Group_33_Project_Report.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Knowledge Level Using User Knowledge Data\n",
    "\n",
    "A user knowledge model has the goal of improving conceptual understanding in users. Its system has the ability to adapt to a certain user’s individual learning ability, improving their competence in grasping new concepts. Therefore, creating a well built learning model is crucial in creating dynamic and automated learning environments. \n",
    "\n",
    "The following project uses a user knowledge modeling data set collected by Hamdi Tolga Kahraman (2013) to answer the following question:\n",
    "\n",
    "**How high will somebody’s knowledge score be based on their study time, exam performance, and prerequisite knowledge?**\n",
    "\n",
    "The data set contains 405 observations from participants who prepared for and took an exam on Electrical DC Machines. They took two exams: one on prerequisite material, and one on targeted material based on prerequisite material. It includes columns for the degree of study time and exam performance for both prerequisite knowledge and new knowledge topics, the degree of repetition, and the user’s knowledge level. The user knowledge level column has four categories: very low, low, middle, and high. No information about the age group or educational background of subjects was found. \n",
    "\n",
    "\n",
    "All columns are recognized as type double with the exception of the user knowledge level (character variable). The data appears to be already normalized since all values (except the user’s knowledge level) fit in the range of 0 and 1. The dataset is almost tidy - however there is a description of the data in an extra column, but the number data is tidy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "________________________________________________________________________________________________________________________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# *Data Analysis*\n",
    "We begin by analyzing our data. First we load the libraries and set our seed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── \u001b[1mAttaching packages\u001b[22m ─────────────────────────────────────── tidyverse 1.3.0 ──\n",
      "\n",
      "\u001b[32m✔\u001b[39m \u001b[34mggplot2\u001b[39m 3.3.2     \u001b[32m✔\u001b[39m \u001b[34mpurrr  \u001b[39m 0.3.4\n",
      "\u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.0.3     \u001b[32m✔\u001b[39m \u001b[34mdplyr  \u001b[39m 1.0.2\n",
      "\u001b[32m✔\u001b[39m \u001b[34mtidyr  \u001b[39m 1.1.2     \u001b[32m✔\u001b[39m \u001b[34mstringr\u001b[39m 1.4.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34mreadr  \u001b[39m 1.3.1     \u001b[32m✔\u001b[39m \u001b[34mforcats\u001b[39m 0.5.0\n",
      "\n",
      "Warning message:\n",
      "“package ‘ggplot2’ was built under R version 4.0.1”\n",
      "Warning message:\n",
      "“package ‘tibble’ was built under R version 4.0.2”\n",
      "Warning message:\n",
      "“package ‘tidyr’ was built under R version 4.0.2”\n",
      "Warning message:\n",
      "“package ‘dplyr’ was built under R version 4.0.2”\n",
      "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
      "\n",
      "Warning message:\n",
      "“package ‘tidymodels’ was built under R version 4.0.2”\n",
      "── \u001b[1mAttaching packages\u001b[22m ────────────────────────────────────── tidymodels 0.1.1 ──\n",
      "\n",
      "\u001b[32m✔\u001b[39m \u001b[34mbroom    \u001b[39m 0.7.0      \u001b[32m✔\u001b[39m \u001b[34mrecipes  \u001b[39m 0.1.13\n",
      "\u001b[32m✔\u001b[39m \u001b[34mdials    \u001b[39m 0.0.9      \u001b[32m✔\u001b[39m \u001b[34mrsample  \u001b[39m 0.0.7 \n",
      "\u001b[32m✔\u001b[39m \u001b[34minfer    \u001b[39m 0.5.4      \u001b[32m✔\u001b[39m \u001b[34mtune     \u001b[39m 0.1.1 \n",
      "\u001b[32m✔\u001b[39m \u001b[34mmodeldata\u001b[39m 0.0.2      \u001b[32m✔\u001b[39m \u001b[34mworkflows\u001b[39m 0.2.0 \n",
      "\u001b[32m✔\u001b[39m \u001b[34mparsnip  \u001b[39m 0.1.3      \u001b[32m✔\u001b[39m \u001b[34myardstick\u001b[39m 0.0.7 \n",
      "\n",
      "Warning message:\n",
      "“package ‘broom’ was built under R version 4.0.2”\n",
      "Warning message:\n",
      "“package ‘dials’ was built under R version 4.0.2”\n",
      "Warning message:\n",
      "“package ‘infer’ was built under R version 4.0.3”\n",
      "Warning message:\n",
      "“package ‘modeldata’ was built under R version 4.0.1”\n",
      "Warning message:\n",
      "“package ‘parsnip’ was built under R version 4.0.2”\n",
      "Warning message:\n",
      "“package ‘recipes’ was built under R version 4.0.1”\n",
      "Warning message:\n",
      "“package ‘tune’ was built under R version 4.0.2”\n",
      "Warning message:\n",
      "“package ‘workflows’ was built under R version 4.0.2”\n",
      "Warning message:\n",
      "“package ‘yardstick’ was built under R version 4.0.2”\n",
      "── \u001b[1mConflicts\u001b[22m ───────────────────────────────────────── tidymodels_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mscales\u001b[39m::\u001b[32mdiscard()\u001b[39m masks \u001b[34mpurrr\u001b[39m::discard()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m   masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mrecipes\u001b[39m::\u001b[32mfixed()\u001b[39m  masks \u001b[34mstringr\u001b[39m::fixed()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m      masks \u001b[34mstats\u001b[39m::lag()\n",
      "\u001b[31m✖\u001b[39m \u001b[34myardstick\u001b[39m::\u001b[32mspec()\u001b[39m masks \u001b[34mreadr\u001b[39m::spec()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mrecipes\u001b[39m::\u001b[32mstep()\u001b[39m   masks \u001b[34mstats\u001b[39m::step()\n",
      "\n",
      "Registered S3 method overwritten by 'GGally':\n",
      "  method from   \n",
      "  +.gg   ggplot2\n",
      "\n",
      "Warning message:\n",
      "“package ‘cowplot’ was built under R version 4.0.3”\n"
     ]
    }
   ],
   "source": [
    "library(tidyverse)\n",
    "library(repr)\n",
    "library(readxl)\n",
    "library(tidymodels)\n",
    "library(GGally)\n",
    "library(cowplot)\n",
    "\n",
    "set.seed(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we will read our dataset from the web; we will clean and wrangle it into a tidy format. We will unselect the data description and two empty columns, rename columns and mutate the classification label to a factor. All predictor variables will be used to later determine which of them are appropriate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "New names:\n",
      "* `` -> ...7\n",
      "* `` -> ...8\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 6 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>targeted_study_time</th><th scope=col>repetition</th><th scope=col>prereq_study_time</th><th scope=col>prereq_exam_performance</th><th scope=col>targeted_exam_performance</th><th scope=col>understanding_level</th></tr>\n",
       "\t<tr><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;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>0.00</td><td>very_low</td></tr>\n",
       "\t<tr><td>0.08</td><td>0.08</td><td>0.10</td><td>0.24</td><td>0.90</td><td>High    </td></tr>\n",
       "\t<tr><td>0.06</td><td>0.06</td><td>0.05</td><td>0.25</td><td>0.33</td><td>Low     </td></tr>\n",
       "\t<tr><td>0.10</td><td>0.10</td><td>0.15</td><td>0.65</td><td>0.30</td><td>Middle  </td></tr>\n",
       "\t<tr><td>0.08</td><td>0.08</td><td>0.08</td><td>0.98</td><td>0.24</td><td>Low     </td></tr>\n",
       "\t<tr><td>0.09</td><td>0.15</td><td>0.40</td><td>0.10</td><td>0.66</td><td>Middle  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 6 × 6\n",
       "\\begin{tabular}{llllll}\n",
       " targeted\\_study\\_time & repetition & prereq\\_study\\_time & prereq\\_exam\\_performance & targeted\\_exam\\_performance & understanding\\_level\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & very\\_low\\\\\n",
       "\t 0.08 & 0.08 & 0.10 & 0.24 & 0.90 & High    \\\\\n",
       "\t 0.06 & 0.06 & 0.05 & 0.25 & 0.33 & Low     \\\\\n",
       "\t 0.10 & 0.10 & 0.15 & 0.65 & 0.30 & Middle  \\\\\n",
       "\t 0.08 & 0.08 & 0.08 & 0.98 & 0.24 & Low     \\\\\n",
       "\t 0.09 & 0.15 & 0.40 & 0.10 & 0.66 & Middle  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 6 × 6\n",
       "\n",
       "| targeted_study_time &lt;dbl&gt; | repetition &lt;dbl&gt; | prereq_study_time &lt;dbl&gt; | prereq_exam_performance &lt;dbl&gt; | targeted_exam_performance &lt;dbl&gt; | understanding_level &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | very_low |\n",
       "| 0.08 | 0.08 | 0.10 | 0.24 | 0.90 | High     |\n",
       "| 0.06 | 0.06 | 0.05 | 0.25 | 0.33 | Low      |\n",
       "| 0.10 | 0.10 | 0.15 | 0.65 | 0.30 | Middle   |\n",
       "| 0.08 | 0.08 | 0.08 | 0.98 | 0.24 | Low      |\n",
       "| 0.09 | 0.15 | 0.40 | 0.10 | 0.66 | Middle   |\n",
       "\n"
      ],
      "text/plain": [
       "  targeted_study_time repetition prereq_study_time prereq_exam_performance\n",
       "1 0.00                0.00       0.00              0.00                   \n",
       "2 0.08                0.08       0.10              0.24                   \n",
       "3 0.06                0.06       0.05              0.25                   \n",
       "4 0.10                0.10       0.15              0.65                   \n",
       "5 0.08                0.08       0.08              0.98                   \n",
       "6 0.09                0.15       0.40              0.10                   \n",
       "  targeted_exam_performance understanding_level\n",
       "1 0.00                      very_low           \n",
       "2 0.90                      High               \n",
       "3 0.33                      Low                \n",
       "4 0.30                      Middle             \n",
       "5 0.24                      Low                \n",
       "6 0.66                      Middle             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "downloaded_data <- download.file(\"https://archive.ics.uci.edu/ml/machine-learning-databases/00257/Data_User_Modeling_Dataset_Hamdi%20Tolga%20KAHRAMAN.xls\", \n",
    "                                \"knowledge.xls\")\n",
    "\n",
    "user_knowledge_data <- read_excel(\"knowledge.xls\", \n",
    "                                  sheet = 2) %>%  #data we want is on page 2 of the excel file\n",
    "    select(-\"...7\", -\"...8\", -\"Attribute Information:\")  # unselect unnecessary columns\n",
    "\n",
    "# rename columns\n",
    "colnames(user_knowledge_data) <- c(\"targeted_study_time\", \n",
    "                                   \"repetition\", \n",
    "                                   \"prereq_study_time\", \n",
    "                                   \"prereq_exam_performance\", \n",
    "                                   \"targeted_exam_performance\", \n",
    "                                   \"understanding_level\")\n",
    "\n",
    "# change class label to factor \n",
    "user_knowledge_data <- user_knowledge_data %>%\n",
    "    mutate(understanding_level = as_factor(understanding_level)) \n",
    "\n",
    "head(user_knowledge_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "                                Table.1 User Knowledge Data\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the data is tidied, we can split it into training and testing sets. Prop values were not discussed in class, so a default 75% split will be used. The testing data set is put aside until the model is built."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(1)\n",
    "knowledge_split <- initial_split(user_knowledge_data, prop = .75, strata = understanding_level)\n",
    "knowledge_train <- training(knowledge_split)\n",
    "knowledge_test <- testing(knowledge_split)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examining Our Data\n",
    "Next, the training data is summarized in informative tables. These include:\n",
    "- means, max, min of each predictor\n",
    "- how many of each label exist in the data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 1 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>target_study_time_mean</th><th scope=col>repetition_mean</th><th scope=col>prereq_study_time_mean</th><th scope=col>prereq_exam_performance_mean</th><th scope=col>targeted_exam_performance_mean</th></tr>\n",
       "\t<tr><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><td>0.3750154</td><td>0.3527385</td><td>0.4640769</td><td>0.4234872</td><td>0.4546821</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " target\\_study\\_time\\_mean & repetition\\_mean & prereq\\_study\\_time\\_mean & prereq\\_exam\\_performance\\_mean & targeted\\_exam\\_performance\\_mean\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 0.3750154 & 0.3527385 & 0.4640769 & 0.4234872 & 0.4546821\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 5\n",
       "\n",
       "| target_study_time_mean &lt;dbl&gt; | repetition_mean &lt;dbl&gt; | prereq_study_time_mean &lt;dbl&gt; | prereq_exam_performance_mean &lt;dbl&gt; | targeted_exam_performance_mean &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 0.3750154 | 0.3527385 | 0.4640769 | 0.4234872 | 0.4546821 |\n",
       "\n"
      ],
      "text/plain": [
       "  target_study_time_mean repetition_mean prereq_study_time_mean\n",
       "1 0.3750154              0.3527385       0.4640769             \n",
       "  prereq_exam_performance_mean targeted_exam_performance_mean\n",
       "1 0.4234872                    0.4546821                     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "knowledge_train_means <- knowledge_train %>%\n",
    "    summarize(target_study_time_mean = mean(targeted_study_time),\n",
    "          repetition_mean = mean(repetition),\n",
    "          prereq_study_time_mean = mean(prereq_study_time),\n",
    "          prereq_exam_performance_mean = mean(prereq_exam_performance),\n",
    "          targeted_exam_performance_mean = mean(targeted_exam_performance)) \n",
    "knowledge_train_means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "                            Table.2 User Knowledge Data Predictor Means\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the mean table, the data appears to be well scaled since the means are all within a similar range. This suggests that we may not need to scale/center our data, although this will be done to ensure accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 1 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>target_study_time_max</th><th scope=col>repetition_max</th><th scope=col>prereq_study_time_max</th><th scope=col>prereq_exam_performance_max</th><th scope=col>targeted_exam_performance_max</th></tr>\n",
       "\t<tr><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><td>0.99</td><td>0.9</td><td>0.95</td><td>0.99</td><td>0.93</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " target\\_study\\_time\\_max & repetition\\_max & prereq\\_study\\_time\\_max & prereq\\_exam\\_performance\\_max & targeted\\_exam\\_performance\\_max\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 0.99 & 0.9 & 0.95 & 0.99 & 0.93\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 5\n",
       "\n",
       "| target_study_time_max &lt;dbl&gt; | repetition_max &lt;dbl&gt; | prereq_study_time_max &lt;dbl&gt; | prereq_exam_performance_max &lt;dbl&gt; | targeted_exam_performance_max &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 0.99 | 0.9 | 0.95 | 0.99 | 0.93 |\n",
       "\n"
      ],
      "text/plain": [
       "  target_study_time_max repetition_max prereq_study_time_max\n",
       "1 0.99                  0.9            0.95                 \n",
       "  prereq_exam_performance_max targeted_exam_performance_max\n",
       "1 0.99                        0.93                         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 1 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>target_study_time_min</th><th scope=col>repetition_min</th><th scope=col>prereq_study_time_min</th><th scope=col>prereq_exam_performance_min</th><th scope=col>targeted_exam_performance_min</th></tr>\n",
       "\t<tr><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><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " target\\_study\\_time\\_min & repetition\\_min & prereq\\_study\\_time\\_min & prereq\\_exam\\_performance\\_min & targeted\\_exam\\_performance\\_min\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 0 & 0 & 0 & 0 & 0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 5\n",
       "\n",
       "| target_study_time_min &lt;dbl&gt; | repetition_min &lt;dbl&gt; | prereq_study_time_min &lt;dbl&gt; | prereq_exam_performance_min &lt;dbl&gt; | targeted_exam_performance_min &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 0 | 0 | 0 | 0 | 0 |\n",
       "\n"
      ],
      "text/plain": [
       "  target_study_time_min repetition_min prereq_study_time_min\n",
       "1 0                     0              0                    \n",
       "  prereq_exam_performance_min targeted_exam_performance_min\n",
       "1 0                           0                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "knowledge_train_max <- knowledge_train %>% \n",
    "    summarize(target_study_time_max = max(targeted_study_time),\n",
    "          repetition_max = max(repetition),\n",
    "          prereq_study_time_max = max(prereq_study_time),\n",
    "          prereq_exam_performance_max = max(prereq_exam_performance),\n",
    "          targeted_exam_performance_max = max(targeted_exam_performance)) \n",
    "knowledge_train_max\n",
    "\n",
    "knowledge_train_min <- knowledge_train %>%\n",
    "    summarize(target_study_time_min = min(targeted_study_time),\n",
    "          repetition_min = min(repetition),\n",
    "          prereq_study_time_min = min(prereq_study_time),\n",
    "          prereq_exam_performance_min = min(prereq_exam_performance),\n",
    "          targeted_exam_performance_min = min(targeted_exam_performance)) \n",
    "knowledge_train_min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "                        Table.3 User Knowledge Data Predictors Min & Max\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The min/max values show the range of each predictor (0-0.99), and confirm that some of the participants indeed had very high or very low levels of understanding. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`summarise()` ungrouping output (override with `.groups` argument)\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 4 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>understanding_level</th><th scope=col>count</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>very_low</td><td>20</td></tr>\n",
       "\t<tr><td>High    </td><td>47</td></tr>\n",
       "\t<tr><td>Low     </td><td>62</td></tr>\n",
       "\t<tr><td>Middle  </td><td>66</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 4 × 2\n",
       "\\begin{tabular}{ll}\n",
       " understanding\\_level & count\\\\\n",
       " <fct> & <int>\\\\\n",
       "\\hline\n",
       "\t very\\_low & 20\\\\\n",
       "\t High     & 47\\\\\n",
       "\t Low      & 62\\\\\n",
       "\t Middle   & 66\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 4 × 2\n",
       "\n",
       "| understanding_level &lt;fct&gt; | count &lt;int&gt; |\n",
       "|---|---|\n",
       "| very_low | 20 |\n",
       "| High     | 47 |\n",
       "| Low      | 62 |\n",
       "| Middle   | 66 |\n",
       "\n"
      ],
      "text/plain": [
       "  understanding_level count\n",
       "1 very_low            20   \n",
       "2 High                47   \n",
       "3 Low                 62   \n",
       "4 Middle              66   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "knowledge_labels <- knowledge_train %>%\n",
    "group_by(understanding_level) %>%\n",
    "    summarize(count = n())\n",
    "knowledge_labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "          Table.4 User Knowledge Data Understanding Level Count\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Regarding the amount of observations in each category, it can be seen a small amount of participants scored very low. Additionally, a small group scored very high. The distributions of every category will help choose the appropriate K value. The K value should not be double our smallest category (very_low). Otherwise, the smallest category will never have enough k-nn \"voting power\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing Our Data\n",
    "Next, we will use plots to observe trends between predictor variables. We will compare our predictors to each other and note how distinct the clusters of `understanding_level` are. Tighter clusters with more separation will make it easier for our KNN model to predict labels correctly. Thus, the more appropriate predictors will be in our final model. The strength of the cluster 'tightness', along with forward selection will help determine which predictors should be used in the final model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in knowledge_train %>% ggpairs(columns = 1:5, mapping = ggplot2::aes(colour = understanding_level)): could not find function \"%>%\"\n",
     "output_type": "error",
     "traceback": [
      "Error in knowledge_train %>% ggpairs(columns = 1:5, mapping = ggplot2::aes(colour = understanding_level)): could not find function \"%>%\"\nTraceback:\n"
     ]
    }
   ],
   "source": [
    "options(repr.plot.width = 10, repr.plot.height = 12)\n",
    "\n",
    "pairs <- knowledge_train %>%\n",
    "    ggpairs(columns = 1:5, mapping=ggplot2::aes(colour = understanding_level)) +\n",
    "        theme(legend.position = \"bottom\") +\n",
    "        labs(tag = \"Figure.1\") +\n",
    "        ggtitle(\"Predictor Combinations\") +\n",
    "        theme(text = element_text(size = 12))\n",
    "\n",
    "pairs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Legend**\n",
    "\n",
    "Green: High\n",
    "\n",
    "Purple: Middle\n",
    "\n",
    "Cyan: Low\n",
    "\n",
    "Red: Very Low"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot, it is visible that targeted_exam_performance should be included in our model, since all other predictors produce tightly clustered groups of `understanding_levels` in comparison. Furthermore, `prereq_exam_performance` and `targeted_exam_performance` form the tightest clustering. However, other predictors coupled with `targeted_exam_performance` form separate clusters in a similar manner. For now, we can be confident that both `prereq_exam_performance` and `targeted_exam_performance` should be used as predictors in our final model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choosing Predictors with Forward Selection\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To choose our final predictors, forward selection will be performed. It creates a model for every possible combination of predictors and compares the accuracies of each one. The combination of predictors that gives us the highest accuracy will be chosen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ****Step 1****\n",
    "First, a tibble that stores our results will be created to begin forward selection. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 0 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>size</th><th scope=col>model_string</th><th scope=col>accuracy</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 0 × 3\n",
       "\\begin{tabular}{lll}\n",
       " size & model\\_string & accuracy\\\\\n",
       " <int> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 0 × 3\n",
       "\n",
       "| size &lt;int&gt; | model_string &lt;chr&gt; | accuracy &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "\n"
      ],
      "text/plain": [
       "     size model_string accuracy"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "accuracies <- tibble(size = integer(), \n",
    "                     model_string = character(), \n",
    "                     accuracy = numeric())\n",
    "accuracies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ****Step 2****\n",
    "Since the same specifications are used throughout the process, we will create it the beginning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_spec <- nearest_neighbor(weight_func = \"rectangular\", neighbors = tune()) %>%\n",
    "  set_engine(\"kknn\") %>%\n",
    "  set_mode(\"classification\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ****Step 3****\n",
    "Next, a 10-vold cross-validation object is created. A 10-fold is used instead of a 5-fold object since the dataset is relatively small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(1)\n",
    "user_vfold <- vfold_cv(knowledge_train, v = 10, strata = understanding_level)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ****Step 4****\n",
    "Since no forward selection exists in R, several things should be prepared. First we get the names of all the potential predictors, and store the total number of predictors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "names <- colnames(knowledge_train %>% select(-understanding_level))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_total <- length(names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The selected predictors should be stored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "selected <- c()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ****Step 5****\n",
    "Now forward selection is performed: we use a loop to iterate through all the unselected predictors to determine the ones that gives the highest accuracy, and store the results into the tibble we created earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 5 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>size</th><th scope=col>model_string</th><th scope=col>accuracy</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1</td><td>understanding_level ~ targeted_exam_performance                                                                         </td><td>0.8524896</td></tr>\n",
       "\t<tr><td>2</td><td>understanding_level ~ targeted_exam_performance+prereq_exam_performance                                                 </td><td>0.9596032</td></tr>\n",
       "\t<tr><td>3</td><td>understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition                                      </td><td>0.9384670</td></tr>\n",
       "\t<tr><td>4</td><td>understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition+targeted_study_time                  </td><td>0.8767502</td></tr>\n",
       "\t<tr><td>5</td><td>understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition+targeted_study_time+prereq_study_time</td><td>0.7860109</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 5 × 3\n",
       "\\begin{tabular}{lll}\n",
       " size & model\\_string & accuracy\\\\\n",
       " <int> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 1 & understanding\\_level \\textasciitilde{} targeted\\_exam\\_performance                                                                          & 0.8524896\\\\\n",
       "\t 2 & understanding\\_level \\textasciitilde{} targeted\\_exam\\_performance+prereq\\_exam\\_performance                                                  & 0.9596032\\\\\n",
       "\t 3 & understanding\\_level \\textasciitilde{} targeted\\_exam\\_performance+prereq\\_exam\\_performance+repetition                                       & 0.9384670\\\\\n",
       "\t 4 & understanding\\_level \\textasciitilde{} targeted\\_exam\\_performance+prereq\\_exam\\_performance+repetition+targeted\\_study\\_time                   & 0.8767502\\\\\n",
       "\t 5 & understanding\\_level \\textasciitilde{} targeted\\_exam\\_performance+prereq\\_exam\\_performance+repetition+targeted\\_study\\_time+prereq\\_study\\_time & 0.7860109\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 5 × 3\n",
       "\n",
       "| size &lt;int&gt; | model_string &lt;chr&gt; | accuracy &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 1 | understanding_level ~ targeted_exam_performance                                                                          | 0.8524896 |\n",
       "| 2 | understanding_level ~ targeted_exam_performance+prereq_exam_performance                                                  | 0.9596032 |\n",
       "| 3 | understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition                                       | 0.9384670 |\n",
       "| 4 | understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition+targeted_study_time                   | 0.8767502 |\n",
       "| 5 | understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition+targeted_study_time+prereq_study_time | 0.7860109 |\n",
       "\n"
      ],
      "text/plain": [
       "  size\n",
       "1 1   \n",
       "2 2   \n",
       "3 3   \n",
       "4 4   \n",
       "5 5   \n",
       "  model_string                                                                                                            \n",
       "1 understanding_level ~ targeted_exam_performance                                                                         \n",
       "2 understanding_level ~ targeted_exam_performance+prereq_exam_performance                                                 \n",
       "3 understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition                                      \n",
       "4 understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition+targeted_study_time                  \n",
       "5 understanding_level ~ targeted_exam_performance+prereq_exam_performance+repetition+targeted_study_time+prereq_study_time\n",
       "  accuracy \n",
       "1 0.8524896\n",
       "2 0.9596032\n",
       "3 0.9384670\n",
       "4 0.8767502\n",
       "5 0.7860109"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1)\n",
    "# for every size from 1 to the total number of predictors\n",
    "for (i in 1:n_total) {\n",
    "    # for every predictor still not added yet\n",
    "    accs <- list()\n",
    "    models <- list()\n",
    "    for (j in 1:length(names)) {\n",
    "        # create a model string for this combination of predictors\n",
    "        preds_new <- c(selected, names[[j]])\n",
    "        model_string <- paste(\"understanding_level\", \"~\", paste(preds_new, collapse=\"+\"))\n",
    "\n",
    "        # create a recipe from the model string\n",
    "        user_recipe <- recipe(as.formula(model_string), \n",
    "                              data = knowledge_train) %>%\n",
    "        step_scale(all_predictors()) %>%\n",
    "        step_center(all_predictors())\n",
    "\n",
    "        # tune the KNN classifier with these predictors, \n",
    "        # and collect the accuracy for the best K\n",
    "        acc <- workflow() %>%\n",
    "          add_recipe(user_recipe) %>%\n",
    "          add_model(knn_spec) %>%\n",
    "          tune_grid(resamples = user_vfold, grid = 10) %>%\n",
    "          collect_metrics() %>%\n",
    "          filter(.metric == \"accuracy\") %>%\n",
    "          summarize(mx = max(mean))\n",
    "        acc <- acc$mx %>% unlist()\n",
    "\n",
    "        # add this result to the dataframe\n",
    "        accs[[j]] <- acc\n",
    "        models[[j]] <- model_string\n",
    "    }\n",
    "    jstar <- which.max(unlist(accs))\n",
    "    accuracies <- accuracies %>%\n",
    "      add_row(size = i, \n",
    "              model_string = models[[jstar]], \n",
    "              accuracy = accs[[jstar]])\n",
    "    selected <- c(selected, names[[jstar]])\n",
    "    names <- names[-jstar]\n",
    "}\n",
    "accuracies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "                     Table.5 Accuracy Based On Predictor Combinations\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion of Choosing Predictors\n",
    "By comparing the accuracies, we can conclude that we should use `targeted_exam_performance` and `prerequisite_exam_performance` as our predictors, since these give the highest accuracy of ~96%. This perfectly matches what we had seen in our visualization earlier, with the tightly clustered groups when we plotted `targeted_exam_performance` and `prerequisite_exam_performance`\n",
    "against each other."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Visualizing Our Results**\n",
    "\n",
    "There are two ways that we will visualize the results of our final model.\n",
    "\n",
    "Firstly, because we expect the accuracy of our model to be very high, and because our data set is quite small, we do not expect many observations from our testing set to be incorrectly predicted. We can thus create two plots, with the x and y axis as our two predictors: one with the observations colour-coded as their predicted class lable, and another with the observations colour-coded as their actual class labels. Then, we can simply circle the observations that the model got incorrect and discuss these inaccuracies.\n",
    "\n",
    "Secondly, because we are interested in analyzing whether the model potentially leaned towards over- or under-predicting the knowledge level of our observations, we can use a confusion matrix to compare false positives and negatives. We can discuss whether a higher false prediction (i.e. predicting an incorrect `high` knowledge level for a `low` observation) or a lower false prediction (i.e. predicting an incorrect `low` knowledge level for a `high` observation) is more meaningful/has greater consequences."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Model Expectations**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have fully analyzed our data, we expect to find that students with higher prerequisite knowledge and exam score will be classified as having a higher knowledge level.     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ***Our Final Classification Model***\n",
    "\n",
    "Now that we know what predictors we are going to use - `targeted_exam_performance` and `prerequisite_exam_performance` - we can create our final model. Note that we use the training data throughout this process.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all, we will create a final recipe with these two predictors. As previously mentioned, we do not *need* to scale and center our data since our data appears to be standardized already, however, we will standardize it again to ensure we get the best possible results from our model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "user_recipe_final <- recipe(understanding_level ~ prereq_exam_performance + targeted_exam_performance, data = knowledge_train) %>%\n",
    "  step_scale(all_predictors()) %>%\n",
    "  step_center(all_predictors())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will need a knn model specification as well, specifying `neighbors = tune()` since we will first be choosing our k value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_spec <- nearest_neighbor(weight_func = \"rectangular\", neighbors = tune()) %>%\n",
    "  set_engine(\"kknn\") %>%\n",
    "  set_mode(\"classification\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To help us choose our k value, we will cross validate. So we create a 10-fold cross-validation model. Recall that we use a 10-fold because our dataset is small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(1)\n",
    "user_vfold <- vfold_cv(knowledge_train, v = 10, strata = understanding_level)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's create a tibble with different k values. As discussed previously, the range of k value that we choose to test depends largely on the size of our smallest class label in our training data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that our smallest class label is `very_low` with only 20 observations. This means that our k value must not *exceed* a value of 40, since any k above 40 would mean that the `very_low` class label will *never* have enough voting power - even if all 20 of the `very_low` observations are within the k nearest points, it would never achieve a majority vote. Our model would never predict the `very_low` category. \n",
    "\n",
    "To reduce the possibility of a 'tie', we will let our 'maximum-k-value-to-try' be 39 instead of 40. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "gridvals <- tibble(neighbors = seq(1,39))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we combine everything into a workflow and collect metrics on our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn_results <- workflow() %>%\n",
    "  add_recipe(user_recipe_final) %>%\n",
    "  add_model(knn_spec) %>%\n",
    "  tune_grid(resamples = user_vfold, grid = gridvals) %>%\n",
    "  collect_metrics()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Filter for the accuracy metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "accuracies <- knn_results %>%\n",
    "  filter(.metric == \"accuracy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us create a graph to visualize the relationship between K values and accuracies. This will help us choose our k value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABLAAAAWgCAMAAAB5XkrSAAADAFBMVEUAAAABAQECAgIDAwME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\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 720,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "accuracy_vs_k <- ggplot(accuracies, aes(x = neighbors, y = mean)) +\n",
    "  geom_point() +\n",
    "  geom_line() +\n",
    "  labs(x = \"Neighbors\", y = \"Accuracy Estimate\") +\n",
    "  labs(tag = \"Figure.2\") +\n",
    "  ggtitle(\"Accuracy vs. K-value\") +\n",
    "  theme(text = element_text(size = 12))\n",
    "\n",
    "accuracy_vs_k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can decide which k value to use. To do this, we will keep three principles in mind. Our k value must:\n",
    "1. ensure we get rough optimal accuracy\n",
    "2. be relatively stable (i.e. increasing or decreasing the k value by a small amount doesn't change the accuracy of our model too much)\n",
    "3. not be too large\n",
    "\n",
    "We can see that between k = 1 and k = 10, our k values are quite high, stable, and obviously not too large. We also note that the accuracy of our model decreases sharply after k = 10, so we do not want to choose our k value to be greater than 10. Furthermore, while there is a seemingly big dip in the k values from k = 2 to k = 5, note that the scale of the x axis means the dip looks much bigger than it truly is. So we know we want to look for a k in that area. \n",
    "\n",
    "Since the k values don't change too much within k = 1 and k = 10, we are free to choose a k that gives us the highest accuracy within this range. This value would be either k = 6 or k = 7. Because their accuracies are exactly the same, we then move to comparing how much the accuracies change when we increase and decrease the k value. \n",
    "\n",
    "Observe that the difference in accuracy between from k = 7 to k = 8 is greater than the difference in accuracy between k = 5 and k = 6. For this reason, we will choose **k = 6**. However, note that the differences between k = 6 and k = 7 are so incredibly minute that it likely would not impact our model significantly if we had chosen k = 7. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ***Our Final Classification Model With K = 6***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we should create a new specification model with k = 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "user_spec_final <- nearest_neighbor(weight_func = \"rectangular\", neighbors = 6) %>%\n",
    "  set_engine(\"kknn\") %>%\n",
    "  set_mode(\"classification\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We put the new specification into the workflow and reuse the previous recipe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "user_fit_final <- workflow() %>%\n",
    "    add_model(user_spec_final) %>%\n",
    "    add_recipe(user_recipe_final) %>%\n",
    "    fit(knowledge_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us predict the test set that we separated earlier. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "user_prediction <- user_fit_final %>%\n",
    "    predict(knowledge_test) %>%\n",
    "    bind_cols(knowledge_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let us view the accuracy of our prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A tibble: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>.metric</th><th scope=col>.estimator</th><th scope=col>.estimate</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>accuracy</td><td>multiclass</td><td>0.9365079</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 1 × 3\n",
       "\\begin{tabular}{lll}\n",
       " .metric & .estimator & .estimate\\\\\n",
       " <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t accuracy & multiclass & 0.9365079\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 1 × 3\n",
       "\n",
       "| .metric &lt;chr&gt; | .estimator &lt;chr&gt; | .estimate &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| accuracy | multiclass | 0.9365079 |\n",
       "\n"
      ],
      "text/plain": [
       "  .metric  .estimator .estimate\n",
       "1 accuracy multiclass 0.9365079"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_prediction_accuracy <-  user_prediction %>%\n",
    "  metrics(truth = understanding_level, estimate = .pred_class) %>%\n",
    "  filter(.metric == \"accuracy\")\n",
    "\n",
    "user_prediction_accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    Table.6 Accuracy Of Optimized K Value\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will analyze the results of our classifiers after we have visualized our results also via plots and a confusion matrix. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization of model results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can visualize our results by plotting two graphs as previously described: one that classifies the observations by their predicted class, and one that classifies them by their actual class. We can then find the incorrectly classified points, circle them, and later analyze them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAACWAAAAPACAIAAAA+Q9WZAAAACXBIWXMAABJ0AAASdAHeZh94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\n0LY+hgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 1200
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width = 20, repr.plot.height = 8)\n",
    "\n",
    "# create vectors containing the coordinates of the incorrectly-labelled points to circle\n",
    "upper_left_point <- c(0.22,0.66)\n",
    "lower_left_points <- c(0.26,0.22)\n",
    "lower_right_point <- c(0.99,0.24)\n",
    "\n",
    "# predicted labels plot\n",
    "user_predicted_plot <- user_prediction %>% \n",
    "    ggplot(aes(x = prereq_exam_performance, y = targeted_exam_performance, color = .pred_class)) +\n",
    "        geom_point() + \n",
    "        labs(x = \"Prereq exam performance\", y = \"Targeted exam performance\", color = \"Predicted user understanding level\") +\n",
    "        ggtitle(\"Predicted user understanding level\") +\n",
    "        # now we circle the incorrectly labelled points\n",
    "        annotate(\"path\", \n",
    "                     x=upper_left_point[1] + 0.01*cos(seq(0,2*pi,length.out=100)),\n",
    "                     y=upper_left_point[2] + 0.02*sin(seq(0,2*pi,length.out=100))) +\n",
    "         annotate(\"path\", \n",
    "                     x=lower_left_points[1] + 0.02*cos(seq(0,2*pi,length.out=100)),\n",
    "                     y=lower_left_points[2] + 0.05*sin(seq(0,2*pi,length.out=100))) +\n",
    "        annotate(\"path\", \n",
    "                     x=lower_right_point[1] + 0.03*cos(seq(0,2*pi,length.out=100)),\n",
    "                     y=lower_right_point[2] + 0.02*sin(seq(0,2*pi,length.out=100))) +\n",
    "        labs(tag = \"Figure.4\") +\n",
    "        theme(text = element_text(size = 14))\n",
    "\n",
    "# actual labels plot\n",
    "user_class_plot <- user_prediction %>% \n",
    "    ggplot(aes(x = prereq_exam_performance, y = targeted_exam_performance, color = understanding_level)) +\n",
    "        geom_point() + \n",
    "        labs(x = \"Prereq exam performance\", y = \"Targeted exam performance\", color = \"Predicted user understanding level\") +\n",
    "        ggtitle(\"Actual user understanding level\") +\n",
    "        labs(tag = \"Figure.3\") +\n",
    "        theme(text = element_text(size = 14))\n",
    "\n",
    "\n",
    "plot_grid(user_class_plot, user_predicted_plot, nrow = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confusion Matrix\n",
    "\n",
    "The final tool in our toolkit for analyzing the results of our model is the confusion matrix. Let's create one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Truth\n",
       "Prediction very_low High Low Middle\n",
       "  very_low        2    0   0      0\n",
       "  High            0   15   0      0\n",
       "  Low             2    0  20      0\n",
       "  Middle          0    1   1     22"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_mat <- user_prediction %>%\n",
    "    conf_mat(truth = understanding_level, estimate = .pred_class)\n",
    "user_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    Table.7 Confusion Matrix\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Final Analysis**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using three analysis tools (accuracy levels, two visualizations, and the confusion matrix) it is possible to analyze the model and its results.\n",
    "\n",
    "As expected, we found that students with higher prerequisite knowledge and exam score will be classified as having a higher knowledge level.\n",
    "\n",
    "These findings could highlight the importance of having a solid foundation of basic knowledge prior to learning more complex materials, and describe how the amount of time studied influences one’s knowledge level. Some future questions that our analysis could lead to are \"what factors determine/influence exam performance?\" and \"what other study methods, other than the amount of time studied, can influence exam performance?\". \n",
    "\n",
    "---\n",
    "## Discussion - Model Accuracy \n",
    "\n",
    "The accuracy of our classifier is high (<90%). Although this might indicate incorrect procedure use upon closer inspection, this matches our expectations. \n",
    "\n",
    "Firstly, forward selection concluded that when two predictors were used, accuracy was at its highest (≈95%). This accuracy occured when a value of k = 6 was used Lastly, in our initial visualization we noticed extremely tight clustering between our `targeted_exam_performance` and `prerequisite_exam_performance` predictors. This visualization explains why our classifier accuracy is this high: a correctly chosen k value and tight clustering signifies that the model will be more efficient in classifying observations.\n",
    "\n",
    "---\n",
    "\n",
    "This accuracy is reflected in our two plots (note - there are only 4 labeled points).  Additionally, some of these points were difficult to label (except the upper left observation), as they were all on the border of two classes. The point might be an anomaly; it is surrounded by middle observations, and is incorrectly classified as high in the original dataset (thus it is incorrect).\n",
    "\n",
    "---\n",
    "The confusion matrix describes the type and amount of incorrect predictions made by the model. Since there are 4 different labels, it is impossible to classify the prediction types as “negative” or “positive”. Instead, they were grouped into two categories - \n",
    "\n",
    "1. **overestimate**: This occurs when the model predicts a *higher* than expected knowledge level for an observation.\n",
    "2. **underestimate**: This is when the model predicts a *lower* than expected knowledge for an observation.\n",
    "    \n",
    "Given the context of our data, two conditions are used to analyze the contextual accuracy of the data:\n",
    "\n",
    "### a. we consider **overestimates** to have \"worse\" consequences than underestimates. \n",
    "\n",
    "### b. the more knowledge levels a prediction \"skips\", the \"worse\" the consequences.\n",
    "\n",
    "*Worse* consequences can be explained as having more severe “real-world” consequences.\n",
    "\n",
    "Consider the following scenario: \n",
    "\n",
    "An online, self-learning module continuously takes input from the user to understand what their current knowledge level is based on previous exam scores. The module is building up an understanding of how well the student understands the topic. Say the module gives students quizzes. It chooses the difficulty of questions to present to the student based on what it thinks the student's understanding level is. Then we consider the following further scenarios: \n",
    "\n",
    "1. It is less favorable to give a student an extremely easy question than an easy one, since an overly easy question will not aid in learning progression. \n",
    "2. It is more favorable to five a student a difficult question than an overly difficult one, as an overly difficult question may discourage students, decreasing motivation. \n",
    "3. Regardless of model accuracy, simpler questions are more effective at reinforcing student understanding in comparison to difficult ones. More difficult questions might be outside of the student’s knowledge scope, while simpler questions test current knowledge.Thus, a smaller challenge will be more beneficial in helping students test their current knowledge, which outweighs the meager benefits of using difficult questions. \n",
    "\n",
    "Points 1 and 2 highlight point b above. Point 3 highlights point a. \n",
    "\n",
    "\n",
    "Another scenario-\n",
    "An employer is open for hiring, and there are two candidates they must choose between. To ensure that the employee's knowledge level is up to par, it is more favorable to underestimate one's knowledge level, than to overestimate their knowledge level. Although this might seem unfair for employees presenting an accurate knowledge level, if one employee is presenting an inflated knowledge level, this precaution prevents them from being accepted.   \n",
    "\n",
    "These two scenarios help us understand that it is better for our model to underestimate user knowledge to a small degree, versus overestimate user knowledge to a large degree. With that in mind, let us analyze our confusion matrix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "          Truth\n",
       "Prediction very_low High Low Middle\n",
       "  very_low        2    0   0      0\n",
       "  High            0   15   0      0\n",
       "  Low             2    0  20      0\n",
       "  Middle          0    1   1     22"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "user_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model made 4 incorrect classifications. Let's categorize them based on what we discussed above. \n",
    "\n",
    "- 3 observations were underestimated (two were supposed to be `low`, but predicted `very_low`; one was supposed to be `middle` but predicted `low`)\n",
    "- 1 observation was overestimated (supposed to be `middle`, but predicted `high`)\n",
    "\n",
    "Thus our model has performed well according to the context-based metrics we discussed. It has predicted more underestimates than overestimates, and each inaccurate prediction was only one category off (i.e. degree of inaccuracy is small). It's important to note that because our data set is so small, the significance of these findings is not incredibly high."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "There are, however, some issues with our model that we can discuss also. \n",
    "\n",
    "Firstly, our data set is very small. Had we had access to a larger data set, it is likely that our model's accuracy would not be this high. There would be many more anomalies in our data like the point in the upper left corner of our plot. Secondly, our model unfortunately doesn't use the much greater variety of data that we have access to: the other predictors. It just so happens that the correlation between our class label and our predictors was strongest in the two predictors we picked, however, it would be interesting to see what other correlations could be drawn from the other predictors. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "We can conclude that our model's accuracy is incredibly high, and also performed well in context-based scenarios. We also note, however, that this high accuracy is partially credited towards our small data set. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Citations\n",
    "\n",
    "1. Kahraman, H. T., Sagiroglu, S., & Colak, I. (2013). The development of intuitive knowledge classifier and the modeling of domain dependent data. *Knowledge-Based Systems, 37*, 283-295.\n",
    "\n",
    "2. Kahraman, H. T. (2009). Designing and Application of Web-Based Adaptive Intelligent Education System. Gazi University Ph. D. Thesis, Turkey, 1-156.\n"
   ]
  }
 ],
 "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": "4.0.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}