surprisal_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing Psychometric Predictive Power of Surprisal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook will walk us through how to analyze how language model surprisal predicts human reading times. The dataset contains eyetracking data for the Dundee corpus and self-paced reading data from the Natural Stories corpus. It has has been pre-processed for us (I can add code for this as well). In addition to surprisal, we will be using length and log frequency as predictors for reading time. To account for spillover effects (where previous information might affect processing of the current word), we also consider these three features for previous tokens.\n",
    "\n",
    "It is possible to use a CSV with quantities that are different from surprisal as well. This CSV should still have the control predictors of length and log unigram frequency, and the relevant predictors for previous tokens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "library(ggplot2)\n",
    "library(reshape2)\n",
    "library(dplyr)\n",
    "gpt2_data <- read.csv(\"gpt2_surprisal_rts.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'token'</li><li>'transcript_id'</li><li>'sentence_id'</li><li>'surprisal'</li><li>'oov'</li><li>'num_tokens'</li><li>'rt'</li><li>'token_uid'</li><li>'exclude_rt'</li><li>'word_length'</li><li>'log_freq'</li><li>'word'</li><li>'prev_freq_1'</li><li>'prev_len_1'</li><li>'prev_surprisal_1'</li><li>'prev_num_tokens_1'</li><li>'corpus'</li><li>'prev_freq_2'</li><li>'prev_len_2'</li><li>'prev_surprisal_2'</li><li>'prev_num_tokens_2'</li><li>'prev_freq_3'</li><li>'prev_len_3'</li><li>'prev_surprisal_3'</li><li>'prev_num_tokens_3'</li><li>'prev_freq_4'</li><li>'prev_len_4'</li><li>'prev_surprisal_4'</li><li>'prev_num_tokens_4'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'token'\n",
       "\\item 'transcript\\_id'\n",
       "\\item 'sentence\\_id'\n",
       "\\item 'surprisal'\n",
       "\\item 'oov'\n",
       "\\item 'num\\_tokens'\n",
       "\\item 'rt'\n",
       "\\item 'token\\_uid'\n",
       "\\item 'exclude\\_rt'\n",
       "\\item 'word\\_length'\n",
       "\\item 'log\\_freq'\n",
       "\\item 'word'\n",
       "\\item 'prev\\_freq\\_1'\n",
       "\\item 'prev\\_len\\_1'\n",
       "\\item 'prev\\_surprisal\\_1'\n",
       "\\item 'prev\\_num\\_tokens\\_1'\n",
       "\\item 'corpus'\n",
       "\\item 'prev\\_freq\\_2'\n",
       "\\item 'prev\\_len\\_2'\n",
       "\\item 'prev\\_surprisal\\_2'\n",
       "\\item 'prev\\_num\\_tokens\\_2'\n",
       "\\item 'prev\\_freq\\_3'\n",
       "\\item 'prev\\_len\\_3'\n",
       "\\item 'prev\\_surprisal\\_3'\n",
       "\\item 'prev\\_num\\_tokens\\_3'\n",
       "\\item 'prev\\_freq\\_4'\n",
       "\\item 'prev\\_len\\_4'\n",
       "\\item 'prev\\_surprisal\\_4'\n",
       "\\item 'prev\\_num\\_tokens\\_4'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'token'\n",
       "2. 'transcript_id'\n",
       "3. 'sentence_id'\n",
       "4. 'surprisal'\n",
       "5. 'oov'\n",
       "6. 'num_tokens'\n",
       "7. 'rt'\n",
       "8. 'token_uid'\n",
       "9. 'exclude_rt'\n",
       "10. 'word_length'\n",
       "11. 'log_freq'\n",
       "12. 'word'\n",
       "13. 'prev_freq_1'\n",
       "14. 'prev_len_1'\n",
       "15. 'prev_surprisal_1'\n",
       "16. 'prev_num_tokens_1'\n",
       "17. 'corpus'\n",
       "18. 'prev_freq_2'\n",
       "19. 'prev_len_2'\n",
       "20. 'prev_surprisal_2'\n",
       "21. 'prev_num_tokens_2'\n",
       "22. 'prev_freq_3'\n",
       "23. 'prev_len_3'\n",
       "24. 'prev_surprisal_3'\n",
       "25. 'prev_num_tokens_3'\n",
       "26. 'prev_freq_4'\n",
       "27. 'prev_len_4'\n",
       "28. 'prev_surprisal_4'\n",
       "29. 'prev_num_tokens_4'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"token\"             \"transcript_id\"     \"sentence_id\"      \n",
       " [4] \"surprisal\"         \"oov\"               \"num_tokens\"       \n",
       " [7] \"rt\"                \"token_uid\"         \"exclude_rt\"       \n",
       "[10] \"word_length\"       \"log_freq\"          \"word\"             \n",
       "[13] \"prev_freq_1\"       \"prev_len_1\"        \"prev_surprisal_1\" \n",
       "[16] \"prev_num_tokens_1\" \"corpus\"            \"prev_freq_2\"      \n",
       "[19] \"prev_len_2\"        \"prev_surprisal_2\"  \"prev_num_tokens_2\"\n",
       "[22] \"prev_freq_3\"       \"prev_len_3\"        \"prev_surprisal_3\" \n",
       "[25] \"prev_num_tokens_3\" \"prev_freq_4\"       \"prev_len_4\"       \n",
       "[28] \"prev_surprisal_4\"  \"prev_num_tokens_4\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colnames(gpt2_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 29</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>token</th><th scope=col>transcript_id</th><th scope=col>sentence_id</th><th scope=col>surprisal</th><th scope=col>oov</th><th scope=col>num_tokens</th><th scope=col>rt</th><th scope=col>token_uid</th><th scope=col>exclude_rt</th><th scope=col>word_length</th><th scope=col>⋯</th><th scope=col>prev_surprisal_2</th><th scope=col>prev_num_tokens_2</th><th scope=col>prev_freq_3</th><th scope=col>prev_len_3</th><th scope=col>prev_surprisal_3</th><th scope=col>prev_num_tokens_3</th><th scope=col>prev_freq_4</th><th scope=col>prev_len_4</th><th scope=col>prev_surprisal_4</th><th scope=col>prev_num_tokens_4</th></tr>\n",
       "\t<tr><th></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><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>⋯</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>renaissance</td><td>13</td><td>0</td><td>16.9963360</td><td>False</td><td>1</td><td>396.4000</td><td>1</td><td>0</td><td>11</td><td>⋯</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>in         </td><td>13</td><td>0</td><td> 4.7848325</td><td>False</td><td>1</td><td>163.2500</td><td>2</td><td>0</td><td> 2</td><td>⋯</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>is         </td><td>13</td><td>0</td><td> 3.5461557</td><td>False</td><td>1</td><td>185.0000</td><td>5</td><td>0</td><td> 2</td><td>⋯</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>turning    </td><td>13</td><td>0</td><td>10.2781897</td><td>False</td><td>1</td><td>326.7778</td><td>6</td><td>0</td><td> 7</td><td>⋯</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>out        </td><td>13</td><td>0</td><td> 2.4884927</td><td>False</td><td>1</td><td>186.8000</td><td>7</td><td>0</td><td> 3</td><td>⋯</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>to         </td><td>13</td><td>0</td><td> 0.3600574</td><td>False</td><td>1</td><td>214.7500</td><td>8</td><td>0</td><td> 2</td><td>⋯</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 29\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & token & transcript\\_id & sentence\\_id & surprisal & oov & num\\_tokens & rt & token\\_uid & exclude\\_rt & word\\_length & ⋯ & prev\\_surprisal\\_2 & prev\\_num\\_tokens\\_2 & prev\\_freq\\_3 & prev\\_len\\_3 & prev\\_surprisal\\_3 & prev\\_num\\_tokens\\_3 & prev\\_freq\\_4 & prev\\_len\\_4 & prev\\_surprisal\\_4 & prev\\_num\\_tokens\\_4\\\\\n",
       "  & <chr> & <int> & <int> & <dbl> & <chr> & <int> & <dbl> & <int> & <int> & <int> & ⋯ & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & renaissance & 13 & 0 & 16.9963360 & False & 1 & 396.4000 & 1 & 0 & 11 & ⋯ & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n",
       "\t2 & in          & 13 & 0 &  4.7848325 & False & 1 & 163.2500 & 2 & 0 &  2 & ⋯ & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n",
       "\t3 & is          & 13 & 0 &  3.5461557 & False & 1 & 185.0000 & 5 & 0 &  2 & ⋯ & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n",
       "\t4 & turning     & 13 & 0 & 10.2781897 & False & 1 & 326.7778 & 6 & 0 &  7 & ⋯ & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n",
       "\t5 & out         & 13 & 0 &  2.4884927 & False & 1 & 186.8000 & 7 & 0 &  3 & ⋯ & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n",
       "\t6 & to          & 13 & 0 &  0.3600574 & False & 1 & 214.7500 & 8 & 0 &  2 & ⋯ & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 29\n",
       "\n",
       "| <!--/--> | token &lt;chr&gt; | transcript_id &lt;int&gt; | sentence_id &lt;int&gt; | surprisal &lt;dbl&gt; | oov &lt;chr&gt; | num_tokens &lt;int&gt; | rt &lt;dbl&gt; | token_uid &lt;int&gt; | exclude_rt &lt;int&gt; | word_length &lt;int&gt; | ⋯ ⋯ | prev_surprisal_2 &lt;dbl&gt; | prev_num_tokens_2 &lt;dbl&gt; | prev_freq_3 &lt;dbl&gt; | prev_len_3 &lt;dbl&gt; | prev_surprisal_3 &lt;dbl&gt; | prev_num_tokens_3 &lt;dbl&gt; | prev_freq_4 &lt;dbl&gt; | prev_len_4 &lt;dbl&gt; | prev_surprisal_4 &lt;dbl&gt; | prev_num_tokens_4 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | renaissance | 13 | 0 | 16.9963360 | False | 1 | 396.4000 | 1 | 0 | 11 | ⋯ | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n",
       "| 2 | in          | 13 | 0 |  4.7848325 | False | 1 | 163.2500 | 2 | 0 |  2 | ⋯ | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n",
       "| 3 | is          | 13 | 0 |  3.5461557 | False | 1 | 185.0000 | 5 | 0 |  2 | ⋯ | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n",
       "| 4 | turning     | 13 | 0 | 10.2781897 | False | 1 | 326.7778 | 6 | 0 |  7 | ⋯ | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n",
       "| 5 | out         | 13 | 0 |  2.4884927 | False | 1 | 186.8000 | 7 | 0 |  3 | ⋯ | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n",
       "| 6 | to          | 13 | 0 |  0.3600574 | False | 1 | 214.7500 | 8 | 0 |  2 | ⋯ | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |\n",
       "\n"
      ],
      "text/plain": [
       "  token       transcript_id sentence_id surprisal  oov   num_tokens rt      \n",
       "1 renaissance 13            0           16.9963360 False 1          396.4000\n",
       "2 in          13            0            4.7848325 False 1          163.2500\n",
       "3 is          13            0            3.5461557 False 1          185.0000\n",
       "4 turning     13            0           10.2781897 False 1          326.7778\n",
       "5 out         13            0            2.4884927 False 1          186.8000\n",
       "6 to          13            0            0.3600574 False 1          214.7500\n",
       "  token_uid exclude_rt word_length ⋯ prev_surprisal_2 prev_num_tokens_2\n",
       "1 1         0          11          ⋯ NA               NA               \n",
       "2 2         0           2          ⋯ NA               NA               \n",
       "3 5         0           2          ⋯ NA               NA               \n",
       "4 6         0           7          ⋯ NA               NA               \n",
       "5 7         0           3          ⋯ NA               NA               \n",
       "6 8         0           2          ⋯ NA               NA               \n",
       "  prev_freq_3 prev_len_3 prev_surprisal_3 prev_num_tokens_3 prev_freq_4\n",
       "1 NA          NA         NA               NA                NA         \n",
       "2 NA          NA         NA               NA                NA         \n",
       "3 NA          NA         NA               NA                NA         \n",
       "4 NA          NA         NA               NA                NA         \n",
       "5 NA          NA         NA               NA                NA         \n",
       "6 NA          NA         NA               NA                NA         \n",
       "  prev_len_4 prev_surprisal_4 prev_num_tokens_4\n",
       "1 NA         NA               NA               \n",
       "2 NA         NA               NA               \n",
       "3 NA         NA               NA               \n",
       "4 NA         NA               NA               \n",
       "5 NA         NA               NA               \n",
       "6 NA         NA               NA               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(gpt2_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now separate the data by corpus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "dundee_gpt <- gpt2_data[gpt2_data$corpus == \"dundee\",]\n",
    "natural_stories_gpt <- gpt2_data[gpt2_data$corpus == \"natural_stories\",]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use formulas following [Wilcox et al (2020)](https://arxiv.org/abs/2006.01912). We compute the psychometric predictive power as the per-token Delta Log Likelihood - or how much a model that considers surprisal as a feature improves over the control predictors of length and log frequency. This is the model's aggregate log likelihood normalized over the number of tokens in the corpus.\n",
    "\n",
    "The formulas for Dundee and Natural Stories are different since the spillover effects for self paced reading data are longer than eyetracking data. So for the Dundee corpus we consider the previous word's surprisal, and for the Natural Stories corpus we look at the previous three words.\n",
    "\n",
    "We use a generalized linear model (GLM), following previous work showing a linear relationship between surprisal and reading time. \n",
    "\n",
    "To use a predictor other than surprisal, simply change the name of `surprisal` in the formulas to the predictor you are using."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "et_control_formula <- 'rt ~ log_freq * word_length + prev_freq_1 * prev_len_1'\n",
    "et_surprisal_formula <- 'rt ~ surprisal + prev_surprisal_1 + log_freq * word_length + prev_freq_1 * prev_len_1'\n",
    "\n",
    "spr_control_formula <- 'rt ~ log_freq * word_length + prev_freq_1 * prev_len_1 + prev_freq_2 * prev_len_2 + prev_freq_3 * prev_len_3'\n",
    "spr_surprisal_formula <- 'rt ~ surprisal + prev_surprisal_1 + prev_surprisal_2 + prev_surprisal_3 + log_freq * word_length + prev_freq_1 * prev_len_1 + prev_freq_2 * prev_len_2 + prev_freq_3 * prev_len_3'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "predictive_power <- function(data, control_formula, surprisal_formula, tokenization, log_values) {\n",
    "    control_model <- glm(control_formula, data, family = 'gaussian')\n",
    "    surprisal_model <- glm(surprisal_formula, data, family = 'gaussian')\n",
    "    if (log_values) {\n",
    "        print(tokenization)\n",
    "        print(summary(surprisal_model)$coefficients)\n",
    "    }\n",
    "    (logLik(surprisal_model) - logLik(control_model)) / nrow(data)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, where we call the `predictive_power` function, we also get the features associated with the regression models. Overall, surprisal is a statistically significant predictor of reading time and the predictive power is over 1, so that tells us that surprisal does tell us something that word length and frequency don't. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results for the Dundee corpus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"bpe\"\n",
      "                          Estimate Std. Error    t value     Pr(>|t|)\n",
      "(Intercept)            220.2726663 4.25017300  51.826753 0.000000e+00\n",
      "surprisal                1.8340967 0.09499248  19.307809 1.201773e-82\n",
      "prev_surprisal_1         0.8558745 0.09024642   9.483750 2.596678e-21\n",
      "log_freq                 5.5268917 0.95210122   5.804941 6.492396e-09\n",
      "word_length             -0.7408914 0.69248186  -1.069907 2.846681e-01\n",
      "prev_freq_1              2.4640931 0.95458146   2.581333 9.845835e-03\n",
      "prev_len_1              -8.8410591 0.70087316 -12.614350 2.099166e-36\n",
      "log_freq:word_length    -2.7657004 0.16713078 -16.548122 2.772926e-61\n",
      "prev_freq_1:prev_len_1  -1.1447509 0.16959805  -6.749788 1.502861e-11\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'log Lik.' 0.006696996 (df=10)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictive_power(dundee_gpt, et_control_formula, et_surprisal_formula, \"bpe\", TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results for the Natural Stories corpus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"bpe\"\n",
      "                           Estimate Std. Error    t value     Pr(>|t|)\n",
      "(Intercept)            317.67153186 6.89744827 46.0563848 0.000000e+00\n",
      "surprisal                1.03500218 0.09937174 10.4154583 3.356685e-25\n",
      "prev_surprisal_1         0.45831894 0.09285295  4.9359651 8.178487e-07\n",
      "prev_surprisal_2         0.12933909 0.08762222  1.4760992 1.399667e-01\n",
      "prev_surprisal_3         0.07842217 0.08743729  0.8968962 3.698082e-01\n",
      "log_freq                 3.70192901 0.99005608  3.7391104 1.862929e-04\n",
      "word_length             -3.88473964 0.78228422 -4.9658929 7.016736e-07\n",
      "prev_freq_1              0.71545150 1.02279355  0.6995072 4.842606e-01\n",
      "prev_len_1              -2.24576078 0.80689800 -2.7832028 5.398384e-03\n",
      "prev_freq_2             -0.75211580 0.98009692 -0.7673892 4.428786e-01\n",
      "prev_len_2               0.14034742 0.79757645  0.1759674 8.603252e-01\n",
      "prev_freq_3              0.41829672 0.95890954  0.4362213 6.626910e-01\n",
      "prev_len_3              -0.91624883 0.78640404 -1.1651121 2.440173e-01\n",
      "log_freq:word_length    -1.46334017 0.19128828 -7.6499208 2.309062e-14\n",
      "prev_freq_1:prev_len_1  -0.79319440 0.19849362 -3.9960700 6.512951e-05\n",
      "prev_freq_2:prev_len_2  -0.14426272 0.19248566 -0.7494726 4.536001e-01\n",
      "prev_freq_3:prev_len_3  -0.31038358 0.18895307 -1.6426490 1.005050e-01\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'log Lik.' 0.01084273 (df=18)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictive_power(natural_stories_gpt, spr_control_formula, spr_surprisal_formula, \"bpe\", TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One issue with training one regression model on the entire dataset is that it is being evaluated on data it was trained on. To address this issue, we perform 10-fold cross-validation, where a model is trained on a random selection of 9/10 of the data and evaluated on 1/10 of the data. This process runs 10 times, such that each tenth of the data gets to be the validation set. We then make a boxplot of the predictive power values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "test_data_loglik <- function(model, test_data) {\n",
    "    predictions <- predict(model, test_data)\n",
    "    stdev <- sigma(model)\n",
    "    dnorm(test_data$rt, predictions, stdev, log = TRUE)\n",
    "}\n",
    "\n",
    "cross_validate <- function(data, indices, control_formula, surprisal_formula) {\n",
    "    data<-data[indices,]\n",
    "    folds <- cut(seq(1,nrow(data)),breaks=10,labels=FALSE) # this is the same for each model\n",
    "    predictive_power <- seq(1:10)\n",
    "    for(i in 1:10){\n",
    "        test_indices <- which(folds==i)\n",
    "        test_data <- data[test_indices, ]\n",
    "        train_data <- data[-test_indices, ]\n",
    "        fold_control_model <- glm(control_formula, train_data, family = 'gaussian')\n",
    "        fold_surprisal_model <- glm(surprisal_formula, train_data, family = 'gaussian')\n",
    "        surprisal_diff <- test_data_loglik(fold_surprisal_model, test_data) - test_data_loglik(fold_control_model, test_data)\n",
    "        predictive_power[i] <- mean(surprisal_diff) # summed per-token log likelihoods, divided by number of tokens \n",
    "        }\n",
    "    predictive_power\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No id variables; using all as measure variables\n",
      "\n"
     ]
    }
   ],
   "source": [
    "dundee_shuffled <- sample(nrow(dundee_gpt))\n",
    "ns_shuffled <- sample(nrow(natural_stories_gpt))\n",
    "cv_results <- data.frame(dundee = cross_validate(dundee_gpt, dundee_shuffled, et_control_formula, et_surprisal_formula),\n",
    "natural_stories = cross_validate(natural_stories_gpt, ns_shuffled, spr_control_formula, spr_surprisal_formula)\n",
    ")\n",
    "cv_results <- melt(cv_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
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6V7+umnS/osrr766rb99tv7OdwvvvjiXARIvEMQQAAB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\nAgQIECBAgEATBP4/4VXGTR1wOZgAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot <- ggplot(cv_results, aes(x=variable, y = value, color = variable)) + geom_boxplot()\n",
    "plot + ylab(expression(paste(Delta, \"LogLik\"))) + xlab(\"Corpus\") + labs(title = \"Psychometric Predictive Power of GPT2 Surprisal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Natural Stories corpus is larger and more syntactically complex, so the variance in predictive power could be higher for this reason."
   ]
  }
 ],
 "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": "4.0.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}