{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a679fddb",
   "metadata": {},
   "source": [
    "# Model Comparison\n",
    "\n",
    "This notebook shows how to compare fitted models using the methods that\n",
    "`statsmodels` provides for the linear regression family (`OLS`, `WLS` and\n",
    "`GLS`).\n",
    "\n",
    "For any two nested models, `statsmodels` gives you information criteria\n",
    "(`AIC`, `BIC`), likelihood-based tests, and `F` tests to decide whether a\n",
    "more flexible model is worth the extra parameters. We will fit the three\n",
    "members of the linear regression family to the same dataset and compare them\n",
    "side by side."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "01a474bf",
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    "execution": {
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     "shell.execute_reply": "2026-09-08T18:32:47.514543Z"
    },
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   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57504755",
   "metadata": {},
   "source": [
    "## The data\n",
    "\n",
    "We use the classic Longley dataset, which is bundled with `statsmodels`.\n",
    "It is a small macroeconomic time series with six predictors and total\n",
    "employment as the response."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "842e3926",
   "metadata": {
    "collapsed": false,
    "execution": {
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   const  GNPDEFL       GNP   UNEMP   ARMED       POP    YEAR\n",
      "0    1.0     83.0  234289.0  2356.0  1590.0  107608.0  1947.0\n",
      "1    1.0     88.5  259426.0  2325.0  1456.0  108632.0  1948.0\n",
      "2    1.0     88.2  258054.0  3682.0  1616.0  109773.0  1949.0\n",
      "3    1.0     89.5  284599.0  3351.0  1650.0  110929.0  1950.0\n",
      "4    1.0     96.2  328975.0  2099.0  3099.0  112075.0  1951.0\n",
      "Index(['const', 'GNPDEFL', 'GNP', 'UNEMP', 'ARMED', 'POP', 'YEAR'], dtype='str')\n"
     ]
    }
   ],
   "source": [
    "data = sm.datasets.longley.load()\n",
    "data.exog = sm.add_constant(data.exog)\n",
    "print(data.exog.head())\n",
    "print(data.exog.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6342a73a",
   "metadata": {},
   "source": [
    "## Baseline: Ordinary Least Squares (OLS)\n",
    "\n",
    "The OLS model assumes the errors are independent and identically\n",
    "distributed. It is the natural baseline that the other two estimators\n",
    "generalize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f83c0471",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-09-08T18:32:47.555638Z",
     "iopub.status.busy": "2026-09-08T18:32:47.555391Z",
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     "shell.execute_reply": "2026-09-08T18:32:47.582927Z"
    },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 TOTEMP   R-squared:                       0.995\n",
      "Model:                            OLS   Adj. R-squared:                  0.992\n",
      "Method:                 Least Squares   F-statistic:                     330.3\n",
      "Date:                Tue, 08 Sep 2026   Prob (F-statistic):           4.98e-10\n",
      "Time:                        18:32:47   Log-Likelihood:                -109.62\n",
      "No. Observations:                  16   AIC:                             233.2\n",
      "Df Residuals:                       9   BIC:                             238.6\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const      -3.482e+06    8.9e+05     -3.911      0.004    -5.5e+06   -1.47e+06\n",
      "GNPDEFL       15.0619     84.915      0.177      0.863    -177.029     207.153\n",
      "GNP           -0.0358      0.033     -1.070      0.313      -0.112       0.040\n",
      "UNEMP         -2.0202      0.488     -4.136      0.003      -3.125      -0.915\n",
      "ARMED         -1.0332      0.214     -4.822      0.001      -1.518      -0.549\n",
      "POP           -0.0511      0.226     -0.226      0.826      -0.563       0.460\n",
      "YEAR        1829.1515    455.478      4.016      0.003     798.788    2859.515\n",
      "==============================================================================\n",
      "Omnibus:                        0.749   Durbin-Watson:                   2.559\n",
      "Prob(Omnibus):                  0.688   Jarque-Bera (JB):                0.684\n",
      "Skew:                           0.420   Prob(JB):                        0.710\n",
      "Kurtosis:                       2.434   Cond. No.                     4.86e+09\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 4.86e+09. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "ols_res = sm.OLS(data.endog, data.exog).fit()\n",
    "print(ols_res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbcb2586",
   "metadata": {},
   "source": [
    "## Weighted Least Squares (WLS)\n",
    "\n",
    "If the error variance is not constant but proportional to a known variable,\n",
    "weighted least squares is more efficient than OLS. Here we weight each\n",
    "observation by the population (`POP`), i.e. we trust observations from years\n",
    "with a larger population relatively more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "90b3fdea",
   "metadata": {
    "collapsed": false,
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            WLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 TOTEMP   R-squared:                       0.995\n",
      "Model:                            WLS   Adj. R-squared:                  0.992\n",
      "Method:                 Least Squares   F-statistic:                     331.2\n",
      "Date:                Tue, 08 Sep 2026   Prob (F-statistic):           4.92e-10\n",
      "Time:                        18:32:47   Log-Likelihood:                -109.59\n",
      "No. Observations:                  16   AIC:                             233.2\n",
      "Df Residuals:                       9   BIC:                             238.6\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const      -3.513e+06   8.92e+05     -3.939      0.003   -5.53e+06    -1.5e+06\n",
      "GNPDEFL       16.6801     85.244      0.196      0.849    -176.154     209.514\n",
      "GNP           -0.0368      0.034     -1.094      0.302      -0.113       0.039\n",
      "UNEMP         -2.0274      0.491     -4.133      0.003      -3.137      -0.918\n",
      "ARMED         -1.0349      0.215     -4.811      0.001      -1.522      -0.548\n",
      "POP           -0.0498      0.226     -0.220      0.831      -0.561       0.461\n",
      "YEAR        1844.6696    456.006      4.045      0.003     813.113    2876.226\n",
      "==============================================================================\n",
      "Omnibus:                        0.958   Durbin-Watson:                   2.548\n",
      "Prob(Omnibus):                  0.619   Jarque-Bera (JB):                0.820\n",
      "Skew:                           0.478   Prob(JB):                        0.664\n",
      "Kurtosis:                       2.437   Cond. No.                     4.94e+09\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 4.94e+09. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "weights = data.exog[\"POP\"].to_numpy(dtype=float)\n",
    "wls_res = sm.WLS(data.endog, data.exog, weights=weights).fit()\n",
    "print(wls_res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e21c5d5c",
   "metadata": {},
   "source": [
    "## Generalized Least Squares (GLS)\n",
    "\n",
    "When the errors are correlated (as is often the case in time series), GLS\n",
    "can take that correlation structure into account. We fit the same model but\n",
    "assume the errors follow an AR(1) process. A consistent estimate of the\n",
    "autocorrelation $\\rho$ is obtained from the OLS residuals, and the\n",
    "corresponding covariance matrix is used in the GLS fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "19262972",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-09-08T18:32:47.652015Z"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            GLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 TOTEMP   R-squared:                       0.998\n",
      "Model:                            GLS   Adj. R-squared:                  0.997\n",
      "Method:                 Least Squares   F-statistic:                     734.7\n",
      "Date:                Tue, 08 Sep 2026   Prob (F-statistic):           1.39e-11\n",
      "Time:                        18:32:47   Log-Likelihood:                -107.46\n",
      "No. Observations:                  16   AIC:                             228.9\n",
      "Df Residuals:                       9   BIC:                             234.3\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const      -3.802e+06   6.67e+05     -5.703      0.000   -5.31e+06   -2.29e+06\n",
      "GNPDEFL      -13.3013     69.084     -0.193      0.852    -169.581     142.978\n",
      "GNP           -0.0380      0.026     -1.456      0.179      -0.097       0.021\n",
      "UNEMP         -2.1894      0.380     -5.758      0.000      -3.049      -1.329\n",
      "ARMED         -1.1536      0.164     -7.020      0.000      -1.525      -0.782\n",
      "POP           -0.0684      0.175     -0.390      0.706      -0.465       0.328\n",
      "YEAR        1995.8864    340.504      5.862      0.000    1225.612    2766.160\n",
      "==============================================================================\n",
      "Omnibus:                        0.124   Durbin-Watson:                   2.612\n",
      "Prob(Omnibus):                  0.940   Jarque-Bera (JB):                0.345\n",
      "Skew:                          -0.049   Prob(JB):                        0.842\n",
      "Kurtosis:                       2.288   Cond. No.                     5.62e+09\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.62e+09. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "ols_resid = np.asarray(ols_res.resid)\n",
    "rho = np.corrcoef(ols_resid[1:], ols_resid[:-1])[0, 1]\n",
    "n = len(data.endog)\n",
    "sigma = rho ** np.abs(np.subtract.outer(np.arange(n), np.arange(n)))\n",
    "gls_res = sm.GLS(data.endog, data.exog, sigma=sigma).fit()\n",
    "print(gls_res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f925c9d",
   "metadata": {},
   "source": [
    "## Comparing the models\n",
    "\n",
    "The simplest comparison uses the information criteria. Lower values of `AIC`\n",
    "and `BIC` indicate a better fit after penalizing model complexity. The\n",
    "log-likelihood (`llf`) measures how well the model fits the data, and\n",
    "`R-squared` is the usual coefficient of determination."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "60501aa0",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-09-08T18:32:47.655321Z",
     "iopub.status.busy": "2026-09-08T18:32:47.654995Z",
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     "shell.execute_reply": "2026-09-08T18:32:47.666290Z"
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     "outputs_hidden": false
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model            AIC         BIC       log-L        R2\n",
      "OLS          233.235     238.643    -109.617    0.9955\n",
      "WLS          233.175     238.584    -109.588    0.9955\n",
      "GLS          228.911     234.320    -107.456    0.9980\n"
     ]
    }
   ],
   "source": [
    "results = [ols_res, wls_res, gls_res]\n",
    "names = [\"OLS\", \"WLS\", \"GLS\"]\n",
    "\n",
    "print(f\"{'Model':<8}{'AIC':>12}{'BIC':>12}{'log-L':>12}{'R2':>10}\")\n",
    "for name, res in zip(names, results, strict=False):\n",
    "    print(\n",
    "        f\"{name:<8}\"\n",
    "        f\"{res.aic:>12.3f}\"\n",
    "        f\"{res.bic:>12.3f}\"\n",
    "        f\"{res.llf:>12.3f}\"\n",
    "        f\"{res.rsquared:>10.4f}\"\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e50438df",
   "metadata": {},
   "source": [
    "## Comparing nested models\n",
    "\n",
    "`statsmodels` also provides formal hypothesis tests for nested models. The\n",
    "methods `compare_lr_test` (likelihood ratio test) and `compare_f_test`\n",
    "(Chow-style F test) compare a larger model against a restricted model that\n",
    "drops one or more regressors.\n",
    "\n",
    "As an example, we take the baseline OLS model and remove the `ARMED`\n",
    "regressor. Both tests tell us whether dropping that regressor significantly\n",
    "worsens the fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "af52880b",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-09-08T18:32:47.669774Z",
     "iopub.status.busy": "2026-09-08T18:32:47.669554Z",
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     "shell.execute_reply": "2026-09-08T18:32:47.683529Z"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Likelihood ratio test: stat=20.421, p-value=0.0000, df=1.0\n",
      "F test:                stat=23.252, p-value=0.0009, df=1.0\n"
     ]
    }
   ],
   "source": [
    "exog_restricted = data.exog.drop(columns=[\"ARMED\"])\n",
    "restricted_res = sm.OLS(data.endog, exog_restricted).fit()\n",
    "\n",
    "lr_stat, lr_pvalue, lr_df = ols_res.compare_lr_test(restricted_res)\n",
    "f_stat, f_pvalue, f_df = ols_res.compare_f_test(restricted_res)\n",
    "\n",
    "print(f\"Likelihood ratio test: stat={lr_stat:.3f}, p-value={lr_pvalue:.4f}, df={lr_df}\")\n",
    "print(f\"F test:                stat={f_stat:.3f}, p-value={f_pvalue:.4f}, df={f_df}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4139483",
   "metadata": {},
   "source": [
    "## Visual check of the fitted values\n",
    "\n",
    "Finally, a quick visual comparison of the fitted values produced by the\n",
    "three estimators. We scatter the fitted values from `OLS`, `WLS` and `GLS`\n",
    "against the observed values on a single plot, using a distinct color for\n",
    "each estimator. The closer the points hug the dashed identity line, the\n",
    "better the fit.\n"
   ]
  },
  {
   "cell_type": "code",
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   "id": "f09abb90",
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    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x550 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = [\"#1f77b4\", \"#ff7f0e\", \"#2ca02c\"]\n",
    "fig, ax = plt.subplots(figsize=(7, 5.5))\n",
    "for name, res, color in zip(names, results, colors, strict=False):\n",
    "    ax.scatter(data.endog, res.fittedvalues, alpha=0.65, label=name, color=color)\n",
    "ymin, ymax = ax.get_ylim()\n",
    "ax.plot([ymin, ymax], [ymin, ymax], color=\"k\", linestyle=\"--\", linewidth=0.8)\n",
    "ax.set_xlabel(\"Observed values\")\n",
    "ax.set_ylabel(\"Fitted values\")\n",
    "ax.set_title(\"Fitted values from OLS, WLS and GLS\")\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13c23686",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "In this example the GLS estimator, which accounts for the serial\n",
    "correlation in the residuals, achieves the lowest `AIC` and `BIC` among the\n",
    "three models. The nested-model tests show that `ARMED` is a statistically\n",
    "significant predictor, so it should be kept in the model.\n",
    "\n",
    "The key takeaway: for nested models `compare_lr_test` and `compare_f_test`\n",
    "give you a formal answer, and for non-nested models the information criteria\n",
    "(`AIC`/`BIC`) are the tool to use."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.14.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}