{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:09.987499Z",
     "iopub.status.busy": "2025-12-05T18:08:09.987225Z",
     "iopub.status.idle": "2025-12-05T18:08:11.321989Z",
     "shell.execute_reply": "2025-12-05T18:08:11.321150Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:11.325820Z",
     "iopub.status.busy": "2025-12-05T18:08:11.325514Z",
     "iopub.status.idle": "2025-12-05T18:08:13.529599Z",
     "shell.execute_reply": "2025-12-05T18:08:13.523876Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "from scipy import stats\n",
    "from statsmodels.iolib.table import SimpleTable, default_txt_fmt\n",
    "\n",
    "np.random.seed(1024)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## WLS Estimation\n",
    "\n",
    "### Artificial data: Heteroscedasticity 2 groups \n",
    "\n",
    "Model assumptions:\n",
    "\n",
    " * Misspecification: true model is quadratic, estimate only linear\n",
    " * Independent noise/error term\n",
    " * Two groups for error variance, low and high variance groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:13.532409Z",
     "iopub.status.busy": "2025-12-05T18:08:13.532045Z",
     "iopub.status.idle": "2025-12-05T18:08:13.542607Z",
     "shell.execute_reply": "2025-12-05T18:08:13.540733Z"
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "x = np.linspace(0, 20, nsample)\n",
    "X = np.column_stack((x, (x - 5) ** 2))\n",
    "X = sm.add_constant(X)\n",
    "beta = [5.0, 0.5, -0.01]\n",
    "sig = 0.5\n",
    "w = np.ones(nsample)\n",
    "w[nsample * 6 // 10 :] = 3\n",
    "y_true = np.dot(X, beta)\n",
    "e = np.random.normal(size=nsample)\n",
    "y = y_true + sig * w * e\n",
    "X = X[:, [0, 1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### WLS knowing the true variance ratio of heteroscedasticity\n",
    "\n",
    "In this example, `w` is the standard deviation of the error.  `WLS` requires that the weights are proportional to the inverse of the error variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:13.547590Z",
     "iopub.status.busy": "2025-12-05T18:08:13.547338Z",
     "iopub.status.idle": "2025-12-05T18:08:13.571064Z",
     "shell.execute_reply": "2025-12-05T18:08:13.569831Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            WLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.927\n",
      "Model:                            WLS   Adj. R-squared:                  0.926\n",
      "Method:                 Least Squares   F-statistic:                     613.2\n",
      "Date:                Fri, 05 Dec 2025   Prob (F-statistic):           5.44e-29\n",
      "Time:                        18:08:13   Log-Likelihood:                -51.136\n",
      "No. Observations:                  50   AIC:                             106.3\n",
      "Df Residuals:                      48   BIC:                             110.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.2469      0.143     36.790      0.000       4.960       5.534\n",
      "x1             0.4466      0.018     24.764      0.000       0.410       0.483\n",
      "==============================================================================\n",
      "Omnibus:                        0.407   Durbin-Watson:                   2.317\n",
      "Prob(Omnibus):                  0.816   Jarque-Bera (JB):                0.103\n",
      "Skew:                          -0.104   Prob(JB):                        0.950\n",
      "Kurtosis:                       3.075   Cond. No.                         14.6\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "mod_wls = sm.WLS(y, X, weights=1.0 / (w ** 2))\n",
    "res_wls = mod_wls.fit()\n",
    "print(res_wls.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS vs. WLS\n",
    "\n",
    "Estimate an OLS model for comparison: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:13.573123Z",
     "iopub.status.busy": "2025-12-05T18:08:13.572896Z",
     "iopub.status.idle": "2025-12-05T18:08:13.584260Z",
     "shell.execute_reply": "2025-12-05T18:08:13.582857Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.24256099 0.43486879]\n",
      "[5.24685499 0.44658241]\n"
     ]
    }
   ],
   "source": [
    "res_ols = sm.OLS(y, X).fit()\n",
    "print(res_ols.params)\n",
    "print(res_wls.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the WLS standard errors to  heteroscedasticity corrected OLS standard errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:13.587129Z",
     "iopub.status.busy": "2025-12-05T18:08:13.586265Z",
     "iopub.status.idle": "2025-12-05T18:08:13.600158Z",
     "shell.execute_reply": "2025-12-05T18:08:13.598915Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=====================\n",
      "          x1   const \n",
      "---------------------\n",
      "WLS     0.1426  0.018\n",
      "OLS     0.2707 0.0233\n",
      "OLS_HC0  0.194 0.0281\n",
      "OLS_HC1  0.198 0.0287\n",
      "OLS_HC3 0.2003  0.029\n",
      "OLS_HC3  0.207   0.03\n",
      "---------------------\n"
     ]
    }
   ],
   "source": [
    "se = np.vstack(\n",
    "    [\n",
    "        [res_wls.bse],\n",
    "        [res_ols.bse],\n",
    "        [res_ols.HC0_se],\n",
    "        [res_ols.HC1_se],\n",
    "        [res_ols.HC2_se],\n",
    "        [res_ols.HC3_se],\n",
    "    ]\n",
    ")\n",
    "se = np.round(se, 4)\n",
    "colnames = [\"x1\", \"const\"]\n",
    "rownames = [\"WLS\", \"OLS\", \"OLS_HC0\", \"OLS_HC1\", \"OLS_HC3\", \"OLS_HC3\"]\n",
    "tabl = SimpleTable(se, colnames, rownames, txt_fmt=default_txt_fmt)\n",
    "print(tabl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate OLS prediction interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:13.602344Z",
     "iopub.status.busy": "2025-12-05T18:08:13.602128Z",
     "iopub.status.idle": "2025-12-05T18:08:13.614236Z",
     "shell.execute_reply": "2025-12-05T18:08:13.613256Z"
    }
   },
   "outputs": [],
   "source": [
    "covb = res_ols.cov_params()\n",
    "prediction_var = res_ols.mse_resid + (X * np.dot(covb, X.T).T).sum(1)\n",
    "prediction_std = np.sqrt(prediction_var)\n",
    "tppf = stats.t.ppf(0.975, res_ols.df_resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:13.617098Z",
     "iopub.status.busy": "2025-12-05T18:08:13.616881Z",
     "iopub.status.idle": "2025-12-05T18:08:13.630608Z",
     "shell.execute_reply": "2025-12-05T18:08:13.629302Z"
    }
   },
   "outputs": [],
   "source": [
    "pred_ols = res_ols.get_prediction()\n",
    "iv_l_ols = pred_ols.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u_ols = pred_ols.summary_frame()[\"obs_ci_upper\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare predicted values in WLS and OLS:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:13.632891Z",
     "iopub.status.busy": "2025-12-05T18:08:13.632661Z",
     "iopub.status.idle": "2025-12-05T18:08:14.070917Z",
     "shell.execute_reply": "2025-12-05T18:08:14.066604Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f3b25f01450>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_wls = res_wls.get_prediction()\n",
    "iv_l = pred_wls.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_wls.summary_frame()[\"obs_ci_upper\"]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.plot(x, y, \"o\", label=\"Data\")\n",
    "ax.plot(x, y_true, \"b-\", label=\"True\")\n",
    "# OLS\n",
    "ax.plot(x, res_ols.fittedvalues, \"r--\")\n",
    "ax.plot(x, iv_u_ols, \"r--\", label=\"OLS\")\n",
    "ax.plot(x, iv_l_ols, \"r--\")\n",
    "# WLS\n",
    "ax.plot(x, res_wls.fittedvalues, \"g--.\")\n",
    "ax.plot(x, iv_u, \"g--\", label=\"WLS\")\n",
    "ax.plot(x, iv_l, \"g--\")\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feasible Weighted Least Squares (2-stage FWLS)\n",
    "\n",
    "Like `w`, `w_est` is proportional to the standard deviation, and so must be squared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-05T18:08:14.073387Z",
     "iopub.status.busy": "2025-12-05T18:08:14.073129Z",
     "iopub.status.idle": "2025-12-05T18:08:14.101807Z",
     "shell.execute_reply": "2025-12-05T18:08:14.100486Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            WLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.931\n",
      "Model:                            WLS   Adj. R-squared:                  0.929\n",
      "Method:                 Least Squares   F-statistic:                     646.7\n",
      "Date:                Fri, 05 Dec 2025   Prob (F-statistic):           1.66e-29\n",
      "Time:                        18:08:14   Log-Likelihood:                -50.716\n",
      "No. Observations:                  50   AIC:                             105.4\n",
      "Df Residuals:                      48   BIC:                             109.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          5.2363      0.135     38.720      0.000       4.964       5.508\n",
      "x1             0.4492      0.018     25.431      0.000       0.414       0.485\n",
      "==============================================================================\n",
      "Omnibus:                        0.247   Durbin-Watson:                   2.343\n",
      "Prob(Omnibus):                  0.884   Jarque-Bera (JB):                0.179\n",
      "Skew:                          -0.136   Prob(JB):                        0.915\n",
      "Kurtosis:                       2.893   Cond. No.                         14.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "resid1 = res_ols.resid[w == 1.0]\n",
    "var1 = resid1.var(ddof=int(res_ols.df_model) + 1)\n",
    "resid2 = res_ols.resid[w != 1.0]\n",
    "var2 = resid2.var(ddof=int(res_ols.df_model) + 1)\n",
    "w_est = w.copy()\n",
    "w_est[w != 1.0] = np.sqrt(var2) / np.sqrt(var1)\n",
    "res_fwls = sm.WLS(y, X, 1.0 / ((w_est ** 2))).fit()\n",
    "print(res_fwls.summary())"
   ]
  }
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