{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "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": {
 
 
 
 
    }
   },
   "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": {
 
 
 
 
    }
   },
   "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:                Thu, 18 Dec 2025   Prob (F-statistic):           5.44e-29\n",
      "Time:                        07:37:30   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": {
 
 
 
 
    }
   },
   "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": {
 
 
 
 
    },
    "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": {
 
 
 
 
    }
   },
   "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": {
 
 
 
 
    }
   },
   "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": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xadde5de1e8ed>"
      ]
     },
     "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": {
 
 
 
 
    }
   },
   "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:                Thu, 18 Dec 2025   Prob (F-statistic):           1.66e-29\n",
      "Time:                        07:37:30   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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