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   "source": [
    "### Dealing with repeated measurements - Exercises & Answers"
   ]
  },
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   "id": "40313b91-40d7-4727-82b2-eaf82368a2cd",
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    "### 1. Educational hierarchies\n",
    "One of the classic examples of using linear mixed models is in education, because the models can incorporate the variation that students contribute to tests, being that they're in different classrooms in different schools. \n",
    "\n",
    "Our first exercise is to examine a simple relationship - what is the association between the number of maths homework assignments a student completes and their scores on their mathematics exam? The dataset however has information on this relatonship from *10* different schools, and we want to incorporate that variability (because some schools may teach mathematics better or worse than others) into our model. \n",
    "\n",
    "The dataset is available here: https://raw.githubusercontent.com/SuryaThiru/hierarchical-model-blog/refs/heads/master/mlmldata.csv\n",
    "\n",
    "First import the usual things we need to get started:"
   ]
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   "id": "b01d8bae-9b53-405c-a323-6e1f19661ee8",
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   "source": [
    "# Your answer here\n",
    "# Imports\n",
    "import pandas as pd # dataframes\n",
    "import seaborn as sns # plots\n",
    "import statsmodels.formula.api as smf # Models\n",
    "import marginaleffects as me # marginal effects\n",
    "import numpy as np # numpy for some functions\n",
    "import statsmodels.tools.eval_measures as measures\n",
    "\n",
    "# Set the style for plots\n",
    "sns.set_style('whitegrid')\n",
    "sns.set_context('talk')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f7ec32d-a063-4b41-a97b-638913826f09",
   "metadata": {},
   "source": [
    "Next, read in the data. There are a lot of columns here but we do not need many, only `schid` (school identifier), `homework`, the number of assignments they completed, and `math`, the students score on a mathematics exam. Read into a dataframe called `school`, show the top 10 rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dc1a21d1-e391-4bfe-8c60-eab3beba5652",
   "metadata": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>schid</th>\n",
       "      <th>stuid</th>\n",
       "      <th>ses</th>\n",
       "      <th>meanses</th>\n",
       "      <th>homework</th>\n",
       "      <th>white</th>\n",
       "      <th>parented</th>\n",
       "      <th>public</th>\n",
       "      <th>ratio</th>\n",
       "      <th>percmin</th>\n",
       "      <th>math</th>\n",
       "      <th>sex</th>\n",
       "      <th>race</th>\n",
       "      <th>sctype</th>\n",
       "      <th>cstr</th>\n",
       "      <th>scsize</th>\n",
       "      <th>urban</th>\n",
       "      <th>region</th>\n",
       "      <th>schnum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "    <tr>\n",
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       "      <td>7472</td>\n",
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       "      <td>-0.39</td>\n",
       "      <td>-0.482609</td>\n",
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       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7472</td>\n",
       "      <td>13</td>\n",
       "      <td>-0.80</td>\n",
       "      <td>-0.482609</td>\n",
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       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7472</td>\n",
       "      <td>17</td>\n",
       "      <td>-0.72</td>\n",
       "      <td>-0.482609</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>42</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7472</td>\n",
       "      <td>27</td>\n",
       "      <td>-0.74</td>\n",
       "      <td>-0.482609</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>43</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
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       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7472</td>\n",
       "      <td>28</td>\n",
       "      <td>-0.58</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
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       "      <td>57</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
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       "      <td>30</td>\n",
       "      <td>-0.83</td>\n",
       "      <td>-0.482609</td>\n",
       "      <td>5</td>\n",
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       "      <td>2</td>\n",
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       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>33</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
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       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7472</td>\n",
       "      <td>36</td>\n",
       "      <td>-0.51</td>\n",
       "      <td>-0.482609</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>64</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>7472</td>\n",
       "      <td>37</td>\n",
       "      <td>-0.56</td>\n",
       "      <td>-0.482609</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>7472</td>\n",
       "      <td>42</td>\n",
       "      <td>0.21</td>\n",
       "      <td>-0.482609</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>56</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   schid  stuid   ses   meanses  homework  white  parented  public  ratio  \\\n",
       "0   7472      3 -0.13 -0.482609         1      1         2       1     19   \n",
       "1   7472      8 -0.39 -0.482609         0      1         2       1     19   \n",
       "2   7472     13 -0.80 -0.482609         0      1         2       1     19   \n",
       "3   7472     17 -0.72 -0.482609         1      1         2       1     19   \n",
       "4   7472     27 -0.74 -0.482609         2      1         2       1     19   \n",
       "5   7472     28 -0.58 -0.482609         1      1         2       1     19   \n",
       "6   7472     30 -0.83 -0.482609         5      1         2       1     19   \n",
       "7   7472     36 -0.51 -0.482609         1      1         3       1     19   \n",
       "8   7472     37 -0.56 -0.482609         1      1         2       1     19   \n",
       "9   7472     42  0.21 -0.482609         2      1         3       1     19   \n",
       "\n",
       "   percmin  math  sex  race  sctype  cstr  scsize  urban  region  schnum  \n",
       "0        0    48    2     4       1     2       3      2       2       1  \n",
       "1        0    48    1     4       1     2       3      2       2       1  \n",
       "2        0    53    1     4       1     2       3      2       2       1  \n",
       "3        0    42    1     4       1     2       3      2       2       1  \n",
       "4        0    43    2     4       1     2       3      2       2       1  \n",
       "5        0    57    2     4       1     2       3      2       2       1  \n",
       "6        0    33    2     4       1     2       3      2       2       1  \n",
       "7        0    64    1     4       1     2       3      2       2       1  \n",
       "8        0    36    2     4       1     2       3      2       2       1  \n",
       "9        0    56    2     4       1     2       3      2       2       1  "
      ]
     },
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Read in data\n",
    "school = pd.read_csv('https://raw.githubusercontent.com/SuryaThiru/hierarchical-model-blog/refs/heads/master/mlmldata.csv')\n",
    "school.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5860ae76-fdd7-4e95-8b93-aaee8b743c15",
   "metadata": {},
   "source": [
    "Can you use `seaborn` to visualise the association between homework and math for each of the ten schools, with a scatterplot?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b61f8500-fc81-4e66-a40d-b3053f738e0d",
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    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1602355d0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 2500x1000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Visualise all associations\n",
    "sns.relplot(data=school,\n",
    "            x='homework', y='math',\n",
    "            col='schid', col_wrap=5,\n",
    "            kind='scatter')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be57fcee-638f-4e52-9243-3701616f2daf",
   "metadata": {},
   "source": [
    "Now, fit a simple GLM predicting math score from homework, which ignores the school id variable. We will use this to compare to a mixed model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ca9ff713-ea36-4b5e-bfbc-988d62887735",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>math</td>    <th>  R-squared:         </th> <td>   0.247</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>               <td>OLS</td>    <th>  Adj. R-squared:    </th> <td>   0.244</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>  <td>   260</td>   <th>  F-statistic:       </th> <td>   84.64</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>  <td>nonrobust</td> <th>  Prob (F-statistic):</th> <td>1.25e-17</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   44.0739</td> <td>    0.989</td> <td>   44.580</td> <td> 0.000</td> <td>   42.127</td> <td>   46.021</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>homework</th>  <td>    3.5719</td> <td>    0.388</td> <td>    9.200</td> <td> 0.000</td> <td>    2.807</td> <td>    4.336</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}    &      math     & \\textbf{  R-squared:         } &     0.247   \\\\\n",
       "\\textbf{Model:}            &      OLS      & \\textbf{  Adj. R-squared:    } &     0.244   \\\\\n",
       "\\textbf{No. Observations:} &        260    & \\textbf{  F-statistic:       } &     84.64   \\\\\n",
       "\\textbf{Covariance Type:}  &   nonrobust   & \\textbf{  Prob (F-statistic):} &  1.25e-17   \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                   & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept} &      44.0739  &        0.989     &    44.580  &         0.000        &       42.127    &       46.021     \\\\\n",
       "\\textbf{homework}  &       3.5719  &        0.388     &     9.200  &         0.000        &        2.807    &        4.336     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{OLS Regression Results}\n",
       "\\end{center}\n",
       "\n",
       "Notes: \\newline\n",
       " [1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   math   R-squared:                       0.247\n",
       "Model:                            OLS   Adj. R-squared:                  0.244\n",
       "No. Observations:                 260   F-statistic:                     84.64\n",
       "Covariance Type:            nonrobust   Prob (F-statistic):           1.25e-17\n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     44.0739      0.989     44.580      0.000      42.127      46.021\n",
       "homework       3.5719      0.388      9.200      0.000       2.807       4.336\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# GLM\n",
    "glm = smf.ols('math ~ homework', data=school).fit()\n",
    "glm.summary(slim=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66bde710-dc78-4e12-8a07-cde9889fe58e",
   "metadata": {},
   "source": [
    "Now, lets incorporate the variability from schools by giving a random intercept to schools, using a mixed model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ce7cc270-a65d-4dfa-8e42-0c09a94c5f99",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td>   <td>math</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>No. Observations:</td>   <td>260</td>         <td>Method:</td>         <td>REML</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>No. Groups:</td>      <td>10</td>          <td>Scale:</td>         <td>64.5228</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Min. group size:</td>    <td>20</td>      <td>Log-Likelihood:</td>   <td>-919.9738</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Max. group size:</td>    <td>67</td>        <td>Converged:</td>         <td>Yes</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Mean group size:</td>   <td>26.0</td>            <td></td>               <td></td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>       <th>Coef.</th> <th>Std.Err.</th>    <th>z</th>   <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>44.982</td>   <td>1.803</td>  <td>24.947</td> <td>0.000</td> <td>41.448</td> <td>48.516</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>homework</th>   <td>2.207</td>   <td>0.381</td>   <td>5.798</td> <td>0.000</td>  <td>1.461</td>  <td>2.952</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>schid Var</th> <td>25.226</td>   <td>1.630</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "</table><br/>\n"
      ],
      "text/latex": [
       "\\begin{table}\n",
       "\\caption{Mixed Linear Model Regression Results}\n",
       "\\label{}\n",
       "\\begin{center}\n",
       "\\begin{tabular}{llll}\n",
       "\\hline\n",
       "Model:            & MixedLM & Dependent Variable: & math       \\\\\n",
       "No. Observations: & 260     & Method:             & REML       \\\\\n",
       "No. Groups:       & 10      & Scale:              & 64.5228    \\\\\n",
       "Min. group size:  & 20      & Log-Likelihood:     & -919.9738  \\\\\n",
       "Max. group size:  & 67      & Converged:          & Yes        \\\\\n",
       "Mean group size:  & 26.0    &                     &            \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\n",
       "\\begin{center}\n",
       "\\begin{tabular}{lrrrrrr}\n",
       "\\hline\n",
       "          &  Coef. & Std.Err. &      z & P$> |$z$|$ & [0.025 & 0.975]  \\\\\n",
       "\\hline\n",
       "Intercept & 44.982 &    1.803 & 24.947 &       0.000 & 41.448 & 48.516  \\\\\n",
       "homework  &  2.207 &    0.381 &  5.798 &       0.000 &  1.461 &  2.952  \\\\\n",
       "schid Var & 25.226 &    1.630 &        &             &        &         \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\\end{table}\n",
       "\\bigskip\n"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "         Mixed Linear Model Regression Results\n",
       "=======================================================\n",
       "Model:            MixedLM Dependent Variable: math     \n",
       "No. Observations: 260     Method:             REML     \n",
       "No. Groups:       10      Scale:              64.5228  \n",
       "Min. group size:  20      Log-Likelihood:     -919.9738\n",
       "Max. group size:  67      Converged:          Yes      \n",
       "Mean group size:  26.0                                 \n",
       "-------------------------------------------------------\n",
       "             Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
       "-------------------------------------------------------\n",
       "Intercept    44.982    1.803 24.947 0.000 41.448 48.516\n",
       "homework      2.207    0.381  5.798 0.000  1.461  2.952\n",
       "schid Var    25.226    1.630                           \n",
       "=======================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Mixed models\n",
    "mix = smf.mixedlm('math ~ homework',\n",
    "                  groups='schid',\n",
    "                  data=school).fit()\n",
    "mix.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "706004f7-cb77-4116-8dc9-bbe08ee4c313",
   "metadata": {},
   "source": [
    "What happened to the association between homework and scores when incorporating the random effect of schools? Bonus points if you can plot the fitted values from the mixed model. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ffae238-b927-456f-b19e-648a1d4b7559",
   "metadata": {},
   "source": [
    "Next, let us add some more complexity. Our existing mixed model incorporates only each schools baseline maths score (a good way to find out which school is over-or-under-performing). It assumes the amount of homework completed has *the same effect on maths exam scores* for every school. That' not realistic. Expand the model so it allows this effect to vary (e.g., a random slope for homework)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4964c9ca-6f12-48cc-b7ff-ff5efff1ba8c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td>   <td>math</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>No. Observations:</td>   <td>260</td>         <td>Method:</td>         <td>REML</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>No. Groups:</td>      <td>10</td>          <td>Scale:</td>         <td>43.0710</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Min. group size:</td>    <td>20</td>      <td>Log-Likelihood:</td>   <td>-881.9772</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Max. group size:</td>    <td>67</td>        <td>Converged:</td>         <td>Yes</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Mean group size:</td>   <td>26.0</td>            <td></td>               <td></td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "            <td></td>            <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>   <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>            <td>44.771</td>    <td>2.744</td>  <td>16.314</td> <td>0.000</td> <td>39.392</td> <td>50.149</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>homework</th>              <td>2.040</td>    <td>1.555</td>   <td>1.312</td> <td>0.190</td> <td>-1.008</td>  <td>5.089</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>schid Var</th>            <td>69.304</td>    <td>5.437</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>schid x homework Cov</th> <td>-31.762</td>   <td>2.812</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>homework Var</th>         <td>22.453</td>    <td>1.787</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "</table><br/>\n"
      ],
      "text/latex": [
       "\\begin{table}\n",
       "\\caption{Mixed Linear Model Regression Results}\n",
       "\\label{}\n",
       "\\begin{center}\n",
       "\\begin{tabular}{llll}\n",
       "\\hline\n",
       "Model:            & MixedLM & Dependent Variable: & math       \\\\\n",
       "No. Observations: & 260     & Method:             & REML       \\\\\n",
       "No. Groups:       & 10      & Scale:              & 43.0710    \\\\\n",
       "Min. group size:  & 20      & Log-Likelihood:     & -881.9772  \\\\\n",
       "Max. group size:  & 67      & Converged:          & Yes        \\\\\n",
       "Mean group size:  & 26.0    &                     &            \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\n",
       "\\begin{center}\n",
       "\\begin{tabular}{lrrrrrr}\n",
       "\\hline\n",
       "                     &   Coef. & Std.Err. &      z & P$> |$z$|$ & [0.025 & 0.975]  \\\\\n",
       "\\hline\n",
       "Intercept            &  44.771 &    2.744 & 16.314 &       0.000 & 39.392 & 50.149  \\\\\n",
       "homework             &   2.040 &    1.555 &  1.312 &       0.190 & -1.008 &  5.089  \\\\\n",
       "schid Var            &  69.304 &    5.437 &        &             &        &         \\\\\n",
       "schid x homework Cov & -31.762 &    2.812 &        &             &        &         \\\\\n",
       "homework Var         &  22.453 &    1.787 &        &             &        &         \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\\end{table}\n",
       "\\bigskip\n"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "             Mixed Linear Model Regression Results\n",
       "================================================================\n",
       "Model:               MixedLM    Dependent Variable:    math     \n",
       "No. Observations:    260        Method:                REML     \n",
       "No. Groups:          10         Scale:                 43.0710  \n",
       "Min. group size:     20         Log-Likelihood:        -881.9772\n",
       "Max. group size:     67         Converged:             Yes      \n",
       "Mean group size:     26.0                                       \n",
       "----------------------------------------------------------------\n",
       "                      Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
       "----------------------------------------------------------------\n",
       "Intercept             44.771    2.744 16.314 0.000 39.392 50.149\n",
       "homework               2.040    1.555  1.312 0.190 -1.008  5.089\n",
       "schid Var             69.304    5.437                           \n",
       "schid x homework Cov -31.762    2.812                           \n",
       "homework Var          22.453    1.787                           \n",
       "================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# mixed model with random slope\n",
    "mix2 = smf.mixedlm('math ~ homework',\n",
    "                   groups='schid',\n",
    "                   re_formula='homework',\n",
    "                   data=school).fit()\n",
    "\n",
    "mix2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fdc9a97-da6e-4dac-bb75-1f93ebe0cb27",
   "metadata": {},
   "source": [
    "**Now** what happens to the association? More bonus points if you can include the predictions in a plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "867168cd-7707-4f12-87a8-aedf2861e98d",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1619750d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 2800.25x1000 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Including fitted values\n",
    "school['fit_slopes'] = mix2.fittedvalues\n",
    "school['fit_intercept'] = mix.fittedvalues\n",
    "(sns.relplot(data=school,\n",
    "             x='homework', y='math',\n",
    "             col='schid', col_wrap=5,\n",
    "             kind='scatter')\n",
    " .map_dataframe(sns.lineplot, x='homework', y='fit_intercept', color='black', label='Intercepts only')\n",
    " .map_dataframe(sns.lineplot, x='homework', y='fit_slopes', color='grey', label='Intercepts and slopes')\n",
    " .add_legend()\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e4dfbfa-cc53-4198-a908-22cf75c0638e",
   "metadata": {},
   "source": [
    "### 2. Cosmetics and attractiveness\n",
    "In the workshop we examined a model that included a random intercept for participants, a random intercept for models (both of those accounting for baseline levels of attractiveness ratings that each participant and model gives) and a random slope for cosmetics for each model (the model figures out the effect of a makeup application on the attractiveness of each model). \n",
    "\n",
    "There's at least one more effect that was not considered here, which is how makeup affects the perceptions of each **rater**. Each rater may differ in their response to cosmetics, with some liking it, and some being put off by it. Can you read in the data from the example and expand the model to include the random slope for raters too?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "630bef2f-50ed-47f7-8047-9620a660fa26",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td>   <td>rating</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>No. Observations:</td>  <td>3003</td>         <td>Method:</td>          <td>REML</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>No. Groups:</td>       <td>1</td>          <td>Scale:</td>          <td>1.4235</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Min. group size:</td>   <td>3003</td>     <td>Log-Likelihood:</td>   <td>-5048.0688</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Max. group size:</td>   <td>3003</td>       <td>Converged:</td>          <td>Yes</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Mean group size:</td>  <td>3003.0</td>           <td></td>                <td></td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>           <th>Coef.</th> <th>Std.Err.</th>    <th>z</th>   <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>           <td>3.231</td>   <td>0.152</td>  <td>21.265</td> <td>0.000</td>  <td>2.933</td>  <td>3.529</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cosmetics_code</th>      <td>1.163</td>   <td>0.145</td>   <td>8.008</td> <td>0.000</td>  <td>0.878</td>  <td>1.448</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cosmetics_model Var</th> <td>0.514</td>   <td>0.122</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cosmetics_pid Var</th>   <td>0.322</td>   <td>0.063</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>model_id Var</th>        <td>0.561</td>   <td>0.125</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pid Var</th>             <td>0.464</td>   <td>0.069</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "</table><br/>\n"
      ],
      "text/latex": [
       "\\begin{table}\n",
       "\\caption{Mixed Linear Model Regression Results}\n",
       "\\label{}\n",
       "\\begin{center}\n",
       "\\begin{tabular}{llll}\n",
       "\\hline\n",
       "Model:            & MixedLM & Dependent Variable: & rating      \\\\\n",
       "No. Observations: & 3003    & Method:             & REML        \\\\\n",
       "No. Groups:       & 1       & Scale:              & 1.4235      \\\\\n",
       "Min. group size:  & 3003    & Log-Likelihood:     & -5048.0688  \\\\\n",
       "Max. group size:  & 3003    & Converged:          & Yes         \\\\\n",
       "Mean group size:  & 3003.0  &                     &             \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\n",
       "\\begin{center}\n",
       "\\begin{tabular}{lrrrrrr}\n",
       "\\hline\n",
       "                     & Coef. & Std.Err. &      z & P$> |$z$|$ & [0.025 & 0.975]  \\\\\n",
       "\\hline\n",
       "Intercept            & 3.231 &    0.152 & 21.265 &       0.000 &  2.933 &  3.529  \\\\\n",
       "cosmetics\\_code      & 1.163 &    0.145 &  8.008 &       0.000 &  0.878 &  1.448  \\\\\n",
       "cosmetics\\_model Var & 0.514 &    0.122 &        &             &        &         \\\\\n",
       "cosmetics\\_pid Var   & 0.322 &    0.063 &        &             &        &         \\\\\n",
       "model\\_id Var        & 0.561 &    0.125 &        &             &        &         \\\\\n",
       "pid Var              & 0.464 &    0.069 &        &             &        &         \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\\end{table}\n",
       "\\bigskip\n"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "            Mixed Linear Model Regression Results\n",
       "=============================================================\n",
       "Model:               MixedLM  Dependent Variable:  rating    \n",
       "No. Observations:    3003     Method:              REML      \n",
       "No. Groups:          1        Scale:               1.4235    \n",
       "Min. group size:     3003     Log-Likelihood:      -5048.0688\n",
       "Max. group size:     3003     Converged:           Yes       \n",
       "Mean group size:     3003.0                                  \n",
       "-------------------------------------------------------------\n",
       "                    Coef. Std.Err.   z    P>|z| [0.025 0.975]\n",
       "-------------------------------------------------------------\n",
       "Intercept           3.231    0.152 21.265 0.000  2.933  3.529\n",
       "cosmetics_code      1.163    0.145  8.008 0.000  0.878  1.448\n",
       "cosmetics_model Var 0.514    0.122                           \n",
       "cosmetics_pid Var   0.322    0.063                           \n",
       "model_id Var        0.561    0.125                           \n",
       "pid Var             0.464    0.069                           \n",
       "=============================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Read in data\n",
    "cosmetics = pd.read_csv('https://raw.githubusercontent.com/alexjonesphd/py4psy2024/refs/heads/main/jones_kramer_2015.csv')\n",
    "\n",
    "# Add the grouping factor\n",
    "cosmetics['grouping'] = 1\n",
    "\n",
    "# Expand the random effects to include rater random slopes like this\n",
    "re = {'pid': '0 + C(pid)', \n",
    "      'model_id': '0 + C(model_id)',\n",
    "      'cosmetics_model': '0 + C(model_id):cosmetics_code',\n",
    "      'cosmetics_pid': '0 + C(pid):cosmetics_code'}\n",
    "\n",
    "# Fit the odel\n",
    "expand = smf.mixedlm('rating ~ cosmetics_code',\n",
    "                     groups='grouping',\n",
    "                     vc_formula=re,\n",
    "                     data=cosmetics).fit()\n",
    "\n",
    "expand.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f01b0cc8-28d9-4c19-b3b2-fcdb588a0229",
   "metadata": {},
   "source": [
    "Once you have estimated this model, can you figure out what source of variation contributes the most to the attractiveness judgements out of:\n",
    "- Baseline attractiveness of models\n",
    "- Baseline tendency of attractiveness ratings of raters\n",
    "- Variation in the effect of cosmetics on models\n",
    "- Variation in the effect of cosmetics on participants?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ff3e63cc-745d-4599-8f94-63b69dbc704f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.15664007, 0.09793443, 0.170859  , 0.14117325])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Sum up all random effects\n",
    "total_variance = expand.vcomp.sum() + expand.scale\n",
    "\n",
    "# Divide the vcomp by the total\n",
    "expand.vcomp/total_variance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f571975-d5ba-49d9-82f3-60549f0bf630",
   "metadata": {},
   "source": [
    "As an additional challenge - can you find the *rater* with the largest and smallest slope for cosmetics? This directly translates into someone for who cosmetics increased their ratings the most, and the one for who makeup was a major turn off. You will need to filter down the random effects which can be quite tricky."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0611e536-66fb-40ec-b199-9fcc32807796",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1    cosmetics_pid[C(pid)[58]:cosmetics_code]\n",
      "dtype: object 1    cosmetics_pid[C(pid)[75]:cosmetics_code]\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Convert random effects to a dataframe\n",
    "ranef = pd.DataFrame(expand.random_effects)\n",
    "\n",
    "# Filter it to include only PID and cosmetics_code\n",
    "ppt_slopes = ranef[ranef.index.str.contains('cosmetics_code') & ranef.index.str.contains('pid')]\n",
    "\n",
    "# With that, find the min + max\n",
    "mini = ppt_slopes.idxmin()\n",
    "maxi = ppt_slopes.idxmax()\n",
    "\n",
    "print(mini, maxi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb2a0663-a2fd-4d4f-9e1c-407b70e35596",
   "metadata": {},
   "source": [
    "### 3. Further challenges in linear mixed effects models \n",
    "Linear mixed models are, essentially, a standard GLM with extra flexibility to account for observations in the data belonging to groups. As such, they are able to incorporate all the usual things a GLM can. Here, we'll use some more education data to examine whether there are differences between male and female A-level students on a Chemistry A-level score, and whether it is linked to their average GCSE score.\n",
    "\n",
    "This data can be found from the Bristol Centre for Multilevel Modelling, [here](https://www.bristol.ac.uk/cmm/learning/mmsoftware/data-rev.html]). Download the datasets, and upload the `chem97.txt` file to the server to access it. The code below will read in the file for you (assuming you have uploaded it) and rename the columns to something meaningful, but you can also see the readout on the above page for more detail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "46d093f1-69c7-4249-b6d4-64df6e3e8092",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>local_education_authority_ID</th>\n",
       "      <th>school_ID</th>\n",
       "      <th>pupil_ID</th>\n",
       "      <th>chem_Alevel_score</th>\n",
       "      <th>female</th>\n",
       "      <th>age_in_months</th>\n",
       "      <th>avg_GCSE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1</td>\n",
       "      <td>-3.0</td>\n",
       "      <td>7.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>7.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>1</td>\n",
       "      <td>-2.0</td>\n",
       "      <td>7.500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>1</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>6.444</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   local_education_authority_ID  school_ID  pupil_ID  chem_Alevel_score  \\\n",
       "0                           1.0        1.0       1.0                4.0   \n",
       "1                           1.0        1.0       2.0               10.0   \n",
       "2                           1.0        1.0       3.0               10.0   \n",
       "3                           1.0        1.0       4.0               10.0   \n",
       "4                           1.0        1.0       5.0                8.0   \n",
       "\n",
       "   female  age_in_months  avg_GCSE  \n",
       "0       1            3.0     6.625  \n",
       "1       1           -3.0     7.625  \n",
       "2       1           -4.0     7.250  \n",
       "3       1           -2.0     7.500  \n",
       "4       1           -1.0     6.444  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reads in data and renames columns\n",
    "chem97 = pd.read_table('chem97.txt', sep='\\s+', header=None)\n",
    "chem97.columns = ['local_education_authority_ID', 'school_ID', 'pupil_ID', 'chem_Alevel_score', 'female', 'age_in_months', 'avg_GCSE']\n",
    "chem97.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1cc4a81-b8c2-4e80-8835-5d7035cec12e",
   "metadata": {},
   "source": [
    "Fit a linear mixed model that predicts chemistry A level score from the interaction between female (1 = yes, 0 = No) and aveage GCSE grade. Include random intercepts for education authority and school ID."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4e7778fe-79a5-42bb-b944-9ff758279e7f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td> <td>chem_Alevel_score</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>No. Observations:</td>  <td>31022</td>        <td>Method:</td>             <td>REML</td>       \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>No. Groups:</td>       <td>1</td>          <td>Scale:</td>             <td>5.0495</td>      \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Min. group size:</td>   <td>31022</td>    <td>Log-Likelihood:</td>      <td>-70526.6060</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Max. group size:</td>   <td>31022</td>      <td>Converged:</td>             <td>Yes</td>       \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Mean group size:</td>  <td>31022.0</td>          <td></td>                   <td></td>         \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "          <td></td>          <th>Coef.</th> <th>Std.Err.</th>    <th>z</th>    <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>        <td>-9.500</td>   <td>0.133</td>  <td>-71.585</td> <td>0.000</td> <td>-9.760</td> <td>-9.240</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>female</th>           <td>-2.377</td>   <td>0.209</td>  <td>-11.375</td> <td>0.000</td> <td>-2.787</td> <td>-1.968</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>avg_GCSE</th>          <td>2.460</td>   <td>0.021</td>  <td>115.526</td> <td>0.000</td>  <td>2.418</td>  <td>2.502</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>female:avg_GCSE</th>   <td>0.262</td>   <td>0.033</td>   <td>7.911</td>  <td>0.000</td>  <td>0.197</td>  <td>0.327</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>ed_authority Var</th>  <td>0.021</td>   <td>0.007</td>     <td></td>       <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>school Var</th>        <td>1.125</td>   <td>0.025</td>     <td></td>       <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "</table><br/>\n"
      ],
      "text/latex": [
       "\\begin{table}\n",
       "\\caption{Mixed Linear Model Regression Results}\n",
       "\\label{}\n",
       "\\begin{center}\n",
       "\\begin{tabular}{llll}\n",
       "\\hline\n",
       "Model:            & MixedLM & Dependent Variable: & chem\\_Alevel\\_score  \\\\\n",
       "No. Observations: & 31022   & Method:             & REML                 \\\\\n",
       "No. Groups:       & 1       & Scale:              & 5.0495               \\\\\n",
       "Min. group size:  & 31022   & Log-Likelihood:     & -70526.6060          \\\\\n",
       "Max. group size:  & 31022   & Converged:          & Yes                  \\\\\n",
       "Mean group size:  & 31022.0 &                     &                      \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\n",
       "\\begin{center}\n",
       "\\begin{tabular}{lrrrrrr}\n",
       "\\hline\n",
       "                  &  Coef. & Std.Err. &       z & P$> |$z$|$ & [0.025 & 0.975]  \\\\\n",
       "\\hline\n",
       "Intercept         & -9.500 &    0.133 & -71.585 &       0.000 & -9.760 & -9.240  \\\\\n",
       "female            & -2.377 &    0.209 & -11.375 &       0.000 & -2.787 & -1.968  \\\\\n",
       "avg\\_GCSE         &  2.460 &    0.021 & 115.526 &       0.000 &  2.418 &  2.502  \\\\\n",
       "female:avg\\_GCSE  &  0.262 &    0.033 &   7.911 &       0.000 &  0.197 &  0.327  \\\\\n",
       "ed\\_authority Var &  0.021 &    0.007 &         &             &        &         \\\\\n",
       "school Var        &  1.125 &    0.025 &         &             &        &         \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\\end{table}\n",
       "\\bigskip\n"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "             Mixed Linear Model Regression Results\n",
       "===============================================================\n",
       "Model:            MixedLM Dependent Variable: chem_Alevel_score\n",
       "No. Observations: 31022   Method:             REML             \n",
       "No. Groups:       1       Scale:              5.0495           \n",
       "Min. group size:  31022   Log-Likelihood:     -70526.6060      \n",
       "Max. group size:  31022   Converged:          Yes              \n",
       "Mean group size:  31022.0                                      \n",
       "---------------------------------------------------------------\n",
       "                    Coef.  Std.Err.    z    P>|z| [0.025 0.975]\n",
       "---------------------------------------------------------------\n",
       "Intercept           -9.500    0.133 -71.585 0.000 -9.760 -9.240\n",
       "female              -2.377    0.209 -11.375 0.000 -2.787 -1.968\n",
       "avg_GCSE             2.460    0.021 115.526 0.000  2.418  2.502\n",
       "female:avg_GCSE      0.262    0.033   7.911 0.000  0.197  0.327\n",
       "ed_authority Var     0.021    0.007                            \n",
       "school Var           1.125    0.025                            \n",
       "===============================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "chem97['grouping'] = 1 # creates group\n",
    "\n",
    "# create random effects\n",
    "re = {'ed_authority': '0 + C(local_education_authority_ID)',\n",
    "      'school': '0 + C(school_ID)'}\n",
    "\n",
    "# Model - this MAY TAKE A WHILE!\n",
    "md = smf.mixedlm('chem_Alevel_score ~ female * avg_GCSE', \n",
    "                 groups='grouping',\n",
    "                 vc_formula=re, \n",
    "                 data=chem97).fit()\n",
    "\n",
    "md.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6b99d99-5c04-4254-a469-ad87a8d09c7f",
   "metadata": {},
   "source": [
    "With the model fitted, note the variance estimates and the coefficients. As with a GLM its not so easy to interpret whats going on - but we can rely on using average slopes to get conditional estimates, like always. Use `marginaleffects` to compute the slope for females and males with regards to GCSEs to explain the interaction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5089e071-4126-42b6-a1ed-705966a854b0",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (2, 10)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>female</th><th>term</th><th>contrast</th><th>estimate</th><th>std_error</th><th>statistic</th><th>p_value</th><th>s_value</th><th>conf_low</th><th>conf_high</th></tr><tr><td>i64</td><td>str</td><td>str</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>0</td><td>&quot;avg_GCSE&quot;</td><td>&quot;mean(dY/dX)&quot;</td><td>2.459902</td><td>0.021293</td><td>115.526716</td><td>0.0</td><td>inf</td><td>2.418169</td><td>2.501635</td></tr><tr><td>1</td><td>&quot;avg_GCSE&quot;</td><td>&quot;mean(dY/dX)&quot;</td><td>2.721689</td><td>0.02665</td><td>102.127443</td><td>0.0</td><td>inf</td><td>2.669456</td><td>2.773922</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (2, 10)\n",
       "┌────────┬──────────┬─────────────┬──────────┬───┬─────────┬─────┬──────┬───────┐\n",
       "│ female ┆ Term     ┆ Contrast    ┆ Estimate ┆ … ┆ P(>|z|) ┆ S   ┆ 2.5% ┆ 97.5% │\n",
       "│ ---    ┆ ---      ┆ ---         ┆ ---      ┆   ┆ ---     ┆ --- ┆ ---  ┆ ---   │\n",
       "│ str    ┆ str      ┆ str         ┆ str      ┆   ┆ str     ┆ str ┆ str  ┆ str   │\n",
       "╞════════╪══════════╪═════════════╪══════════╪═══╪═════════╪═════╪══════╪═══════╡\n",
       "│ 0      ┆ avg_GCSE ┆ mean(dY/dX) ┆ 2.46     ┆ … ┆ 0       ┆ inf ┆ 2.42 ┆ 2.5   │\n",
       "│ 1      ┆ avg_GCSE ┆ mean(dY/dX) ┆ 2.72     ┆ … ┆ 0       ┆ inf ┆ 2.67 ┆ 2.77  │\n",
       "└────────┴──────────┴─────────────┴──────────┴───┴─────────┴─────┴──────┴───────┘\n",
       "\n",
       "Columns: female, term, contrast, estimate, std_error, statistic, p_value, s_value, conf_low, conf_high"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# Get the slopes of GCSE for each sex\n",
    "me.slopes(md, variables=['avg_GCSE'], by='female')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf89b20f-1a7a-4bb9-9a16-faa570aabd8d",
   "metadata": {},
   "source": [
    "### 4. Studying individual differences with mixed models\n",
    "As a final example, lets see how mixed models can be used to understand measures of individual differences. \n",
    "\n",
    "In the next dataset, we'll see how individual raters are sensitive to facial cues of symmetry, averageness, and sexual dimorphism, three important predictors of facial attractiveness. Participants rated 100 faces on how attractive they thought they were (on a scale of 1-100). For each of the faces, we measured how symmetrical, distinctive, and sexually dimorphic it was. \n",
    "\n",
    "First, read in the data from the following link and display the top 10 rows: https://raw.githubusercontent.com/alexjonesphd/py4psy2024/refs/heads/main/cue_sensitivity.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b907c005-ae73-4259-862e-64133d056811",
   "metadata": {
    "editable": true,
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    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pid</th>\n",
       "      <th>face_id</th>\n",
       "      <th>face_sex</th>\n",
       "      <th>attractiveness</th>\n",
       "      <th>distinctiveness</th>\n",
       "      <th>symmetry</th>\n",
       "      <th>dimorphism</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>galina</td>\n",
       "      <td>female</td>\n",
       "      <td>44</td>\n",
       "      <td>-1.535898</td>\n",
       "      <td>-0.926857</td>\n",
       "      <td>0.056173</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>tamara</td>\n",
       "      <td>female</td>\n",
       "      <td>25</td>\n",
       "      <td>1.506863</td>\n",
       "      <td>0.567697</td>\n",
       "      <td>-1.542840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>blazej</td>\n",
       "      <td>male</td>\n",
       "      <td>50</td>\n",
       "      <td>1.066100</td>\n",
       "      <td>-1.977071</td>\n",
       "      <td>0.758609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>irena</td>\n",
       "      <td>female</td>\n",
       "      <td>58</td>\n",
       "      <td>-1.196141</td>\n",
       "      <td>-0.929967</td>\n",
       "      <td>0.751037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>jan</td>\n",
       "      <td>male</td>\n",
       "      <td>27</td>\n",
       "      <td>0.039301</td>\n",
       "      <td>0.769465</td>\n",
       "      <td>-0.082505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>svatopluk</td>\n",
       "      <td>male</td>\n",
       "      <td>32</td>\n",
       "      <td>-0.676461</td>\n",
       "      <td>-1.102852</td>\n",
       "      <td>-0.591465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>miroslav1</td>\n",
       "      <td>male</td>\n",
       "      <td>35</td>\n",
       "      <td>0.479499</td>\n",
       "      <td>1.627821</td>\n",
       "      <td>-0.714593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>viola</td>\n",
       "      <td>female</td>\n",
       "      <td>61</td>\n",
       "      <td>-1.300203</td>\n",
       "      <td>1.283004</td>\n",
       "      <td>0.304360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>vincent</td>\n",
       "      <td>male</td>\n",
       "      <td>2</td>\n",
       "      <td>0.715087</td>\n",
       "      <td>-1.160949</td>\n",
       "      <td>1.252532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>3168134.0</td>\n",
       "      <td>blazana</td>\n",
       "      <td>female</td>\n",
       "      <td>69</td>\n",
       "      <td>-1.004162</td>\n",
       "      <td>0.838649</td>\n",
       "      <td>-0.965687</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         pid    face_id face_sex  attractiveness  distinctiveness  symmetry  \\\n",
       "0  3168134.0     galina   female              44        -1.535898 -0.926857   \n",
       "1  3168134.0     tamara   female              25         1.506863  0.567697   \n",
       "2  3168134.0     blazej     male              50         1.066100 -1.977071   \n",
       "3  3168134.0      irena   female              58        -1.196141 -0.929967   \n",
       "4  3168134.0        jan     male              27         0.039301  0.769465   \n",
       "5  3168134.0  svatopluk     male              32        -0.676461 -1.102852   \n",
       "6  3168134.0  miroslav1     male              35         0.479499  1.627821   \n",
       "7  3168134.0      viola   female              61        -1.300203  1.283004   \n",
       "8  3168134.0    vincent     male               2         0.715087 -1.160949   \n",
       "9  3168134.0    blazana   female              69        -1.004162  0.838649   \n",
       "\n",
       "   dimorphism  \n",
       "0    0.056173  \n",
       "1   -1.542840  \n",
       "2    0.758609  \n",
       "3    0.751037  \n",
       "4   -0.082505  \n",
       "5   -0.591465  \n",
       "6   -0.714593  \n",
       "7    0.304360  \n",
       "8    1.252532  \n",
       "9   -0.965687  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "cues = pd.read_csv('https://raw.githubusercontent.com/alexjonesphd/py4psy2024/refs/heads/main/cue_sensitivity.csv')\n",
    "cues.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f591df0c-f4e1-4f8e-9ce6-4287df1e8c1c",
   "metadata": {},
   "source": [
    "Each participant rates 100 faces and we know the measurements of those faces. Lets fit a model that uses those measurements as predictors and accounts for participant and face variability with random slopes, as a starter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b9da4e9b-eadf-41d2-a8a6-2155808441c1",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td> <td>attractiveness</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>No. Observations:</td>  <td>3200</td>         <td>Method:</td>            <td>REML</td>     \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>No. Groups:</td>       <td>1</td>          <td>Scale:</td>           <td>227.0840</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Min. group size:</td>   <td>3200</td>     <td>Log-Likelihood:</td>     <td>-13408.9376</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Max. group size:</td>   <td>3200</td>       <td>Converged:</td>            <td>Yes</td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Mean group size:</td>  <td>3200.0</td>           <td></td>                  <td></td>       \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "         <td></td>          <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>   <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>       <td>35.681</td>    <td>2.225</td>  <td>16.038</td> <td>0.000</td> <td>31.321</td> <td>40.042</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>distinctiveness</th> <td>-2.398</td>    <td>1.013</td>  <td>-2.367</td> <td>0.018</td> <td>-4.383</td> <td>-0.413</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>symmetry</th>        <td>-1.763</td>    <td>1.007</td>  <td>-1.752</td> <td>0.080</td> <td>-3.736</td>  <td>0.209</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dimorphism</th>      <td>-0.389</td>    <td>1.034</td>  <td>-0.376</td> <td>0.707</td> <td>-2.415</td>  <td>1.638</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>face Var</th>        <td>89.992</td>    <td>0.944</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pid Var</th>         <td>127.324</td>   <td>2.195</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "</table><br/>\n"
      ],
      "text/latex": [
       "\\begin{table}\n",
       "\\caption{Mixed Linear Model Regression Results}\n",
       "\\label{}\n",
       "\\begin{center}\n",
       "\\begin{tabular}{llll}\n",
       "\\hline\n",
       "Model:            & MixedLM & Dependent Variable: & attractiveness  \\\\\n",
       "No. Observations: & 3200    & Method:             & REML            \\\\\n",
       "No. Groups:       & 1       & Scale:              & 227.0840        \\\\\n",
       "Min. group size:  & 3200    & Log-Likelihood:     & -13408.9376     \\\\\n",
       "Max. group size:  & 3200    & Converged:          & Yes             \\\\\n",
       "Mean group size:  & 3200.0  &                     &                 \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\n",
       "\\begin{center}\n",
       "\\begin{tabular}{lrrrrrr}\n",
       "\\hline\n",
       "                &   Coef. & Std.Err. &      z & P$> |$z$|$ & [0.025 & 0.975]  \\\\\n",
       "\\hline\n",
       "Intercept       &  35.681 &    2.225 & 16.038 &       0.000 & 31.321 & 40.042  \\\\\n",
       "distinctiveness &  -2.398 &    1.013 & -2.367 &       0.018 & -4.383 & -0.413  \\\\\n",
       "symmetry        &  -1.763 &    1.007 & -1.752 &       0.080 & -3.736 &  0.209  \\\\\n",
       "dimorphism      &  -0.389 &    1.034 & -0.376 &       0.707 & -2.415 &  1.638  \\\\\n",
       "face Var        &  89.992 &    0.944 &        &             &        &         \\\\\n",
       "pid Var         & 127.324 &    2.195 &        &             &        &         \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\\end{table}\n",
       "\\bigskip\n"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "           Mixed Linear Model Regression Results\n",
       "============================================================\n",
       "Model:            MixedLM Dependent Variable: attractiveness\n",
       "No. Observations: 3200    Method:             REML          \n",
       "No. Groups:       1       Scale:              227.0840      \n",
       "Min. group size:  3200    Log-Likelihood:     -13408.9376   \n",
       "Max. group size:  3200    Converged:          Yes           \n",
       "Mean group size:  3200.0                                    \n",
       "------------------------------------------------------------\n",
       "                  Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
       "------------------------------------------------------------\n",
       "Intercept         35.681    2.225 16.038 0.000 31.321 40.042\n",
       "distinctiveness   -2.398    1.013 -2.367 0.018 -4.383 -0.413\n",
       "symmetry          -1.763    1.007 -1.752 0.080 -3.736  0.209\n",
       "dimorphism        -0.389    1.034 -0.376 0.707 -2.415  1.638\n",
       "face Var          89.992    0.944                           \n",
       "pid Var          127.324    2.195                           \n",
       "============================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "cues['grouping'] = 1\n",
    "\n",
    "# VC\n",
    "vc = {'pid': '0 + C(pid)',\n",
    "      'face': '0 + C(face_id)'}\n",
    "\n",
    "# models\n",
    "model1 = smf.mixedlm('attractiveness ~ distinctiveness + symmetry + dimorphism',\n",
    "                     groups='grouping', vc_formula=vc, data=cues).fit()\n",
    "\n",
    "model1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a700948-b732-4d46-b44f-1cedfb376ed0",
   "metadata": {},
   "source": [
    "This model efffectively accounts for participant variability and face variability, and suggests only distinctiveness decreases attractiveness. But we must be clear on what it implies - it says that the effect of, say, distinctiveness is *exactly* the same for all raters. That is, raters are influenced by the distinctiveness of the face in the same way. Is this realistic? Would it be better to allow each rater their own distinctiveness slope (as well as others) to allow their own preferences to come out? We can do this of course by including a random slope for each rater for each trait. Do that below and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "282d72e8-be8d-4254-8c43-b6c17684eecc",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/miniconda3/envs/py11/lib/python3.11/site-packages/statsmodels/base/model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "/opt/miniconda3/envs/py11/lib/python3.11/site-packages/statsmodels/regression/mixed_linear_model.py:2201: ConvergenceWarning: Retrying MixedLM optimization with lbfgs\n",
      "/opt/miniconda3/envs/py11/lib/python3.11/site-packages/statsmodels/regression/mixed_linear_model.py:2262: ConvergenceWarning: The Hessian matrix at the estimated parameter values is not positive definite.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td>Model:</td>       <td>MixedLM</td> <td>Dependent Variable:</td> <td>attractiveness</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>No. Observations:</td>  <td>3200</td>         <td>Method:</td>            <td>REML</td>     \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>No. Groups:</td>       <td>1</td>          <td>Scale:</td>           <td>222.5967</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Min. group size:</td>   <td>3200</td>     <td>Log-Likelihood:</td>     <td>-13424.8905</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Max. group size:</td>   <td>3200</td>       <td>Converged:</td>            <td>Yes</td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Mean group size:</td>  <td>3200.0</td>           <td></td>                  <td></td>       \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>            <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>   <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>           <td>35.681</td>    <td>2.282</td>  <td>15.633</td> <td>0.000</td> <td>31.208</td> <td>40.155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>distinctiveness</th>     <td>-2.398</td>    <td>1.517</td>  <td>-1.581</td> <td>0.114</td> <td>-5.371</td>  <td>0.575</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>symmetry</th>            <td>-1.763</td>    <td>1.509</td>  <td>-1.169</td> <td>0.243</td> <td>-4.721</td>  <td>1.194</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dimorphism</th>          <td>-0.389</td>    <td>1.549</td>  <td>-0.251</td> <td>0.802</td> <td>-3.425</td>  <td>2.648</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>dimorphism Var</th>       <td>0.670</td>    <td>0.121</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>distinctiveness Var</th>  <td>0.591</td>    <td>0.060</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>face Var</th>            <td>209.005</td>     <td></td>        <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>pid Var</th>             <td>97.593</td>    <td>1.352</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>symmetry Var</th>         <td>0.769</td>    <td>0.143</td>     <td></td>      <td></td>       <td></td>       <td></td>   \n",
       "</tr>\n",
       "</table><br/>\n"
      ],
      "text/latex": [
       "\\begin{table}\n",
       "\\caption{Mixed Linear Model Regression Results}\n",
       "\\label{}\n",
       "\\begin{center}\n",
       "\\begin{tabular}{llll}\n",
       "\\hline\n",
       "Model:            & MixedLM & Dependent Variable: & attractiveness  \\\\\n",
       "No. Observations: & 3200    & Method:             & REML            \\\\\n",
       "No. Groups:       & 1       & Scale:              & 222.5967        \\\\\n",
       "Min. group size:  & 3200    & Log-Likelihood:     & -13424.8905     \\\\\n",
       "Max. group size:  & 3200    & Converged:          & Yes             \\\\\n",
       "Mean group size:  & 3200.0  &                     &                 \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\n",
       "\\begin{center}\n",
       "\\begin{tabular}{lrrrrrr}\n",
       "\\hline\n",
       "                    &   Coef. & Std.Err. &      z & P$> |$z$|$ & [0.025 & 0.975]  \\\\\n",
       "\\hline\n",
       "Intercept           &  35.681 &    2.282 & 15.633 &       0.000 & 31.208 & 40.155  \\\\\n",
       "distinctiveness     &  -2.398 &    1.517 & -1.581 &       0.114 & -5.371 &  0.575  \\\\\n",
       "symmetry            &  -1.763 &    1.509 & -1.169 &       0.243 & -4.721 &  1.194  \\\\\n",
       "dimorphism          &  -0.389 &    1.549 & -0.251 &       0.802 & -3.425 &  2.648  \\\\\n",
       "dimorphism Var      &   0.670 &    0.121 &        &             &        &         \\\\\n",
       "distinctiveness Var &   0.591 &    0.060 &        &             &        &         \\\\\n",
       "face Var            & 209.005 &          &        &             &        &         \\\\\n",
       "pid Var             &  97.593 &    1.352 &        &             &        &         \\\\\n",
       "symmetry Var        &   0.769 &    0.143 &        &             &        &         \\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "\\end{center}\n",
       "\\end{table}\n",
       "\\bigskip\n"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "             Mixed Linear Model Regression Results\n",
       "===============================================================\n",
       "Model:             MixedLM  Dependent Variable:  attractiveness\n",
       "No. Observations:  3200     Method:              REML          \n",
       "No. Groups:        1        Scale:               222.5967      \n",
       "Min. group size:   3200     Log-Likelihood:      -13424.8905   \n",
       "Max. group size:   3200     Converged:           Yes           \n",
       "Mean group size:   3200.0                                      \n",
       "---------------------------------------------------------------\n",
       "                     Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
       "---------------------------------------------------------------\n",
       "Intercept            35.681    2.282 15.633 0.000 31.208 40.155\n",
       "distinctiveness      -2.398    1.517 -1.581 0.114 -5.371  0.575\n",
       "symmetry             -1.763    1.509 -1.169 0.243 -4.721  1.194\n",
       "dimorphism           -0.389    1.549 -0.251 0.802 -3.425  2.648\n",
       "dimorphism Var        0.670    0.121                           \n",
       "distinctiveness Var   0.591    0.060                           \n",
       "face Var            209.005                                    \n",
       "pid Var              97.593    1.352                           \n",
       "symmetry Var          0.769    0.143                           \n",
       "===============================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Your answer here\n",
    "# VC\n",
    "re = {'pid': '0 + C(pid)',\n",
    "      'face': '0 + C(face_id)',\n",
    "      'distinctiveness': '0 + C(pid):distinctiveness',\n",
    "      'symmetry': '0 + C(pid):symmetry',\n",
    "      'dimorphism': '0 + C(pid):dimorphism'}\n",
    "\n",
    "# models\n",
    "model2 = smf.mixedlm('attractiveness ~ distinctiveness + symmetry + dimorphism',\n",
    "                     groups='grouping', vc_formula=re, data=cues).fit()\n",
    "\n",
    "model2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "893abe23-0aef-4ba1-9ed1-9a8b114abd90",
   "metadata": {},
   "source": [
    "Now the effects go away when you consider how variable these effects are for people. If we wanted, we could extract each persons individual slope to see how sensitive they are to an individual cue."
   ]
  }
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