    "\n",
    "We'll start by first modelling if the user navigated to another task or not. Then, we'll repeat the procedure for whether the user clicked on a task or not.\n",
    "\n",
    "## Variant C/D as a predictor\n",
    "\n",
    "In this first model, we predict whether the user edited based on the variant the user was in, while allowing the overall probability of editing to vary by wiki."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 1: only variant as a predictor:\n",
    "nav.model.1 = glmer(formula = did_navigate ~ hp_variant + (1 | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + (1 | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24647.7  24672.2 -12320.8  24641.7    26089 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.6360 -0.4972 -0.4424 -0.3952  2.6910 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name        Variance Std.Dev.\n",
       " wiki_db (Intercept) 0.05811  0.2411  \n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -1.33192    0.06710 -19.850  < 2e-16 ***\n",
       "hp_variantD -0.22582    0.03224  -7.005 2.47e-12 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "hp_variantD -0.222"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model suggests that overall, variant D is associated with a lower probability of a user clicking to navigate to another task.\n",
    "\n",
    "Let us see if there's variation by wiki on this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 1: variant as a group-level predictor\n",
    "nav.model.1.2 = glmer(formula = did_navigate ~ hp_variant + (1 + hp_variant | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + (1 + hp_variant | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24642.9  24683.8 -12316.5  24632.9    26087 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.6406 -0.4884 -0.4258 -0.3992  2.5788 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name        Variance Std.Dev. Corr \n",
       " wiki_db (Intercept) 0.08050  0.2837        \n",
       "         hp_variantD 0.01681  0.1296   -0.76\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -1.32114    0.07795 -16.949  < 2e-16 ***\n",
       "hp_variantD -0.24465    0.05116  -4.783 1.73e-06 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "hp_variantD -0.640"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.1.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$wiki_db\n",
       "        (Intercept) hp_variantD\n",
       "arwiki -0.515548158  0.18665967\n",
       "cswiki  0.310026039 -0.13353815\n",
       "fawiki -0.413357380  0.22011876\n",
       "frwiki -0.115555679 -0.04256411\n",
       "hewiki  0.008747447 -0.02444740\n",
       "huwiki -0.094877413  0.04086996\n",
       "hywiki  0.072321848  0.01187544\n",
       "kowiki -0.267034837  0.07335061\n",
       "plwiki  0.178268728 -0.04561649\n",
       "ptwiki -0.201062600  0.05918507\n",
       "ruwiki  0.242230288 -0.05334706\n",
       "srwiki  0.137621354 -0.08203056\n",
       "svwiki -0.058987132 -0.03318886\n",
       "trwiki  0.430562537 -0.03588451\n",
       "ukwiki -0.012228529 -0.01658084\n",
       "viwiki  0.342760361 -0.13717501\n",
       "\n",
       "with conditional variances for “wiki_db” "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ranef(nav.model.1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is not singular, which suggests that there's enough variation and data to support it. However, the BIC is much worse than the first model. So while there *is* some variation between wikis, it's not clear that it's large enough to be meaningful.\n",
    "\n",
    "## Desktop/mobile registration\n",
    "\n",
    "We add whether the user registered on desktop or mobile as a predictor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 2: add desktop/mobile\n",
    "nav.model.2 = glmer(formula = did_navigate ~ hp_variant + reg_on_mobile + (1 | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + reg_on_mobile + (1 | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24451.8  24484.5 -12221.9  24443.8    26088 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.6884 -0.5095 -0.4319 -0.3586  2.9772 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name        Variance Std.Dev.\n",
       " wiki_db (Intercept) 0.04385  0.2094  \n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -1.16858    0.06087 -19.197  < 2e-16 ***\n",
       "hp_variantD   -0.22246    0.03235  -6.876 6.15e-12 ***\n",
       "reg_on_mobile -0.49182    0.03548 -13.862  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD\n",
       "hp_variantD -0.245       \n",
       "reg_on_mobl -0.177 -0.003"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 2: desktop/mobile with group-level variation\n",
    "nav.model.2.1 = glmer(formula = did_navigate ~ hp_variant + reg_on_mobile + (1 + reg_on_mobile | wiki_db),\n",
    "                      family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + reg_on_mobile + (1 + reg_on_mobile |  \n",
       "    wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24424.1  24473.1 -12206.0  24412.1    26086 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.7161 -0.5059 -0.4408 -0.3352  2.9872 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.05438  0.2332        \n",
       "         reg_on_mobile 0.05761  0.2400   -0.50\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -1.17252    0.06693 -17.518  < 2e-16 ***\n",
       "hp_variantD   -0.22319    0.03238  -6.893 5.47e-12 ***\n",
       "reg_on_mobile -0.46869    0.07867  -5.958 2.56e-09 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD\n",
       "hp_variantD -0.223       \n",
       "reg_on_mobl -0.476 -0.002"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.2.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$wiki_db\n",
       "       (Intercept) reg_on_mobile\n",
       "arwiki -0.28339073  -0.040906985\n",
       "cswiki  0.18349192  -0.080352011\n",
       "fawiki -0.13204157  -0.078081501\n",
       "frwiki -0.19043205   0.044456144\n",
       "hewiki -0.01393726   0.016980118\n",
       "huwiki -0.12756729   0.108101585\n",
       "hywiki  0.14236969  -0.145623758\n",
       "kowiki -0.31990016   0.259099557\n",
       "plwiki  0.13852223  -0.121741263\n",
       "ptwiki  0.02358572  -0.344953588\n",
       "ruwiki  0.10203630   0.325563591\n",
       "srwiki  0.06110605  -0.000561578\n",
       "svwiki -0.22430722   0.336343092\n",
       "trwiki  0.50463695  -0.280154273\n",
       "ukwiki -0.04706044  -0.005512077\n",
       "viwiki  0.22126917   0.024209141\n",
       "\n",
       "with conditional variances for “wiki_db” "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ranef(nav.model.2.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$wiki_db\n",
       "       (Intercept) hp_variantD reg_on_mobile\n",
       "arwiki  -1.4559097  -0.2231905    -0.5095994\n",
       "cswiki  -0.9890270  -0.2231905    -0.5490444\n",
       "fawiki  -1.3045605  -0.2231905    -0.5467739\n",
       "frwiki  -1.3629510  -0.2231905    -0.4242362\n",
       "hewiki  -1.1864562  -0.2231905    -0.4517123\n",
       "huwiki  -1.3000862  -0.2231905    -0.3605908\n",
       "hywiki  -1.0301493  -0.2231905    -0.6143161\n",
       "kowiki  -1.4924191  -0.2231905    -0.2095928\n",
       "plwiki  -1.0339967  -0.2231905    -0.5904336\n",
       "ptwiki  -1.1489332  -0.2231905    -0.8136460\n",
       "ruwiki  -1.0704826  -0.2231905    -0.1431288\n",
       "srwiki  -1.1114129  -0.2231905    -0.4692539\n",
       "svwiki  -1.3968262  -0.2231905    -0.1323493\n",
       "trwiki  -0.6678820  -0.2231905    -0.7488466\n",
       "ukwiki  -1.2195794  -0.2231905    -0.4742044\n",
       "viwiki  -0.9512498  -0.2231905    -0.4444832\n",
       "\n",
       "attr(,\"class\")\n",
       "[1] \"coef.mer\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef(nav.model.2.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see indications that the user registering on mobile is strongly associated with lower probability of task navigation, and that there's meaningful variation between wikis when it comes to this effect.\n",
    "\n",
    "## Interaction between variant and desktop/mobile\n",
    "\n",
    "One of the key findings of our previous analysis was that there was a strong interaction effect between which variant group the user was in, and whether they registered on desktop or mobile. An *interaction effect* means that the effect of one of the predictors is altered by the effect of another predictor. In our case, since both predictor are binary categorical variables, it means that the outcome is altered depending on the combination of those categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 3: desktop/mobile interaction\n",
    "nav.model.3 = glmer(formula = did_navigate ~ hp_variant * reg_on_mobile + (1 | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant * reg_on_mobile + (1 | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24453.5  24494.3 -12221.7  24443.5    26087 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.6904 -0.5109 -0.4347 -0.3610  2.9579 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name        Variance Std.Dev.\n",
       " wiki_db (Intercept) 0.04384  0.2094  \n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               -1.16283    0.06177 -18.824  < 2e-16 ***\n",
       "hp_variantD               -0.23487    0.03971  -5.915 3.32e-09 ***\n",
       "reg_on_mobile             -0.50907    0.04783 -10.644  < 2e-16 ***\n",
       "hp_variantD:reg_on_mobile  0.03694    0.06848   0.539     0.59    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m\n",
       "hp_variantD -0.296              \n",
       "reg_on_mobl -0.244  0.384       \n",
       "hp_vrntD:__  0.172 -0.580 -0.671"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is different from what we've seen in previous analyses, where there's been an interaction effect. In this case, we instead find no indication of that. This means that the negative association with Variant D is consistent between desktop & mobile, and that the negative effect of mobile is consistent between variants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_ROC(edit.model.3, exp_users_validate, 'did_edit', \"Model 3 ROC\", cutoff_steps = 0.025)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variation across wikis\n",
    "\n",
    "We test if the effect of these predictors vary significantly by wiki."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 4: both variant and platform as group-level predictors\n",
    "nav.model.4 = glmer(formula = did_navigate ~ hp_variant + reg_on_mobile +\n",
    "                      (1 + hp_variant + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## If model didn't converge, restart and give it some more iterations:\n",
    "start_vals = getME(nav.model.4, c(\"theta\", \"fixef\"))\n",
    "nav.model.4 = update(nav.model.4, start = start_vals,\n",
    "                     control = glmerControl(optCtrl = list(maxfun = 2e4)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + reg_on_mobile + (1 + hp_variant +  \n",
       "    reg_on_mobile | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24421.7  24495.3 -12201.9  24403.7    26083 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.7119 -0.5124 -0.4440 -0.3458  2.9170 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr       \n",
       " wiki_db (Intercept)   0.06088  0.2467              \n",
       "         hp_variantD   0.01936  0.1391   -0.32      \n",
       "         reg_on_mobile 0.06296  0.2509   -0.33 -0.55\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -1.16391    0.07064 -16.477  < 2e-16 ***\n",
       "hp_variantD   -0.24683    0.05424  -4.550 5.35e-06 ***\n",
       "reg_on_mobile -0.45285    0.08084  -5.602 2.12e-08 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD\n",
       "hp_variantD -0.374       \n",
       "reg_on_mobl -0.330 -0.350"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model converges, and it's not singular. However, we notice that the BIC is much worse compared to the one that only has desktop/mobile as a group-level predictor. This indicates that we want to discard this more complex model in favour of having just desktop/mobile as a group-level predictor.\n",
    "\n",
    "## Time as a predictor\n",
    "\n",
    "Lastly, we add time as a predictor, in this case a variable measuring the number of weeks between when the user registered and the start of the experiment. This enables us to understand if the probability of a user editing changes as time progresses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 5: add time\n",
    "nav.model.5 = glmer(formula = did_navigate ~ hp_variant + reg_on_mobile +\n",
    "                      ln_exp_weeks + (1 + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + reg_on_mobile + ln_exp_weeks + (1 +  \n",
       "    reg_on_mobile | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24425.5  24482.6 -12205.7  24411.5    26085 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.7270 -0.5099 -0.4419 -0.3398  3.0132 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.05430  0.2330        \n",
       "         reg_on_mobile 0.05757  0.2399   -0.50\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -1.14136    0.07726 -14.774  < 2e-16 ***\n",
       "hp_variantD   -0.22319    0.03238  -6.893 5.48e-12 ***\n",
       "reg_on_mobile -0.46918    0.07865  -5.965 2.44e-09 ***\n",
       "ln_exp_weeks  -0.03002    0.03726  -0.806     0.42    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m\n",
       "hp_variantD -0.193              \n",
       "reg_on_mobl -0.416 -0.002       \n",
       "ln_exp_weks -0.500  0.000  0.008"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 5.1: time in days\n",
    "nav.model.5.1 = glmer(formula = did_navigate ~ hp_variant + reg_on_mobile +\n",
    "                      ln_exp_days + (1 + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + reg_on_mobile + ln_exp_days + (1 +  \n",
       "    reg_on_mobile | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24425.3  24482.5 -12205.6  24411.3    26085 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.7334 -0.5100 -0.4418 -0.3418  3.0121 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.05430  0.233         \n",
       "         reg_on_mobile 0.05759  0.240    -0.50\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -1.12295    0.08631 -13.011  < 2e-16 ***\n",
       "hp_variantD   -0.22315    0.03238  -6.891 5.53e-12 ***\n",
       "reg_on_mobile -0.46917    0.07866  -5.964 2.46e-09 ***\n",
       "ln_exp_days   -0.01959    0.02157  -0.908    0.364    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m\n",
       "hp_variantD -0.172              \n",
       "reg_on_mobl -0.374 -0.002       \n",
       "ln_exp_days -0.632 -0.001  0.007"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.5.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears that time does not have an effect in this experiment, and adding it does not improve fitness as the BIC is lower. Since the experiment only ran over 4 weeks, and there isn't anything that significantly changes wiki processes (e.g. there's not a need for support systems to ramp up capacity), it makes sense that time isn't a strong factor here. Given the lower BIC and the lack of a significant predictor, I choose to remove it again.\n",
    "\n",
    "I went back and looked at the Variant A/B analysis, and there we again found that time was not a significant predictor and kept it out of the models. This indicates to me that for these relatively short experiments, time is a factor if there is some specific component that it accounts for (e.g. ramping up as mentioned above). Alternatively, we might model it using some kind of autoregressive function to account for weekly variation, if that's meaningful. In short, we need specific hypotheses about time effects for them to be meaningful, and they're likely going to need more advanced methods for them to work.\n",
    "\n",
    "## Model across the entire dataset\n",
    "\n",
    "Our previous models were trained on a random 80% of our dataset. We switch to the full dataset and model again to get a sense of the predictors across all available data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 7: full model\n",
    "nav.model.full = glmer(formula = did_navigate ~ hp_variant + reg_on_mobile + (1 + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant + reg_on_mobile + (1 + reg_on_mobile |  \n",
       "    wiki_db)\n",
       "   Data: exp_users\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 30510.9  30561.2 -15249.4  30498.9    32609 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.7258 -0.5108 -0.4402 -0.3343  3.0216 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.05391  0.2322        \n",
       "         reg_on_mobile 0.05488  0.2343   -0.38\n",
       "Number of obs: 32615, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "              Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -1.18263    0.06511 -18.164  < 2e-16 ***\n",
       "hp_variantD   -0.21941    0.02896  -7.577 3.53e-14 ***\n",
       "reg_on_mobile -0.47528    0.07484  -6.351 2.14e-10 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD\n",
       "hp_variantD -0.204       \n",
       "reg_on_mobl -0.384 -0.002"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.full)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimating the effects using the \"divide by 4 rule\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>hp_variantD:</strong> -0.054852717277384"
      ],
      "text/latex": [
       "\\textbf{hp\\textbackslash{}\\_variantD:} -0.054852717277384"
      ],
      "text/markdown": [
       "**hp_variantD:** -0.054852717277384"
      ],
      "text/plain": [
       "hp_variantD \n",
       "-0.05485272 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fixef(nav.model.full)[2] / 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 16 × 2 of type chr</caption>\n",
       "<tbody>\n",
       "\t<tr><td>arwiki</td><td>-12.367</td></tr>\n",
       "\t<tr><td>cswiki</td><td>-10.158</td></tr>\n",
       "\t<tr><td>fawiki</td><td>-13.572</td></tr>\n",
       "\t<tr><td>frwiki</td><td>-10.93 </td></tr>\n",
       "\t<tr><td>hewiki</td><td>-12.485</td></tr>\n",
       "\t<tr><td>huwiki</td><td>-10.368</td></tr>\n",
       "\t<tr><td>hywiki</td><td>-15.895</td></tr>\n",
       "\t<tr><td>kowiki</td><td>-8.167 </td></tr>\n",
       "\t<tr><td>plwiki</td><td>-14.816</td></tr>\n",
       "\t<tr><td>ptwiki</td><td>-21.191</td></tr>\n",
       "\t<tr><td>ruwiki</td><td>-3.267 </td></tr>\n",
       "\t<tr><td>srwiki</td><td>-11.717</td></tr>\n",
       "\t<tr><td>svwiki</td><td>-4.386 </td></tr>\n",
       "\t<tr><td>trwiki</td><td>-19.511</td></tr>\n",
       "\t<tr><td>ukwiki</td><td>-12.621</td></tr>\n",
       "\t<tr><td>viwiki</td><td>-8.066 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 16 × 2 of type chr\n",
       "\\begin{tabular}{ll}\n",
       "\t arwiki & -12.367\\\\\n",
       "\t cswiki & -10.158\\\\\n",
       "\t fawiki & -13.572\\\\\n",
       "\t frwiki & -10.93 \\\\\n",
       "\t hewiki & -12.485\\\\\n",
       "\t huwiki & -10.368\\\\\n",
       "\t hywiki & -15.895\\\\\n",
       "\t kowiki & -8.167 \\\\\n",
       "\t plwiki & -14.816\\\\\n",
       "\t ptwiki & -21.191\\\\\n",
       "\t ruwiki & -3.267 \\\\\n",
       "\t srwiki & -11.717\\\\\n",
       "\t svwiki & -4.386 \\\\\n",
       "\t trwiki & -19.511\\\\\n",
       "\t ukwiki & -12.621\\\\\n",
       "\t viwiki & -8.066 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 16 × 2 of type chr\n",
       "\n",
       "| arwiki | -12.367 |\n",
       "| cswiki | -10.158 |\n",
       "| fawiki | -13.572 |\n",
       "| frwiki | -10.93  |\n",
       "| hewiki | -12.485 |\n",
       "| huwiki | -10.368 |\n",
       "| hywiki | -15.895 |\n",
       "| kowiki | -8.167  |\n",
       "| plwiki | -14.816 |\n",
       "| ptwiki | -21.191 |\n",
       "| ruwiki | -3.267  |\n",
       "| srwiki | -11.717 |\n",
       "| svwiki | -4.386  |\n",
       "| trwiki | -19.511 |\n",
       "| ukwiki | -12.621 |\n",
       "| viwiki | -8.066  |\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]   [,2]   \n",
       " [1,] arwiki -12.367\n",
       " [2,] cswiki -10.158\n",
       " [3,] fawiki -13.572\n",
       " [4,] frwiki -10.93 \n",
       " [5,] hewiki -12.485\n",
       " [6,] huwiki -10.368\n",
       " [7,] hywiki -15.895\n",
       " [8,] kowiki -8.167 \n",
       " [9,] plwiki -14.816\n",
       "[10,] ptwiki -21.191\n",
       "[11,] ruwiki -3.267 \n",
       "[12,] srwiki -11.717\n",
       "[13,] svwiki -4.386 \n",
       "[14,] trwiki -19.511\n",
       "[15,] ukwiki -12.621\n",
       "[16,] viwiki -8.066 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cbind(rownames(coef(nav.model.full)$wiki_db),\n",
    "      round(100 * coef(nav.model.full)$wiki_db$reg_on_mobile / 4, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model across the full dataset shows the same trends as we saw with this model on the smaller dataset. In summary:\n",
    "\n",
    "1. We find indication of meaningful variation between wikis when it comes to the effects of individual predictors, but this variation does not change the direction of the effects. Instead it modifies the magnitude. It's unclear whether including this in the model is meaningful.\n",
    "2. Users who are on mobile are less likely to navigate between tasks.\n",
    "3. Users who get Variant D are less likely to navigate between tasks.\n",
    "\n",
    "### Interaction sanity check\n",
    "\n",
    "Let's just test for interaction because we can."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 7: full model\n",
    "nav.model.full.2 = glmer(formula = did_navigate ~ hp_variant * reg_on_mobile + (1 + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_navigate ~ hp_variant * reg_on_mobile + (1 + reg_on_mobile |  \n",
       "    wiki_db)\n",
       "   Data: exp_users\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 30512.2  30570.9 -15249.1  30498.2    32608 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.7287 -0.5103 -0.4442 -0.3374  2.9942 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.05395  0.2323        \n",
       "         reg_on_mobile 0.05478  0.2340   -0.38\n",
       "Number of obs: 32615, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               -1.17482    0.06587 -17.836  < 2e-16 ***\n",
       "hp_variantD               -0.23644    0.03553  -6.655 2.84e-11 ***\n",
       "reg_on_mobile             -0.49902    0.08019  -6.223 4.87e-10 ***\n",
       "hp_variantD:reg_on_mobile  0.05089    0.06138   0.829    0.407    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m\n",
       "hp_variantD -0.247              \n",
       "reg_on_mobl -0.406  0.203       \n",
       "hp_vrntD:__  0.143 -0.579 -0.358"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nav.model.full.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nah, there's no interaction.\n",
    "\n",
    "## Overview table\n",
    "\n",
    "Since we've found that results vary by wiki, where the user registered, and what variant they saw, we create an overview table to show how the probability changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "visit_counts = exp_users[, list(n_visitors = sum(.N)),\n",
    "                       by = c('wiki_db', 'reg_on_mobile', 'hp_variant')]\n",
    "nav_counts = exp_users[did_navigate == 1, list(n_navigated = sum(.N)),\n",
    "                        by = c('wiki_db', 'reg_on_mobile', 'hp_variant')]\n",
    "merged_nav_counts = merge(visit_counts, nav_counts, by = c('wiki_db', 'reg_on_mobile', 'hp_variant'))\n",
    "merged_nav_counts[, percent_navigated := 100 * n_navigated / n_visitors]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.table: 16 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>wiki_db</th><th scope=col>reg_on_mobile</th><th scope=col>hp_variant</th><th scope=col>n_visitors</th><th scope=col>n_navigated</th><th scope=col>percent_navigated</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>arwiki</td><td>0</td><td>C</td><td> 720</td><td>122</td><td>16.94444</td></tr>\n",
       "\t<tr><td>arwiki</td><td>0</td><td>D</td><td> 679</td><td>109</td><td>16.05302</td></tr>\n",
       "\t<tr><td>arwiki</td><td>1</td><td>C</td><td>1182</td><td>121</td><td>10.23689</td></tr>\n",
       "\t<tr><td>arwiki</td><td>1</td><td>D</td><td>1186</td><td>135</td><td>11.38280</td></tr>\n",
       "\t<tr><td>cswiki</td><td>0</td><td>C</td><td> 277</td><td> 85</td><td>30.68592</td></tr>\n",
       "\t<tr><td>cswiki</td><td>0</td><td>D</td><td> 302</td><td> 58</td><td>19.20530</td></tr>\n",
       "\t<tr><td>cswiki</td><td>1</td><td>C</td><td>  74</td><td> 18</td><td>24.32432</td></tr>\n",
       "\t<tr><td>cswiki</td><td>1</td><td>D</td><td>  79</td><td> 12</td><td>15.18987</td></tr>\n",
       "\t<tr><td>kowiki</td><td>0</td><td>C</td><td> 165</td><td> 28</td><td>16.96970</td></tr>\n",
       "\t<tr><td>kowiki</td><td>0</td><td>D</td><td> 149</td><td> 17</td><td>11.40940</td></tr>\n",
       "\t<tr><td>kowiki</td><td>1</td><td>C</td><td>  73</td><td>  9</td><td>12.32877</td></tr>\n",
       "\t<tr><td>kowiki</td><td>1</td><td>D</td><td>  69</td><td>  9</td><td>13.04348</td></tr>\n",
       "\t<tr><td>viwiki</td><td>0</td><td>C</td><td> 279</td><td> 81</td><td>29.03226</td></tr>\n",
       "\t<tr><td>viwiki</td><td>0</td><td>D</td><td> 280</td><td> 60</td><td>21.42857</td></tr>\n",
       "\t<tr><td>viwiki</td><td>1</td><td>C</td><td> 114</td><td> 27</td><td>23.68421</td></tr>\n",
       "\t<tr><td>viwiki</td><td>1</td><td>D</td><td> 123</td><td> 24</td><td>19.51220</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.table: 16 × 6\n",
       "\\begin{tabular}{llllll}\n",
       " wiki\\_db & reg\\_on\\_mobile & hp\\_variant & n\\_visitors & n\\_navigated & percent\\_navigated\\\\\n",
       " <fct> & <int> & <chr> & <int> & <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t arwiki & 0 & C &  720 & 122 & 16.94444\\\\\n",
       "\t arwiki & 0 & D &  679 & 109 & 16.05302\\\\\n",
       "\t arwiki & 1 & C & 1182 & 121 & 10.23689\\\\\n",
       "\t arwiki & 1 & D & 1186 & 135 & 11.38280\\\\\n",
       "\t cswiki & 0 & C &  277 &  85 & 30.68592\\\\\n",
       "\t cswiki & 0 & D &  302 &  58 & 19.20530\\\\\n",
       "\t cswiki & 1 & C &   74 &  18 & 24.32432\\\\\n",
       "\t cswiki & 1 & D &   79 &  12 & 15.18987\\\\\n",
       "\t kowiki & 0 & C &  165 &  28 & 16.96970\\\\\n",
       "\t kowiki & 0 & D &  149 &  17 & 11.40940\\\\\n",
       "\t kowiki & 1 & C &   73 &   9 & 12.32877\\\\\n",
       "\t kowiki & 1 & D &   69 &   9 & 13.04348\\\\\n",
       "\t viwiki & 0 & C &  279 &  81 & 29.03226\\\\\n",
       "\t viwiki & 0 & D &  280 &  60 & 21.42857\\\\\n",
       "\t viwiki & 1 & C &  114 &  27 & 23.68421\\\\\n",
       "\t viwiki & 1 & D &  123 &  24 & 19.51220\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.table: 16 × 6\n",
       "\n",
       "| wiki_db &lt;fct&gt; | reg_on_mobile &lt;int&gt; | hp_variant &lt;chr&gt; | n_visitors &lt;int&gt; | n_navigated &lt;int&gt; | percent_navigated &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| arwiki | 0 | C |  720 | 122 | 16.94444 |\n",
       "| arwiki | 0 | D |  679 | 109 | 16.05302 |\n",
       "| arwiki | 1 | C | 1182 | 121 | 10.23689 |\n",
       "| arwiki | 1 | D | 1186 | 135 | 11.38280 |\n",
       "| cswiki | 0 | C |  277 |  85 | 30.68592 |\n",
       "| cswiki | 0 | D |  302 |  58 | 19.20530 |\n",
       "| cswiki | 1 | C |   74 |  18 | 24.32432 |\n",
       "| cswiki | 1 | D |   79 |  12 | 15.18987 |\n",
       "| kowiki | 0 | C |  165 |  28 | 16.96970 |\n",
       "| kowiki | 0 | D |  149 |  17 | 11.40940 |\n",
       "| kowiki | 1 | C |   73 |   9 | 12.32877 |\n",
       "| kowiki | 1 | D |   69 |   9 | 13.04348 |\n",
       "| viwiki | 0 | C |  279 |  81 | 29.03226 |\n",
       "| viwiki | 0 | D |  280 |  60 | 21.42857 |\n",
       "| viwiki | 1 | C |  114 |  27 | 23.68421 |\n",
       "| viwiki | 1 | D |  123 |  24 | 19.51220 |\n",
       "\n"
      ],
      "text/plain": [
       "   wiki_db reg_on_mobile hp_variant n_visitors n_navigated percent_navigated\n",
       "1  arwiki  0             C           720       122         16.94444         \n",
       "2  arwiki  0             D           679       109         16.05302         \n",
       "3  arwiki  1             C          1182       121         10.23689         \n",
       "4  arwiki  1             D          1186       135         11.38280         \n",
       "5  cswiki  0             C           277        85         30.68592         \n",
       "6  cswiki  0             D           302        58         19.20530         \n",
       "7  cswiki  1             C            74        18         24.32432         \n",
       "8  cswiki  1             D            79        12         15.18987         \n",
       "9  kowiki  0             C           165        28         16.96970         \n",
       "10 kowiki  0             D           149        17         11.40940         \n",
       "11 kowiki  1             C            73         9         12.32877         \n",
       "12 kowiki  1             D            69         9         13.04348         \n",
       "13 viwiki  0             C           279        81         29.03226         \n",
       "14 viwiki  0             D           280        60         21.42857         \n",
       "15 viwiki  1             C           114        27         23.68421         \n",
       "16 viwiki  1             D           123        24         19.51220         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## We'll focus on Arabic, Czech, Korean, and Vietnamese, to compare the numbers with Variant A/B\n",
    "merged_nav_counts[wiki_db %in% c('arwiki', 'cswiki', 'kowiki', 'viwiki')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "merged_nav_counts[, platform := 'desktop']\n",
    "merged_nav_counts[reg_on_mobile == 1, platform := 'mobile']\n",
    "merged_nav_counts$platform = factor(merged_nav_counts$platform)\n",
    "\n",
    "merged_nav_counts$hp_variant = factor(merged_nav_counts$hp_variant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "plots = lapply(unique(merged_nav_counts$wiki_db), function(w) {\n",
    "    ggplot(merged_nav_counts[wiki_db == w], aes(x = platform, y = percent_navigated, fill = hp_variant)) +\n",
    "        theme_bw() +\n",
    "        theme(axis.title.x = element_text(size = rel(1.5)),\n",
    "            axis.text.x = element_text(size = rel(1.25)),\n",
    "            axis.title.y = element_text(size = rel(1.5)),\n",
    "            axis.text.y = element_text(size = rel(1.25))) +\n",
    "        scale_fill_brewer(\"Variant\", palette = 'Set1') +\n",
    "        labs(x = \"Platform\", y = \"Probability (in %)\", title = w) +\n",
    "        geom_col(position = \"dodge2\")\n",
    "})\n",
    "\n",
    "# ggsave(plot = g, file = \"graphs/tagged_edit_probabilities.png\",\n",
    "#       width = 14, height = 7, units = \"in\", dpi = \"retina\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1YsWKlStXTps2zbhnbGzsL7/8Ii27uLi4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\n8uVOTk6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wyA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\nTZkyxXp1FKVevXp79+49e/ZsQECAcfDcuXNqtTowMLD86wE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21OnQAA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\njz/+uOzVlBWUlQEAAKBB5DoAAAAts6Nh9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68YyMjNat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\nKhMZgGWLjIxUfhssWbIk36qMjAxfX19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Fg4g+e6jh07ZmZmXrly5dixY1qt1s3N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\ndOgwZ84cO0UIAAAAO2t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fv35dkqStW7d6eHjc2y05OXnbtm2XL1/W6XQRERFRUVEhISHOjxYAAMCKTqd79tln\nV61aNWnSJKvbndy8eVNtt7EDAABAcVSV1xVbsLt165a84OfnJ1+NbG4po4CAgFL7rFmzxsfH\nJzw8PDc39/bt20X22b59+/Llyxs0aBAVFaXX6xMTE6dMmbJgwYI6derYFA8AAIAjfPTRRwcO\nHGjXrt306dM7dOjg7+9/8uTJFStWPP300yq5SZxz8joAAABXp568rtiCXWBgoLywZ8+eyMhI\ny5YyKsulv8uWLZMfPTZ58uQiC3ZZWVmrV68ODQ396KOP5MeOtG/ffvLkybGxsTNnzrQpHgAA\nAEeoVq3awYMHFy5cuG7duujoaG9v70aNGg0fPnz8+PFKh/YfzsnrAAAAXJ168jqFL4mVq3Ul\n2L9/v8Fg6NOnj/khwY0aNWrRosWRI0f0en2VKlUcHyMAAEApKleuPGvWrFmzZikdCAAAAMpF\nJXldsQW7pUuXyguNGze2anGmM2fOCCGaN29u2di8efOUlJTU1NTWrVs7PyQAAADXopK8DgAA\nAGVUbMFuwoQJpbY4QUZGhhCievXqlo3yS3mVWXJy8l9//SUvm0wmk8mUm5vrrDChRlYDwGQy\nCSGMRiMDQynsefdR5LFm9sFKfn6+0iG4EZXkdQAAACgjhS+JLZWczXt5eVk2ypfHWiX6P/zw\nw86dO+Vlf3//oKCg7OxsZ4UJNSpyABQWFhYWFjo/GIhijggqpCKPtdFoZAzAEgVcAAAAoDhq\nL9h5e3sLIQoKCuQFmcFgMK8ye/755/v16ycv5+bmfvHFF/7+/k6MtKxuKB2A+7AaACaTSa/X\ne3l5+fr6KhWSm1N8SjL7nMbqWEuSdOfOHWYfrPj5+SkdAgAAAKBSai/Yma9+tUzri7xONjw8\nPDw8XF7OysrSaDRW5+XB3VgNAKPRKITQarUMDKWw592H1bGWHy7JxzKseHqqPQkBAAAAlFJs\nrnzr1q1ybjogIKCcWxBCNG7ceO/evSdPngwLCzM3njp1SqvVmstzAAAAKIFK8joAAACUUbEF\nu8DAwHJuWj6lopw6d+68atWqhISE7t27y6dmpKampqSktG3btmrVquXfPgAAQIWnkrwOAAAA\nZaTw1Sh79+69fv26ECIzM1MIsWnTJo1G4+HhMXjwYLlDYGDgc889FxsbO3Xq1MjISL1en5iY\n6OvrO3bsWCXjBgAAahWS9rfSIQAAAMAO3DmvK7Zgt3TpUie8fVJS0rFjx8wv169fL4Tw8vIy\nF+yEEAMGDAgICIiPj1+zZo2Xl1dERERUVFRISIgTwgMAAKgAnJPXAQAAwF6KLdhNmDDBCW8f\nExNTlm6RkZGRkZEOjgUAAFQEHd/bZd8NHpj9pH036HzOyesAAADsy53zOq3SAQAAAAAAAAD4\nHwp2AAAAAAAAgIpQsAMAAAAAAABUpNh72N26dUte8PPz8/T0tGwpo4CAgPJEBgAAALsgrwMA\nAHAtxRbsAgMD5YU9e/bID3wwt5SRJEnlCAwAAAD2QV4HAADgWrgkFgAAAAAAAFCRYs+wW7p0\nqbzQuHFjqxYAAAC4EPI6AAAA11JswW7ChAmltgAAAODNN9/89NNPhRBarbZKlSrh4eFdu3ad\nOHFiWFiY0qH9B3kdAABAWagnryu2YAcAAIAyqlmz5t69eyVJ0uv1x44d+/zzz5cuXfrdd991\n7dpV6dCcJy4u7ty5c+fPn79+/bokSVu3bvXw8Li3W3Jy8rZt2y5fvqzT6SIiIqKiokJCQpwf\nLQAAQJFUktdRsAMAACgvT0/Ppk2bysvt27cfPXr0E088ERUVdf78eW9vb2Vjc5o1a9b4+PiE\nh4fn5ubevn27yD7bt29fvnx5gwYNoqKi9Hp9YmLilClTFixYUKdOHSdHCwAAUCSV5HX389CJ\nW7duLVmy5JlnnmnSpElwcHBwcHCTJk2eeeaZJUuW3Lp1y+4hAgAAuBadTjdt2rS0tLRffvlF\n6VhKYce8btmyZRs2bJgzZ07NmjWL7JCVlbV69erQ0NCPPvqoX79+I0eOnD17dnZ2dmxsrD1+\nFQAAAPtTKq+zuWC3dOnSsLCwV199NS4u7uzZs+np6enp6WfPno2Li3v11VfDwsK4hzEAAEBE\nRIQQ4vz580oHUhL75nW1atUqucP+/fsNBkOfPn10Op3c0qhRoxYtWhw5ckSv19//rwEAAOBI\niuR1tl0SO3ny5I8//lheDg4Obt26dY0aNYQQN27cOHr0aHp6+p07d1555ZULFy7Mnz/f/sEC\nAAC4CEmShBAajUbpQIrl/LzuzJkzQojmzZtbNjZv3jwlJSU1NbV169Z2eRcAAAD7UiSvs6Fg\nt2PHDjmra9iw4T//+c+nn35aq/3fCXomkykxMfHNN9+8cOHCggULunbt2qtXL/vHCwAA4AqO\nHz8uhAgPD1c6kKIpktdlZGQIIapXr27ZKL+UVwEAAKiQInmdDQU7+bm29erVO3DggFWmJYTQ\narV9+/Z95JFH2rRpc/ny5cWLFytYsJMkyWg0ZmVlKRUA1MBqAMgVcYPBwMBQCnvefRR5rAsK\nChgDsFSxL4E0GAwffvjhAw888OijjyodS9EUyevy8/OFEF5eXpaN8uWx8iqzmTNn7ty5U172\n9/cPCgpKT08vfwBwXUUOgPz8fKuRA6dhSrqPIo+1wWBgDChFnXu+Yj/PQKm8zoaC3eHDh4UQ\n77zzzr1ZnVlQUNDMmTNffPFFubNSNBqNh4dHYGCggjEUJ0fpANyH1QCQa7g6na5KlSpKheTm\nFJ+SzD6nsTrWkiRlZGR4eXlVrVpVqZCgQhXs07iwsPD06dNCCL1ef+zYsc8++yw1NfW7774z\n36xNbRTJ6+QHqxUUFFg+Yc1gMJhXmdWpU6dZs2bycqVKlfR6vaenbTdycQ5qRU5jNQDkr+fl\nnF+pkNyc4lOS2ec09x7rwsJCZp+CFJ99RVJnVPdNJXmdDfs0JydHCNG2bduSu8kdsrOzyxMW\nAACAC7l+/XqzZs20Wq2fn1+DBg26d+8eHx8fFhamdFzFUiSvM1/96ufnZ24s8jrZV1555ZVX\nXpGXs7KyJk6cGBAQYJcY7It812msBgBfxCpO8SnJ7HMaq2PNF7GKU3z2FcnyL3sFoJK8zoaC\nXWho6Llz50rN2OQOdevWLVdcAAAALuKTTz755JNPlI7CNorkdY0bN967d+/JkyctU95Tp05p\ntVrV3uwPAAC4FfXkddrSu/zXgAEDhBDbtm0rudvWrVuFEAMHDixPWAAAAHAcRfK6zp0763S6\nhISEgoICuSU1NTUlJaVNmzacqQEAAGDJhjPspkyZ8s0333z66aeRkZG9e/cuss933323aNGi\nunXrTp482U4RAgAAwM4ckdft3bv3+vXrQojMzEwhxKZNm+SbHA0ePFjuEBgY+Nxzz8XGxk6d\nOjUyMlKv1ycmJvr6+o4dO9ZOvxYAAEAFYUPBLjg4ePfu3UOHDu3bt+/QoUNHjRrVpk2b4OBg\nIcTNmzePHDmyZs2azZs3t2zZctOmTSXcwBgAAADKckRel5SUdOzYMfPL9evXCyG8vLzMBTsh\nxIABAwICAuLj49esWePl5RUREREVFRUSEmLv3w8AAMC1FVuwK+4ZH5IkSZK0cePGjRs3Ftkh\nJSVFfqpXYWGhXUIEAABAeTgnr4uJiSlLMJGRkZGRkWXpCQAA4LaKLdgZjcb726LJZLrfYAAA\nAGB/5HUAAACupdiC3XvvvefMOAAAAOAg5HUAAACupdiCXXR0tBPDAAC4o47v7VI6BLdwYPaT\nSocAhZHXAQAAuBat0gEAAAAAAAAA+B8bnhILAACgfpxRCAAAUDG4c17HGXYAAAAAAACAitzn\nGXZZWVnHjx/PyMjIzc2VJKnIPs8991w5AgMAAIAzkNcBAACojc0Fu6SkpPfff//nn38uLp8z\nI7EDAABQM/I6AAAAdbKtYPfpp5/+4x//KDWlsyOj0Thw4MB729euXVu1alWnhQEAAFDBOD+v\nAwAAQBnZULA7fvz4W2+9JUlSixYtZs+eHRER0bhxYyHE5cuXs7Kyjhw5snz58gMHDnTs2HHl\nypX2rabVr1+/U6dOli2VKlWy4/YBAADcioJ5HQAAAEplQ8Fu8eLFJpMpKCjo559/DggIKCws\nlNtDQ0NDQ0Nbtmz5/PPPR0dHv//+++PHj9+3b58dowwLCxs2bJgdNwgAAODOFMzrAAAAUCob\nnhIr52qvvfZaQEBAkR00Gs3s2bN79+69f//+5cuX2yfA/8rJyUlPTzdnkwAAALhvyuZ1AAAA\nKJkNBbu0tDQhxMMPP/yfn9T+52cNBoNlt3Hjxgkh1q1bZ58AhRBC/Prrr88+++zYsWOHDRs2\nZ86cK1eu2HHjAAAA7kbBvA4AAAClsuGS2IKCAiFEzZo15ZdarVan0xkMhoyMjNq1a5u7NWjQ\nQAhx5swZu8Sn0WjCwsI6dOhQu3btvLy8P/744+DBg3/++eeCBQtCQkIse2ZmZubm5srLer1e\nkiSj0WiXGOCirAaA/JKBoSD2vPuwOtbyLe2ZfQpS5543mUxKh+DWFMnrAAAAUEY2FOyqV69+\n7dq1O3fumFtq16596dKl06dPWyZ2165dE0JYdisPrVa7ePFi88vevXvHx8evXLly9erVM2bM\nsOy5cOHCnTt3ysv+/v5BQUFZWVl2iQEuqsgBYDAYrM4dgNMwJd1Hkce6oKCAMaAUde55e6UK\nuD+K5HUAAAAoIxsKdk2bNr127dqpU6e6desmtzz88MOXLl369ttvn3jiCXM3+aIJy1TPvvr1\n67d58+ajR49atbdo0cJ8hztPT8/U1FRvb28HxVAe+UoH4D6sB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T379/dzqdIlJW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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1260,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width = 14, repr.plot.height = 21)\n",
    "grid.arrange(grobs = plots, ncol = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task clicks\n",
    "\n",
    "We'll next model if the user clicked on a suggested task. This is the same procedure as for task navigation, except with a different outcome.\n",
    "\n",
    "## Variant C/D as a predictor\n",
    "\n",
    "In this first model, we predict whether the user clicked on a task based on the variant the user was in, while allowing the overall probability of editing to vary by wiki."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 1: only variant as a predictor:\n",
    "click.model.1 = glmer(formula = did_click ~ hp_variant + (1 | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_click ~ hp_variant + (1 | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 19613.9  19638.4  -9804.0  19607.9    26089 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.4700 -0.4069 -0.3653 -0.3193  3.4810 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name        Variance Std.Dev.\n",
       " wiki_db (Intercept) 0.06267  0.2503  \n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "            Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept) -1.88818    0.07243 -26.070  < 2e-16 ***\n",
       "hp_variantD -0.17161    0.03753  -4.573 4.82e-06 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr)\n",
       "hp_variantD -0.240"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(click.model.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model suggests that overall, variant D is associated with a lower probability of a user clicking on a suggested task.\n",
    "\n",
    "Let us see if there's variation by wiki on this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "boundary (singular) fit: see ?isSingular\n",
      "\n"
     ]
    }
   ],
   "source": [
    "## 1: variant as a group-level predictor\n",
    "click.model.1.2 = glmer(formula = did_click ~ hp_variant + (1 + hp_variant | wiki_db),\n",
    "                        family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "summary(click.model.1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is singular, which suggests that there's not enough variation to identify it. We've come across this many times before, and as we did then we again discard this model.\n",
    "\n",
    "## Desktop/mobile registration\n",
    "\n",
    "We add whether the user registered on desktop or mobile as a predictor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 2: add desktop/mobile\n",
    "click.model.2 = glmer(formula = did_click ~ hp_variant + reg_on_mobile + (1 | wiki_db),\n",
    "                      family = binomial(link = \"logit\"), data = exp_users_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_click ~ hp_variant + reg_on_mobile + (1 | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 19615.9  19648.6  -9803.9  19607.9    26088 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.4705 -0.4065 -0.3645 -0.3189  3.4880 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name        Variance Std.Dev.\n",
       " wiki_db (Intercept) 0.06275  0.2505  \n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "               Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)   -1.886095   0.073890 -25.526  < 2e-16 ***\n",
       "hp_variantD   -0.171549   0.037531  -4.571 4.86e-06 ***\n",
       "reg_on_mobile -0.005756   0.039662  -0.145    0.885    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD\n",
       "hp_variantD -0.233       \n",
       "reg_on_mobl -0.193 -0.010"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(click.model.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do not see any indication that mobile is associated with more or less likelihood of clicking on a suggested task.\n",
    "\n",
    "## Interaction between variant and desktop/mobile\n",
    "\n",
    "One of the key findings of our previous analysis was that there was a strong interaction effect between which variant group the user was in, and whether they registered on desktop or mobile. An *interaction effect* means that the effect of one of the predictors is altered by the effect of another predictor. In our case, since both predictor are binary categorical variables, it means that the outcome is altered depending on the combination of those categories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 3: desktop/mobile interaction\n",
    "click.model.3 = glmer(formula = did_click ~ hp_variant * reg_on_mobile + (1 | wiki_db),\n",
    "                      family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_click ~ hp_variant * reg_on_mobile + (1 | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 19606.6  19647.4  -9798.3  19596.6    26087 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.4856 -0.4126 -0.3593 -0.3279  3.6315 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name        Variance Std.Dev.\n",
       " wiki_db (Intercept) 0.06296  0.2509  \n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               -1.93732    0.07573 -25.583  < 2e-16 ***\n",
       "hp_variantD               -0.06351    0.04930  -1.288 0.197657    \n",
       "reg_on_mobile              0.11372    0.05306   2.143 0.032107 *  \n",
       "hp_variantD:reg_on_mobile -0.25616    0.07610  -3.366 0.000762 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m\n",
       "hp_variantD -0.313              \n",
       "reg_on_mobl -0.285  0.449       \n",
       "hp_vrntD:__  0.204 -0.648 -0.663"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(click.model.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now things are starting to get interesting as we see the interaction effect pop up. In this case, the model suggests that there's no difference between the variants on desktop. Variant C on desktop is associated with slightly less likelihood of clicking on a suggested task compared to Variant C on mobile. For Variant D, however, mobile is associated with a strong negative likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_ROC(edit.model.3, exp_users_validate, 'did_edit', \"Model 3 ROC\", cutoff_steps = 0.025)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variation across wikis\n",
    "\n",
    "We test if the effect of these predictors vary significantly by wiki."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "boundary (singular) fit: see ?isSingular\n",
      "\n"
     ]
    }
   ],
   "source": [
    "## 4: both variant and platform as group-level predictors, interacting\n",
    "click.model.4 = glmer(formula = did_click ~ hp_variant * reg_on_mobile +\n",
    "                      (1 + hp_variant * reg_on_mobile | wiki_db),\n",
    "                      family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "boundary (singular) fit: see ?isSingular\n",
      "\n"
     ]
    }
   ],
   "source": [
    "## 4: both variant and platform as group-level predictors, no group-level interaction\n",
    "click.model.4.1 = glmer(formula = did_click ~ hp_variant * reg_on_mobile +\n",
    "                        (1 + hp_variant + reg_on_mobile | wiki_db),\n",
    "                        family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "boundary (singular) fit: see ?isSingular\n",
      "\n"
     ]
    }
   ],
   "source": [
    "## 4: only variant as a group-level predictor\n",
    "click.model.4.2 = glmer(formula = did_click ~ hp_variant * reg_on_mobile +\n",
    "                        (1 + hp_variant | wiki_db),\n",
    "                        family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 4: only platform as a group-level predictor\n",
    "click.model.4.3 = glmer(formula = did_click ~ hp_variant * reg_on_mobile +\n",
    "                        (1 + reg_on_mobile | wiki_db),\n",
    "                        family = binomial(link = \"logit\"), data = exp_users_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_click ~ hp_variant * reg_on_mobile + (1 + reg_on_mobile |  \n",
       "    wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 19576.6  19633.8  -9781.3  19562.6    26085 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.5031 -0.4035 -0.3625 -0.3230  3.6568 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.08913  0.2985        \n",
       "         reg_on_mobile 0.08607  0.2934   -0.66\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               -1.93510    0.08758 -22.094  < 2e-16 ***\n",
       "hp_variantD               -0.06196    0.04936  -1.255 0.209402    \n",
       "reg_on_mobile              0.09928    0.10132   0.980 0.327170    \n",
       "hp_variantD:reg_on_mobile -0.25980    0.07621  -3.409 0.000652 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m\n",
       "hp_variantD -0.271              \n",
       "reg_on_mobl -0.627  0.235       \n",
       "hp_vrntD:__  0.176 -0.648 -0.346"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(click.model.4.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$wiki_db\n",
       "        (Intercept) reg_on_mobile\n",
       "arwiki  0.185135634   -0.14270810\n",
       "cswiki  0.158917099   -0.13720459\n",
       "fawiki  0.100208086    0.20422972\n",
       "frwiki -0.296630475    0.23219903\n",
       "hewiki  0.209087762   -0.03190380\n",
       "huwiki  0.054462378   -0.02018441\n",
       "hywiki -0.002171716   -0.02468044\n",
       "kowiki -0.596095191    0.41158582\n",
       "plwiki  0.182014363   -0.29564098\n",
       "ptwiki -0.094308163   -0.25189258\n",
       "ruwiki  0.080984825    0.28233519\n",
       "srwiki -0.208052604   -0.03818516\n",
       "svwiki -0.216830482    0.20467951\n",
       "trwiki  0.561135263   -0.52836053\n",
       "ukwiki -0.262928643    0.08079070\n",
       "viwiki  0.223099247    0.04588382\n",
       "\n",
       "with conditional variances for “wiki_db” "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ranef(click.model.4.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$wiki_db\n",
       "       (Intercept) hp_variantD reg_on_mobile hp_variantD:reg_on_mobile\n",
       "arwiki   -1.749966 -0.06195892   -0.04342845                -0.2598034\n",
       "cswiki   -1.776185 -0.06195892   -0.03792493                -0.2598034\n",
       "fawiki   -1.834894 -0.06195892    0.30350937                -0.2598034\n",
       "frwiki   -2.231732 -0.06195892    0.33147869                -0.2598034\n",
       "hewiki   -1.726014 -0.06195892    0.06737585                -0.2598034\n",
       "huwiki   -1.880639 -0.06195892    0.07909524                -0.2598034\n",
       "hywiki   -1.937274 -0.06195892    0.07459921                -0.2598034\n",
       "kowiki   -2.531197 -0.06195892    0.51086548                -0.2598034\n",
       "plwiki   -1.753087 -0.06195892   -0.19636132                -0.2598034\n",
       "ptwiki   -2.029410 -0.06195892   -0.15261293                -0.2598034\n",
       "ruwiki   -1.854117 -0.06195892    0.38161484                -0.2598034\n",
       "srwiki   -2.143154 -0.06195892    0.06109449                -0.2598034\n",
       "svwiki   -2.151932 -0.06195892    0.30395916                -0.2598034\n",
       "trwiki   -1.373967 -0.06195892   -0.42908088                -0.2598034\n",
       "ukwiki   -2.198030 -0.06195892    0.18007035                -0.2598034\n",
       "viwiki   -1.712003 -0.06195892    0.14516347                -0.2598034\n",
       "\n",
       "attr(,\"class\")\n",
       "[1] \"coef.mer\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef(click.model.4.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have only one model that is not singular, and that is the one with mobile as a group-level predictor. It has a significantly lower BIC, indicating that this is definitely a better fit for the data. Looking at the combined effects, we do find a lot of variation in the effect of mobile registration, with some wikis having a strong positive effect on task clicks, and some having a strong negative effect.\n",
    "\n",
    "## Time as a predictor\n",
    "\n",
    "Lastly, we add time as a predictor, in this case a variable measuring the number of weeks between when the user registered and the start of the experiment. This enables us to understand if the probability of a user editing changes as time progresses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 5: add time\n",
    "click.model.5 = glmer(formula = did_click ~ hp_variant * reg_on_mobile + ln_exp_weeks +\n",
    "                        (1 + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_click ~ hp_variant * reg_on_mobile + ln_exp_weeks + (1 +  \n",
       "    reg_on_mobile | wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 19578.3  19643.6  -9781.1  19562.3    26084 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.5095 -0.4021 -0.3616 -0.3248  3.6821 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.08903  0.2984        \n",
       "         reg_on_mobile 0.08594  0.2932   -0.66\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               -1.90881    0.09828 -19.422  < 2e-16 ***\n",
       "hp_variantD               -0.06194    0.04935  -1.255 0.209442    \n",
       "reg_on_mobile              0.09894    0.10119   0.978 0.328230    \n",
       "ln_exp_weeks              -0.02532    0.04319  -0.586 0.557775    \n",
       "hp_variantD:reg_on_mobile -0.25992    0.07619  -3.411 0.000646 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m ln_xp_\n",
       "hp_variantD -0.241                     \n",
       "reg_on_mobl -0.560  0.235              \n",
       "ln_exp_weks -0.456 -0.001  0.006       \n",
       "hp_vrntD:__  0.155 -0.648 -0.346  0.003"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(click.model.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 5.1: time in days\n",
    "click.model.5.1 = glmer(formula = did_click ~ hp_variant * reg_on_mobile + ln_exp_days +\n",
    "                        (1 + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users_train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: \n",
       "did_click ~ hp_variant * reg_on_mobile + ln_exp_days + (1 + reg_on_mobile |  \n",
       "    wiki_db)\n",
       "   Data: exp_users_train\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 19578.3  19643.7  -9781.2  19562.3    26084 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.5112 -0.4022 -0.3617 -0.3244  3.6759 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.08903  0.2984        \n",
       "         reg_on_mobile 0.08595  0.2932   -0.66\n",
       "Number of obs: 26092, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               -1.90182    0.10791 -17.624  < 2e-16 ***\n",
       "hp_variantD               -0.06188    0.04935  -1.254 0.209837    \n",
       "reg_on_mobile              0.09907    0.10118   0.979 0.327534    \n",
       "ln_exp_days               -0.01315    0.02500  -0.526 0.598864    \n",
       "hp_variantD:reg_on_mobile -0.25999    0.07618  -3.413 0.000643 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m ln_xp_\n",
       "hp_variantD -0.218                     \n",
       "reg_on_mobl -0.510  0.235              \n",
       "ln_exp_days -0.585 -0.003  0.004       \n",
       "hp_vrntD:__  0.140 -0.648 -0.346  0.005"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(click.model.5.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a similar result as for the other models we've fitted, there's not a significant effect of time. That might simply be because the experiment only lasted four weeks.\n",
    "\n",
    "## Model across the entire dataset\n",
    "\n",
    "Our previous models were trained on a random 80% of our dataset. We switch to the full dataset and model again to get a sense of the predictors across all available data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "## 7: full model\n",
    "click.model.full = glmer(formula = did_click ~ hp_variant * reg_on_mobile +\n",
    "                        (1 + reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
       "  Approximation) [glmerMod]\n",
       " Family: binomial  ( logit )\n",
       "Formula: did_click ~ hp_variant * reg_on_mobile + (1 + reg_on_mobile |  \n",
       "    wiki_db)\n",
       "   Data: exp_users\n",
       "\n",
       "     AIC      BIC   logLik deviance df.resid \n",
       " 24409.6  24468.3 -12197.8  24395.6    32608 \n",
       "\n",
       "Scaled residuals: \n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.5101 -0.4024 -0.3591 -0.3193  3.8267 \n",
       "\n",
       "Random effects:\n",
       " Groups  Name          Variance Std.Dev. Corr \n",
       " wiki_db (Intercept)   0.10084  0.3175        \n",
       "         reg_on_mobile 0.06848  0.2617   -0.56\n",
       "Number of obs: 32615, groups:  wiki_db, 16\n",
       "\n",
       "Fixed effects:\n",
       "                          Estimate Std. Error z value Pr(>|z|)    \n",
       "(Intercept)               -1.95994    0.08969 -21.852  < 2e-16 ***\n",
       "hp_variantD               -0.06905    0.04419  -1.562  0.11817    \n",
       "reg_on_mobile              0.10126    0.09159   1.106  0.26890    \n",
       "hp_variantD:reg_on_mobile -0.26354    0.06815  -3.867  0.00011 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Correlation of Fixed Effects:\n",
       "            (Intr) hp_vrD rg_n_m\n",
       "hp_variantD -0.233              \n",
       "reg_on_mobl -0.537  0.229       \n",
       "hp_vrntD:__  0.151 -0.647 -0.338"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(click.model.full)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "boundary (singular) fit: see ?isSingular\n",
      "\n"
     ]
    }
   ],
   "source": [
    "## 7: full model with group-level interaction\n",
    "click.model.full.2 = glmer(formula = did_click ~ hp_variant * reg_on_mobile +\n",
    "                        (1 + hp_variant * reg_on_mobile | wiki_db),\n",
    "                    family = binomial(link = \"logit\"), data = exp_users)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "summary(click.model.full.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the full dataset is fuller, there is still not enough variation in the effect of the variant to include it as a group-level variable. Thus, we stick with the model that has mobile as a group-level variable.\n",
    "\n",
    "Let's estimate the effects using the \"divide by 4 rule\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-6.58861214490764"
      ],
      "text/latex": [
       "-6.58861214490764"
      ],
      "text/markdown": [
       "-6.58861214490764"
      ],
      "text/plain": [
       "[1] -6.588612"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "100 * coef(click.model.full)$wiki_db$`hp_variantD:reg_on_mobile`[1] / 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So users seeing Variant D on mobile are associated with having at most a -6.6% likelihood of clicking on a suggested task.\n",
    "\n",
    "For the effect of mobile, we'll treat the population-level estimate as 0, since it's not found to be significant there. That means we'll estimate the group-level effects using just the random estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 16 × 2 of type chr</caption>\n",
       "<tbody>\n",
       "\t<tr><td>arwiki</td><td>-2.118 </td></tr>\n",
       "\t<tr><td>cswiki</td><td>0.88   </td></tr>\n",
       "\t<tr><td>fawiki</td><td>2.803  </td></tr>\n",
       "\t<tr><td>frwiki</td><td>6.012  </td></tr>\n",
       "\t<tr><td>hewiki</td><td>-0.324 </td></tr>\n",
       "\t<tr><td>huwiki</td><td>-1.414 </td></tr>\n",
       "\t<tr><td>hywiki</td><td>0.947  </td></tr>\n",
       "\t<tr><td>kowiki</td><td>8.116  </td></tr>\n",
       "\t<tr><td>plwiki</td><td>-6.868 </td></tr>\n",
       "\t<tr><td>ptwiki</td><td>-5.82  </td></tr>\n",
       "\t<tr><td>ruwiki</td><td>6.6    </td></tr>\n",
       "\t<tr><td>srwiki</td><td>-1.07  </td></tr>\n",
       "\t<tr><td>svwiki</td><td>4.976  </td></tr>\n",
       "\t<tr><td>trwiki</td><td>-12.357</td></tr>\n",
       "\t<tr><td>ukwiki</td><td>-0.884 </td></tr>\n",
       "\t<tr><td>viwiki</td><td>0.521  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 16 × 2 of type chr\n",
       "\\begin{tabular}{ll}\n",
       "\t arwiki & -2.118 \\\\\n",
       "\t cswiki & 0.88   \\\\\n",
       "\t fawiki & 2.803  \\\\\n",
       "\t frwiki & 6.012  \\\\\n",
       "\t hewiki & -0.324 \\\\\n",
       "\t huwiki & -1.414 \\\\\n",
       "\t hywiki & 0.947  \\\\\n",
       "\t kowiki & 8.116  \\\\\n",
       "\t plwiki & -6.868 \\\\\n",
       "\t ptwiki & -5.82  \\\\\n",
       "\t ruwiki & 6.6    \\\\\n",
       "\t srwiki & -1.07  \\\\\n",
       "\t svwiki & 4.976  \\\\\n",
       "\t trwiki & -12.357\\\\\n",
       "\t ukwiki & -0.884 \\\\\n",
       "\t viwiki & 0.521  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 16 × 2 of type chr\n",
       "\n",
       "| arwiki | -2.118  |\n",
       "| cswiki | 0.88    |\n",
       "| fawiki | 2.803   |\n",
       "| frwiki | 6.012   |\n",
       "| hewiki | -0.324  |\n",
       "| huwiki | -1.414  |\n",
       "| hywiki | 0.947   |\n",
       "| kowiki | 8.116   |\n",
       "| plwiki | -6.868  |\n",
       "| ptwiki | -5.82   |\n",
       "| ruwiki | 6.6     |\n",
       "| srwiki | -1.07   |\n",
       "| svwiki | 4.976   |\n",
       "| trwiki | -12.357 |\n",
       "| ukwiki | -0.884  |\n",
       "| viwiki | 0.521   |\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]   [,2]   \n",
       " [1,] arwiki -2.118 \n",
       " [2,] cswiki 0.88   \n",
       " [3,] fawiki 2.803  \n",
       " [4,] frwiki 6.012  \n",
       " [5,] hewiki -0.324 \n",
       " [6,] huwiki -1.414 \n",
       " [7,] hywiki 0.947  \n",
       " [8,] kowiki 8.116  \n",
       " [9,] plwiki -6.868 \n",
       "[10,] ptwiki -5.82  \n",
       "[11,] ruwiki 6.6    \n",
       "[12,] srwiki -1.07  \n",
       "[13,] svwiki 4.976  \n",
       "[14,] trwiki -12.357\n",
       "[15,] ukwiki -0.884 \n",
       "[16,] viwiki 0.521  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cbind(rownames(ranef(click.model.full)$wiki_db),\n",
    "      round(100 * ranef(click.model.full)$wiki_db$reg_on_mobile / 4, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the effect of mobile for Variant C varies from  -12.4% on Turkish to +8.1% in Korean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview table\n",
    "\n",
    "Since we've found that results vary by wiki, where the user registered, and what variant they saw, we create an overview table to show how the probability changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "click_counts = exp_users[did_click == 1, list(n_clicked = sum(.N)),\n",
    "                         by = c('wiki_db', 'reg_on_mobile', 'hp_variant')]\n",
    "merged_click_counts = merge(visit_counts, click_counts, by = c('wiki_db', 'reg_on_mobile', 'hp_variant'))\n",
    "merged_click_counts[, percent_clicked := 100 * n_clicked / n_visitors]\n",
    "merged_click_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "merged_click_counts[, platform := 'desktop']\n",
    "merged_click_counts[reg_on_mobile == 1, platform := 'mobile']\n",
    "merged_click_counts$platform = factor(merged_click_counts$platform)\n",
    "\n",
    "merged_click_counts$hp_variant = factor(merged_click_counts$hp_variant)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "plots = lapply(unique(merged_click_counts$wiki_db), function(w) {\n",
    "    ggplot(merged_click_counts[wiki_db == w], aes(x = platform, y = percent_clicked, fill = hp_variant)) +\n",
    "        theme_bw() +\n",
    "        theme(axis.title.x = element_text(size = rel(1.5)),\n",
    "            axis.text.x = element_text(size = rel(1.25)),\n",
    "            axis.title.y = element_text(size = rel(1.5)),\n",
    "            axis.text.y = element_text(size = rel(1.25))) +\n",
    "        scale_fill_brewer(\"Variant\", palette = 'Set1') +\n",
    "        labs(x = \"Platform\", y = \"Probability (in %)\", title = w) +\n",
    "        geom_col(position = \"dodge2\")\n",
    "})\n",
    "\n",
    "# ggsave(plot = g, file = \"graphs/tagged_edit_probabilities.png\",\n",
    "#       width = 14, height = 7, units = \"in\", dpi = \"retina\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
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t6uzsXHSkjHx8fCpSGQAA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U+Lvm6FOQOj/57OxspUuwLUVyXSkadtu2bZNTXaonchYAACAASURBVL169b744otn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\nKBC5DgAAQMlK0LAbOnSoEGLr1q2zZ8/W6XR5J+j1+s8+++zHH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HJiQk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\nAOsi1wEAAKiZBQ27o0ePCiHefvttnU5X7Oa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95G/N+OGHHyIjI2vX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KFDh8oTqlWr9vLLL0dEREydOjUgICA1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\nxcVl8uTJer1eCDFs2LB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E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\nAKhGyirY3b59WwjRoUOH4qtMjampqVURFgAAAOyIvA4AAKAaK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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1260,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width = 14, repr.plot.height = 21)\n",
    "grid.arrange(grobs = plots, ncol = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "\n",
    "## Additional analysis\n",
    "\n",
    "What's the probability difference of navigating and clicking across the dataset for C vs D?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.table: 4 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>platform</th><th scope=col>hp_variant</th><th scope=col>n_visitors</th><th scope=col>n_navigated</th><th scope=col>perc_navigated</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>desktop</td><td>C</td><td>9567</td><td>2267</td><td>23.69604</td></tr>\n",
       "\t<tr><td>desktop</td><td>D</td><td>9379</td><td>1854</td><td>19.76757</td></tr>\n",
       "\t<tr><td>mobile </td><td>C</td><td>6798</td><td>1008</td><td>14.82789</td></tr>\n",
       "\t<tr><td>mobile </td><td>D</td><td>6871</td><td> 875</td><td>12.73468</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.table: 4 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " platform & hp\\_variant & n\\_visitors & n\\_navigated & perc\\_navigated\\\\\n",
       " <fct> & <fct> & <int> & <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t desktop & C & 9567 & 2267 & 23.69604\\\\\n",
       "\t desktop & D & 9379 & 1854 & 19.76757\\\\\n",
       "\t mobile  & C & 6798 & 1008 & 14.82789\\\\\n",
       "\t mobile  & D & 6871 &  875 & 12.73468\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.table: 4 × 5\n",
       "\n",
       "| platform &lt;fct&gt; | hp_variant &lt;fct&gt; | n_visitors &lt;int&gt; | n_navigated &lt;int&gt; | perc_navigated &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| desktop | C | 9567 | 2267 | 23.69604 |\n",
       "| desktop | D | 9379 | 1854 | 19.76757 |\n",
       "| mobile  | C | 6798 | 1008 | 14.82789 |\n",
       "| mobile  | D | 6871 |  875 | 12.73468 |\n",
       "\n"
      ],
      "text/plain": [
       "  platform hp_variant n_visitors n_navigated perc_navigated\n",
       "1 desktop  C          9567       2267        23.69604      \n",
       "2 desktop  D          9379       1854        19.76757      \n",
       "3 mobile   C          6798       1008        14.82789      \n",
       "4 mobile   D          6871        875        12.73468      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "merged_nav_counts[, list(n_visitors = sum(n_visitors), n_navigated = sum(n_navigated),\n",
    "                      perc_navigated = 100 * sum(n_navigated) / sum(n_visitors)),\n",
    "              by = c('platform', 'hp_variant')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.table: 4 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>platform</th><th scope=col>hp_variant</th><th scope=col>n_visitors</th><th scope=col>n_clicked</th><th scope=col>perc_clicked</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>desktop</td><td>C</td><td>9567</td><td>1223</td><td>12.78353</td></tr>\n",
       "\t<tr><td>desktop</td><td>D</td><td>9379</td><td>1133</td><td>12.08018</td></tr>\n",
       "\t<tr><td>mobile </td><td>C</td><td>6798</td><td> 987</td><td>14.51898</td></tr>\n",
       "\t<tr><td>mobile </td><td>D</td><td>6871</td><td> 749</td><td>10.90089</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.table: 4 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " platform & hp\\_variant & n\\_visitors & n\\_clicked & perc\\_clicked\\\\\n",
       " <fct> & <fct> & <int> & <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t desktop & C & 9567 & 1223 & 12.78353\\\\\n",
       "\t desktop & D & 9379 & 1133 & 12.08018\\\\\n",
       "\t mobile  & C & 6798 &  987 & 14.51898\\\\\n",
       "\t mobile  & D & 6871 &  749 & 10.90089\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.table: 4 × 5\n",
       "\n",
       "| platform &lt;fct&gt; | hp_variant &lt;fct&gt; | n_visitors &lt;int&gt; | n_clicked &lt;int&gt; | perc_clicked &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| desktop | C | 9567 | 1223 | 12.78353 |\n",
       "| desktop | D | 9379 | 1133 | 12.08018 |\n",
       "| mobile  | C | 6798 |  987 | 14.51898 |\n",
       "| mobile  | D | 6871 |  749 | 10.90089 |\n",
       "\n"
      ],
      "text/plain": [
       "  platform hp_variant n_visitors n_clicked perc_clicked\n",
       "1 desktop  C          9567       1223      12.78353    \n",
       "2 desktop  D          9379       1133      12.08018    \n",
       "3 mobile   C          6798        987      14.51898    \n",
       "4 mobile   D          6871        749      10.90089    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "merged_click_counts[, list(n_visitors = sum(n_visitors), n_clicked = sum(n_clicked),\n",
    "                      perc_clicked = 100 * sum(n_clicked) / sum(n_visitors)),\n",
    "              by = c('platform', 'hp_variant')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "(1.409 - 0.820) / 1.409"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "32615"
      ],
      "text/latex": [
       "32615"
      ],
      "text/markdown": [
       "32615"
      ],
      "text/plain": [
       "[1] 32615"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(merged_click_counts$n_visitors)"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
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}