{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:42:22.464461Z",
     "iopub.status.busy": "2023-12-14T14:42:22.464215Z",
     "iopub.status.idle": "2023-12-14T14:42:23.712521Z",
     "shell.execute_reply": "2023-12-14T14:42:23.711676Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:42:23.716584Z",
     "iopub.status.busy": "2023-12-14T14:42:23.716102Z",
     "iopub.status.idle": "2023-12-14T14:42:25.477785Z",
     "shell.execute_reply": "2023-12-14T14:42:25.476786Z"
    }
   },
   "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": "2023-12-14T14:42:25.482015Z",
     "iopub.status.busy": "2023-12-14T14:42:25.481401Z",
     "iopub.status.idle": "2023-12-14T14:42:25.489694Z",
     "shell.execute_reply": "2023-12-14T14:42:25.488907Z"
    }
   },
   "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": "2023-12-14T14:42:25.493381Z",
     "iopub.status.busy": "2023-12-14T14:42:25.492991Z",
     "iopub.status.idle": "2023-12-14T14:42:25.520977Z",
     "shell.execute_reply": "2023-12-14T14:42:25.520231Z"
    }
   },
   "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, 14 Dec 2023   Prob (F-statistic):           5.44e-29\n",
      "Time:                        14:42:25   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": "2023-12-14T14:42:25.524598Z",
     "iopub.status.busy": "2023-12-14T14:42:25.524249Z",
     "iopub.status.idle": "2023-12-14T14:42:25.531413Z",
     "shell.execute_reply": "2023-12-14T14:42:25.530570Z"
    }
   },
   "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": "2023-12-14T14:42:25.535170Z",
     "iopub.status.busy": "2023-12-14T14:42:25.534746Z",
     "iopub.status.idle": "2023-12-14T14:42:25.546770Z",
     "shell.execute_reply": "2023-12-14T14:42:25.545956Z"
    },
    "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": "2023-12-14T14:42:25.550478Z",
     "iopub.status.busy": "2023-12-14T14:42:25.549980Z",
     "iopub.status.idle": "2023-12-14T14:42:25.558486Z",
     "shell.execute_reply": "2023-12-14T14:42:25.557302Z"
    }
   },
   "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": "2023-12-14T14:42:25.561900Z",
     "iopub.status.busy": "2023-12-14T14:42:25.561457Z",
     "iopub.status.idle": "2023-12-14T14:42:25.575857Z",
     "shell.execute_reply": "2023-12-14T14:42:25.575011Z"
    }
   },
   "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": "2023-12-14T14:42:25.579766Z",
     "iopub.status.busy": "2023-12-14T14:42:25.579324Z",
     "iopub.status.idle": "2023-12-14T14:42:26.016469Z",
     "shell.execute_reply": "2023-12-14T14:42:26.015709Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f48641b51b0>"
      ]
     },
     "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": "2023-12-14T14:42:26.020369Z",
     "iopub.status.busy": "2023-12-14T14:42:26.019862Z",
     "iopub.status.idle": "2023-12-14T14:42:26.046538Z",
     "shell.execute_reply": "2023-12-14T14:42:26.045695Z"
    }
   },
   "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, 14 Dec 2023   Prob (F-statistic):           1.66e-29\n",
      "Time:                        14:42:26   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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