{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Mixed Effects Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:30.459745Z",
     "iopub.status.busy": "2026-07-28T19:02:30.459543Z",
     "iopub.status.idle": "2026-07-28T19:02:34.249320Z",
     "shell.execute_reply": "2026-07-28T19:02:34.248748Z"
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   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "from statsmodels.tools.sm_exceptions import ConvergenceWarning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: The R code and the results in this notebook has been converted to markdown so that R is not required to build the documents. The R results in the notebook were computed using R 3.5.1 and lme4 1.1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%load_ext rpy2.ipython\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R library(lme4)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "array(['lme4', 'Matrix', 'tools', 'stats', 'graphics', 'grDevices',\n",
    "       'utils', 'datasets', 'methods', 'base'], dtype='<U9')\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing R lmer to statsmodels MixedLM\n",
    "=======================================\n",
    "\n",
    "The statsmodels implementation of linear mixed models (MixedLM) closely follows the approach outlined in Lindstrom and Bates (JASA 1988).  This is also the approach followed in the  R package LME4.  Other packages such as Stata, SAS, etc. should also be consistent with this approach, as the basic techniques in this area are mostly mature.\n",
    "\n",
    "Here we show how linear mixed models can be fit using the MixedLM procedure in statsmodels.  Results from R (LME4) are included for comparison.\n",
    "\n",
    "Here are our import statements:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Growth curves of pigs\n",
    "\n",
    "These are longitudinal data from a factorial experiment. The outcome variable is the weight of each pig, and the only predictor variable we will use here is \"time\".  First we fit a model that expresses the mean weight as a linear function of time, with a random intercept for each pig. The model is specified using formulas. Since the random effects structure is not specified, the default random effects structure (a random intercept for each group) is automatically used. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:34.256404Z",
     "iopub.status.busy": "2026-07-28T19:02:34.256036Z",
     "iopub.status.idle": "2026-07-28T19:02:34.985879Z",
     "shell.execute_reply": "2026-07-28T19:02:34.980560Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Mixed Linear Model Regression Results\n",
      "========================================================\n",
      "Model:            MixedLM Dependent Variable: Weight    \n",
      "No. Observations: 861     Method:             REML      \n",
      "No. Groups:       72      Scale:              11.3669   \n",
      "Min. group size:  11      Log-Likelihood:     -2404.7753\n",
      "Max. group size:  12      Converged:          Yes       \n",
      "Mean group size:  12.0                                  \n",
      "--------------------------------------------------------\n",
      "             Coef.  Std.Err.    z    P>|z| [0.025 0.975]\n",
      "--------------------------------------------------------\n",
      "Intercept    15.724    0.788  19.952 0.000 14.179 17.268\n",
      "Time          6.943    0.033 207.939 0.000  6.877  7.008\n",
      "Group Var    40.395    2.149                            \n",
      "========================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "data = sm.datasets.get_rdataset(\"dietox\", \"geepack\").data\n",
    "md = smf.mixedlm(\"Weight ~ Time\", data, groups=data[\"Pig\"])\n",
    "mdf = md.fit(method=[\"lbfgs\"])\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the same model fit in R using LMER:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%%R\n",
    "data(dietox, package='geepack')\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer('Weight ~ Time + (1|Pig)', data=dietox)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: Weight ~ Time + (1 | Pig)\n",
    "   Data: dietox\n",
    "\n",
    "REML criterion at convergence: 4809.6\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-4.7118 -0.5696 -0.0943  0.4877  4.7732 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev.\n",
    " Pig      (Intercept) 40.39    6.356   \n",
    " Residual             11.37    3.371   \n",
    "Number of obs: 861, groups:  Pig, 72\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 15.72352    0.78805   19.95\n",
    "Time         6.94251    0.03339  207.94\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.275\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that in the statsmodels summary of results, the fixed effects and random effects parameter estimates are shown in a single table.  The random effect for animal is labeled \"Intercept RE\" in the statsmodels output above.  In the LME4 output, this effect is the pig intercept under the random effects section.\n",
    "\n",
    "There has been a lot of debate about whether the standard errors for random effect variance and covariance parameters are useful.  In LME4, these standard errors are not displayed, because the authors of the package believe they are not very informative.  While there is good reason to question their utility, we elected to include the standard errors in the summary table, but do not show the corresponding Wald confidence intervals.\n",
    "\n",
    "Next we fit a model with two random effects for each animal: a random intercept, and a random slope (with respect to time).  This means that each pig may have a different baseline weight, as well as growing at a different rate. The formula specifies that \"Time\" is a covariate with a random coefficient.  By default, formulas always include an intercept (which could be suppressed here using \"0 + Time\" as the formula)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:34.995347Z",
     "iopub.status.busy": "2026-07-28T19:02:34.995123Z",
     "iopub.status.idle": "2026-07-28T19:02:35.765176Z",
     "shell.execute_reply": "2026-07-28T19:02:35.764619Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mixed Linear Model Regression Results\n",
      "===========================================================\n",
      "Model:             MixedLM  Dependent Variable:  Weight    \n",
      "No. Observations:  861      Method:              REML      \n",
      "No. Groups:        72       Scale:               6.0372    \n",
      "Min. group size:   11       Log-Likelihood:      -2217.0475\n",
      "Max. group size:   12       Converged:           Yes       \n",
      "Mean group size:   12.0                                    \n",
      "-----------------------------------------------------------\n",
      "                 Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
      "-----------------------------------------------------------\n",
      "Intercept        15.739    0.550 28.603 0.000 14.660 16.817\n",
      "Time              6.939    0.080 86.925 0.000  6.783  7.095\n",
      "Group Var        19.503    1.561                           \n",
      "Group x Time Cov  0.294    0.153                           \n",
      "Time Var          0.416    0.033                           \n",
      "===========================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "md = smf.mixedlm(\"Weight ~ Time\", data, groups=data[\"Pig\"], re_formula=\"~Time\")\n",
    "mdf = md.fit(method=[\"lbfgs\"])\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the same model fit using LMER in R:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer(\"Weight ~ Time + (1 + Time | Pig)\", data=dietox)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: Weight ~ Time + (1 + Time | Pig)\n",
    "   Data: dietox\n",
    "\n",
    "REML criterion at convergence: 4434.1\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-6.4286 -0.5529 -0.0416  0.4841  3.5624 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev. Corr\n",
    " Pig      (Intercept) 19.493   4.415        \n",
    "          Time         0.416   0.645    0.10\n",
    " Residual              6.038   2.457        \n",
    "Number of obs: 861, groups:  Pig, 72\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 15.73865    0.55012   28.61\n",
    "Time         6.93901    0.07982   86.93\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time 0.006 \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The random intercept and random slope are only weakly correlated $(0.294 / \\sqrt{19.493 * 0.416} \\approx 0.1)$.  So next we fit a model in which the two random effects are constrained to be uncorrelated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:35.775067Z",
     "iopub.status.busy": "2026-07-28T19:02:35.773596Z",
     "iopub.status.idle": "2026-07-28T19:02:35.795528Z",
     "shell.execute_reply": "2026-07-28T19:02:35.790183Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10324316832591753"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.294 / (19.493 * 0.416) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:35.798241Z",
     "iopub.status.busy": "2026-07-28T19:02:35.798046Z",
     "iopub.status.idle": "2026-07-28T19:02:36.395282Z",
     "shell.execute_reply": "2026-07-28T19:02:36.394738Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mixed Linear Model Regression Results\n",
      "===========================================================\n",
      "Model:             MixedLM  Dependent Variable:  Weight    \n",
      "No. Observations:  861      Method:              REML      \n",
      "No. Groups:        72       Scale:               6.0283    \n",
      "Min. group size:   11       Log-Likelihood:      -2217.3481\n",
      "Max. group size:   12       Converged:           Yes       \n",
      "Mean group size:   12.0                                    \n",
      "-----------------------------------------------------------\n",
      "                 Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
      "-----------------------------------------------------------\n",
      "Intercept        15.739    0.554 28.388 0.000 14.652 16.825\n",
      "Time              6.939    0.080 86.248 0.000  6.781  7.097\n",
      "Group Var        19.837    1.571                           \n",
      "Group x Time Cov  0.000    0.000                           \n",
      "Time Var          0.423    0.033                           \n",
      "===========================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "md = smf.mixedlm(\"Weight ~ Time\", data, groups=data[\"Pig\"], re_formula=\"~Time\")\n",
    "free = sm.regression.mixed_linear_model.MixedLMParams.from_components(\n",
    "    np.ones(2), np.eye(2)\n",
    ")\n",
    "\n",
    "mdf = md.fit(free=free, method=[\"lbfgs\"])\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The likelihood drops by 0.3 when we fix the correlation parameter to 0.  Comparing 2 x 0.3 = 0.6 to the $\\chi^2$ 1 df reference distribution suggests that the data are very consistent with a model in which this parameter is equal to 0.\n",
    "\n",
    "Here is the same model fit using LMER in R (note that here R is reporting the REML criterion instead of the likelihood, where the REML criterion is twice the log likelihood):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer(\"Weight ~ Time + (1 | Pig) + (0 + Time | Pig)\", data=dietox)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: Weight ~ Time + (1 | Pig) + (0 + Time | Pig)\n",
    "   Data: dietox\n",
    "\n",
    "REML criterion at convergence: 4434.7\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-6.4281 -0.5527 -0.0405  0.4840  3.5661 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev.\n",
    " Pig      (Intercept) 19.8404  4.4543  \n",
    " Pig.1    Time         0.4234  0.6507  \n",
    " Residual              6.0282  2.4552  \n",
    "Number of obs: 861, groups:  Pig, 72\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 15.73875    0.55444   28.39\n",
    "Time         6.93899    0.08045   86.25\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.086\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sitka growth data\n",
    "\n",
    "This is one of the example data sets provided in the LMER R library.  The outcome variable is the size of the tree, and the covariate used here is a time value.  The data are grouped by tree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:36.399890Z",
     "iopub.status.busy": "2026-07-28T19:02:36.399639Z",
     "iopub.status.idle": "2026-07-28T19:02:36.592931Z",
     "shell.execute_reply": "2026-07-28T19:02:36.591321Z"
    }
   },
   "outputs": [],
   "source": [
    "data = sm.datasets.get_rdataset(\"Sitka\", \"MASS\").data\n",
    "endog = data[\"size\"]\n",
    "data[\"Intercept\"] = 1\n",
    "exog = data[[\"Intercept\", \"Time\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the statsmodels LME fit for a basic model with a random intercept.  We are passing the endog and exog data directly to the LME init function as arrays.  Also note that endog_re is specified explicitly in argument 4 as a random intercept (although this would also be the default if it were not specified)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:36.595167Z",
     "iopub.status.busy": "2026-07-28T19:02:36.594895Z",
     "iopub.status.idle": "2026-07-28T19:02:37.097752Z",
     "shell.execute_reply": "2026-07-28T19:02:37.096157Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Mixed Linear Model Regression Results\n",
      "=======================================================\n",
      "Model:             MixedLM Dependent Variable: size    \n",
      "No. Observations:  395     Method:             REML    \n",
      "No. Groups:        79      Scale:              0.0392  \n",
      "Min. group size:   5       Log-Likelihood:     -82.3884\n",
      "Max. group size:   5       Converged:          Yes     \n",
      "Mean group size:   5.0                                 \n",
      "-------------------------------------------------------\n",
      "              Coef. Std.Err.   z    P>|z| [0.025 0.975]\n",
      "-------------------------------------------------------\n",
      "Intercept     2.273    0.088 25.864 0.000  2.101  2.446\n",
      "Time          0.013    0.000 47.796 0.000  0.012  0.013\n",
      "Intercept Var 0.374    0.345                           \n",
      "=======================================================\n",
      "\n"
     ]
    }
   ],
   "source": [
    "md = sm.MixedLM(endog, exog, groups=data[\"tree\"], exog_re=exog[\"Intercept\"])\n",
    "mdf = md.fit()\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the same model fit in R using LMER:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R\n",
    "data(Sitka, package=\"MASS\")\n",
    "print(summary(lmer(\"size ~ Time + (1 | tree)\", data=Sitka)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: size ~ Time + (1 | tree)\n",
    "   Data: Sitka\n",
    "\n",
    "REML criterion at convergence: 164.8\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-2.9979 -0.5169  0.1576  0.5392  4.4012 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance Std.Dev.\n",
    " tree     (Intercept) 0.37451  0.612   \n",
    " Residual             0.03921  0.198   \n",
    "Number of obs: 395, groups:  tree, 79\n",
    "\n",
    "Fixed effects:\n",
    "             Estimate Std. Error t value\n",
    "(Intercept) 2.2732443  0.0878955   25.86\n",
    "Time        0.0126855  0.0002654   47.80\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.611\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now try to add a random slope.  We start with R this time.  From the code and output below we see that the REML estimate of the variance of the random slope is nearly zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```ipython\n",
    "%R print(summary(lmer(\"size ~ Time + (1 + Time | tree)\", data=Sitka)))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Linear mixed model fit by REML ['lmerMod']\n",
    "Formula: size ~ Time + (1 + Time | tree)\n",
    "   Data: Sitka\n",
    "\n",
    "REML criterion at convergence: 153.4\n",
    "\n",
    "Scaled residuals: \n",
    "    Min      1Q  Median      3Q     Max \n",
    "-2.7609 -0.5173  0.1188  0.5270  3.5466 \n",
    "\n",
    "Random effects:\n",
    " Groups   Name        Variance  Std.Dev. Corr \n",
    " tree     (Intercept) 2.217e-01 0.470842      \n",
    "          Time        3.288e-06 0.001813 -0.17\n",
    " Residual             3.634e-02 0.190642      \n",
    "Number of obs: 395, groups:  tree, 79\n",
    "\n",
    "Fixed effects:\n",
    "            Estimate Std. Error t value\n",
    "(Intercept) 2.273244   0.074655   30.45\n",
    "Time        0.012686   0.000327   38.80\n",
    "\n",
    "Correlation of Fixed Effects:\n",
    "     (Intr)\n",
    "Time -0.615\n",
    "convergence code: 0\n",
    "Model failed to converge with max|grad| = 0.793203 (tol = 0.002, component 1)\n",
    "Model is nearly unidentifiable: very large eigenvalue\n",
    " - Rescale variables?\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run this in statsmodels LME with defaults, we see that the variance estimate is indeed very small, which leads to a warning about the solution being on the boundary of the parameter space.  The regression slopes agree very well with R, but the likelihood value is much higher than that returned by R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:37.102720Z",
     "iopub.status.busy": "2026-07-28T19:02:37.102505Z",
     "iopub.status.idle": "2026-07-28T19:02:38.972346Z",
     "shell.execute_reply": "2026-07-28T19:02:38.971748Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             Mixed Linear Model Regression Results\n",
      "===============================================================\n",
      "Model:               MixedLM    Dependent Variable:    size    \n",
      "No. Observations:    395        Method:                REML    \n",
      "No. Groups:          79         Scale:                 0.0264  \n",
      "Min. group size:     5          Log-Likelihood:        -62.4834\n",
      "Max. group size:     5          Converged:             Yes     \n",
      "Mean group size:     5.0                                       \n",
      "---------------------------------------------------------------\n",
      "                     Coef.  Std.Err.   z    P>|z| [0.025 0.975]\n",
      "---------------------------------------------------------------\n",
      "Intercept             2.273    0.101 22.513 0.000  2.075  2.471\n",
      "Time                  0.013    0.000 33.888 0.000  0.012  0.013\n",
      "Intercept Var         0.646    0.914                           \n",
      "Intercept x Time Cov -0.001    0.003                           \n",
      "Time Var              0.000    0.000                           \n",
      "===============================================================\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_4715/4173103950.py:3: ConvergenceWarning: The MLE may be on the boundary of the parameter space.\n",
      "  mdf = md.fit()\n"
     ]
    }
   ],
   "source": [
    "exog_re = exog.copy()\n",
    "md = sm.MixedLM(endog, exog, data[\"tree\"], exog_re)\n",
    "mdf = md.fit()\n",
    "print(mdf.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can further explore the random effects structure by constructing plots of the profile likelihoods. We start with the random intercept, generating a plot of the profile likelihood from 0.1 units below to 0.1 units above the MLE. Since each optimization inside the profile likelihood generates a warning (due to the random slope variance being close to zero), we turn off the warnings here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:38.975889Z",
     "iopub.status.busy": "2026-07-28T19:02:38.975634Z",
     "iopub.status.idle": "2026-07-28T19:02:43.996653Z",
     "shell.execute_reply": "2026-07-28T19:02:43.995767Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "with warnings.catch_warnings():\n",
    "    warnings.filterwarnings(\"ignore\")\n",
    "    likev = mdf.profile_re(0, \"re\", dist_low=0.1, dist_high=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a plot of the profile likelihood function.  We multiply the log-likelihood difference by 2 to obtain the usual $\\chi^2$ reference distribution with 1 degree of freedom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:44.000415Z",
     "iopub.status.busy": "2026-07-28T19:02:44.000176Z",
     "iopub.status.idle": "2026-07-28T19:02:44.005197Z",
     "shell.execute_reply": "2026-07-28T19:02:44.004731Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:44.007946Z",
     "iopub.status.busy": "2026-07-28T19:02:44.007675Z",
     "iopub.status.idle": "2026-07-28T19:02:44.427346Z",
     "shell.execute_reply": "2026-07-28T19:02:44.426829Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '-2 times profile log likelihood')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(likev[:, 0], 2 * likev[:, 1])\n",
    "plt.xlabel(\"Variance of random intercept\", size=17)\n",
    "plt.ylabel(\"-2 times profile log likelihood\", size=17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a plot of the profile likelihood function. The profile likelihood plot shows that the MLE of the random slope variance parameter is a very small positive number, and that there is low uncertainty in this estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:02:44.431670Z",
     "iopub.status.busy": "2026-07-28T19:02:44.431452Z",
     "iopub.status.idle": "2026-07-28T19:02:51.734488Z",
     "shell.execute_reply": "2026-07-28T19:02:51.733740Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "re = mdf.cov_re.iloc[1, 1]\n",
    "with warnings.catch_warnings():\n",
    "    # Parameter is often on the boundary\n",
    "    warnings.simplefilter(\"ignore\", ConvergenceWarning)\n",
    "    likev = mdf.profile_re(1, \"re\", dist_low=0.5 * re, dist_high=0.8 * re)\n",
    "\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(likev[:, 0], 2 * likev[:, 1])\n",
    "plt.xlabel(\"Variance of random slope\", size=17)\n",
    "lbl = plt.ylabel(\"-2 times profile log likelihood\", size=17)"
   ]
  }
 ],
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