{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:07:42.966405Z",
     "iopub.status.busy": "2022-11-02T17:07:42.963726Z",
     "iopub.status.idle": "2022-11-02T17:07:43.449324Z",
     "shell.execute_reply": "2022-11-02T17:07:43.448688Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:07:43.453025Z",
     "iopub.status.busy": "2022-11-02T17:07:43.452542Z",
     "iopub.status.idle": "2022-11-02T17:07:44.267443Z",
     "shell.execute_reply": "2022-11-02T17:07:44.266597Z"
    }
   },
   "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": "2022-11-02T17:07:44.271640Z",
     "iopub.status.busy": "2022-11-02T17:07:44.271105Z",
     "iopub.status.idle": "2022-11-02T17:07:44.284079Z",
     "shell.execute_reply": "2022-11-02T17:07:44.283352Z"
    }
   },
   "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": "2022-11-02T17:07:44.287653Z",
     "iopub.status.busy": "2022-11-02T17:07:44.287254Z",
     "iopub.status.idle": "2022-11-02T17:07:44.312474Z",
     "shell.execute_reply": "2022-11-02T17:07:44.311658Z"
    }
   },
   "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:                Wed, 02 Nov 2022   Prob (F-statistic):           5.44e-29\n",
      "Time:                        17:07:44   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": "2022-11-02T17:07:44.315627Z",
     "iopub.status.busy": "2022-11-02T17:07:44.315248Z",
     "iopub.status.idle": "2022-11-02T17:07:44.322125Z",
     "shell.execute_reply": "2022-11-02T17:07:44.320797Z"
    }
   },
   "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": "2022-11-02T17:07:44.325367Z",
     "iopub.status.busy": "2022-11-02T17:07:44.324995Z",
     "iopub.status.idle": "2022-11-02T17:07:44.336178Z",
     "shell.execute_reply": "2022-11-02T17:07:44.335468Z"
    },
    "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": "2022-11-02T17:07:44.339256Z",
     "iopub.status.busy": "2022-11-02T17:07:44.338880Z",
     "iopub.status.idle": "2022-11-02T17:07:44.344263Z",
     "shell.execute_reply": "2022-11-02T17:07:44.343583Z"
    }
   },
   "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": "2022-11-02T17:07:44.347466Z",
     "iopub.status.busy": "2022-11-02T17:07:44.347122Z",
     "iopub.status.idle": "2022-11-02T17:07:44.356957Z",
     "shell.execute_reply": "2022-11-02T17:07:44.356277Z"
    }
   },
   "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": "2022-11-02T17:07:44.360287Z",
     "iopub.status.busy": "2022-11-02T17:07:44.359935Z",
     "iopub.status.idle": "2022-11-02T17:07:44.610907Z",
     "shell.execute_reply": "2022-11-02T17:07:44.610247Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4baeee04f0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "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": "2022-11-02T17:07:44.614898Z",
     "iopub.status.busy": "2022-11-02T17:07:44.614654Z",
     "iopub.status.idle": "2022-11-02T17:07:44.628202Z",
     "shell.execute_reply": "2022-11-02T17:07:44.627652Z"
    }
   },
   "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:                Wed, 02 Nov 2022   Prob (F-statistic):           1.66e-29\n",
      "Time:                        17:07:44   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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