code and notes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Outline\n",
    "\n",
    "`Linear regression` is the most basic of the most basic statistical measurement models, supervised learning models.\n",
    "\n",
    "- preprocessing\n",
    "\n",
    "- modelling & solving optimization problems.\n",
    "\n",
    "- Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Management\n",
    "import pandas as pd\n",
    "# Data modeling\n",
    "import numpy as np # matrix computation\n",
    "import statsmodels.api as sm # Econometrics and statistics\n",
    "import sklearn as sk # Artificial Intelligence and data mining\n",
    "# Data visualization\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Preprocessing\n",
    "- Data structure\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Survey data ≠ observational data\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Observation units: `(individual, given time) -> Cross Sectional Data` or `(individual, time) -> Time Series Data` or `(given individual, time)--> Panel Data`\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Covariate, independent variable, dependent variable\n",
    "\n",
    "- Data set segmentation\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  In the field of Artificial Intelligence and data mining: Train: Validation: Test = 70% : 10% : 20%\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp;  Train: Used for parameter estimation\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp;  Validation: Finding the optimal hyperparameter (to prevent failure, always make a cluster of similar models)\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp;  Test: Performing a downstream evaluation\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp;  Application: Deploying the model to the real life!\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  In the field of Econometrics and statistics:\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp;  In the past, there was no concept of splitting datasets, because the focus was on `parameter estimation and hypothesis testing` and less on the `prediction` problem.\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp;  But it is now moving towards the former."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['ORCID', 'to_China', 'last_phd', 'total_pub', 'age', 'work1_avg',\n",
      "       'conn', 'is_Chinese', 'work_diff'],\n",
      "      dtype='object')\n",
      "True\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "# pandas数据导入\n",
    "df = pd.read_csv('Regression-SciTech.csv')\n",
    "print(df.columns)\n",
    "\n",
    "# 数据校验 - 1重复\n",
    "dup = df[['ORCID', 'age']].duplicated() \n",
    "print(dup.any()) # True !  \n",
    "print(dup.sum()) # 35个重复数据   # 当重复仅考虑ORCID和age时有两个"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>to_China</th>\n",
       "      <td>0.557654</td>\n",
       "      <td>0.496765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>last_phd</th>\n",
       "      <td>0.312977</td>\n",
       "      <td>0.463798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total_pub</th>\n",
       "      <td>11.539172</td>\n",
       "      <td>20.344880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>4.837686</td>\n",
       "      <td>3.633558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>work1_avg</th>\n",
       "      <td>0.138418</td>\n",
       "      <td>0.241913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>conn</th>\n",
       "      <td>0.459622</td>\n",
       "      <td>0.927039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>is_Chinese</th>\n",
       "      <td>0.842909</td>\n",
       "      <td>0.363960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>work_diff</th>\n",
       "      <td>0.056021</td>\n",
       "      <td>0.304667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean        std\n",
       "to_China     0.557654   0.496765\n",
       "last_phd     0.312977   0.463798\n",
       "total_pub   11.539172  20.344880\n",
       "age          4.837686   3.633558\n",
       "work1_avg    0.138418   0.241913\n",
       "conn         0.459622   0.927039\n",
       "is_Chinese   0.842909   0.363960\n",
       "work_diff    0.056021   0.304667"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 描述统计\n",
    "statsdf = df.drop('ORCID', axis=1) # 去除id，统计其他的\n",
    "pd.DataFrame({'mean': statsdf.mean(), 'std':statsdf.std()})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Modeling and solving optimization problems\n",
    "- 2.1 Model setting\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  'Linear model' is a classical model\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; Univariate Version: $Y=\\beta_{0}·\\boldsymbol{1} + \\beta_{1}·X_{1} + \\epsilon$\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; &emsp; Multivariate Version: $Y=\\beta_{0}·\\boldsymbol{1} + \\beta_{1}·X_{1} + (\\beta_{2}·X_{2} + ...   \\beta_{K}·X_{K}) + \\epsilon$\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  `Explainable Nonlinear model` is the frontier model and many statisticians are exploring this topics!\n",
    "\n",
    "I'm sure some people find linear models inplausible (as I did when I first learned them), but believer me it's a good start to understanding data.\n",
    "\n",
    "- 2.2 Optimization objectives and constraints (repeatedly found in history, also known as the `parameter estimation'` problem)\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Elementary mathematical problems: profit `maximization`, area `maximization`, `maximum value` problem\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Economics problem: `Utility function maximization`\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Operational research problems: `combinatorial optimization problem`, `discrete optimization problem`\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Physics problem: `Lagrange multiplier method` (essentially a data optimization algorithm)\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Statistics problem: `Maximizing the likelihood function`\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Artificial Intelligence and Data Mining problems:\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  The first understanding: `minimize the loss function`\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  Gaussian invented a special `least squares method (OLS)` for linear regression\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  a.k.a finds a set of parameters that minimizes the prediction error\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;   $min_{\\boldsymbol{\\beta}}RMSE = min_{\\boldsymbol{\\beta}}\\sqrt{\\frac{1}{m}\\sum^{m}_{i=1}(y_{i}-\\hat{y_{i}})^2}$\n",
    "\n",
    "&emsp;\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  Second understanding: '`Minimize the log-likelihood function (MLE)` (equivalent in linear regression when our sample are large enough)\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  It is necessary to use more advanced numerical optimization algorithms such as' quasi-Newton method 'and' Adam algorithm '\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  a.k.a finds a set of parameters that maximizes the probability that a sample will be observed\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  We need to add an assumption: Suppose that the perturbation term satisfies $\\boldsymbol{\\epsilon|X} \\sim N(\\boldsymbol{0}, \\sigma^2\\boldsymbol{I_{n}})$\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  $min_{\\beta,  \\sigma^2}\\it{f(\\boldsymbol{y}|\\boldsymbol{X})}=(2\\pi\\sigma^2)^{-\\frac{n}{2}}exp\\{\\frac{(y_{i}-\\hat{y_{i}})^2}{2\\sigma^2} The \\} $\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  &emsp; &emsp; &emsp; &emsp;  which is equivalent to optimizing $min_{\\beta, \\sigma^2}\\it{ln(f(\\boldsymbol{y}|\\boldsymbol{X}))}=CONSTANT-\\frac{n}{2}ln\\sigma^2-\\frac{(y_{i}-\\hat{y_{i}})^2}{2\\sigma^2 } $\n",
    "\n",
    "2.3 Using the trained model to do downstream tasks (output something)\n",
    "\n",
    "> Linear regression is explicit modeling (can write a relatively simple formula, ChatGPT is also a model but can not be written), some will fit the model to the report for migration application.\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  In-sample `Fitting`\n",
    "\n",
    "&emsp; &emsp; &emsp; &emsp;  Out-of-sample `predictions (continuous values, discrete categories)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              work_diff   R-squared:                       0.035\n",
      "Model:                            OLS   Adj. R-squared:                  0.032\n",
      "Method:                 Least Squares   F-statistic:                     14.86\n",
      "Date:                Mon, 16 Oct 2023   Prob (F-statistic):           9.17e-17\n",
      "Time:                        20:29:19   Log-Likelihood:                -529.04\n",
      "No. Observations:                2489   AIC:                             1072.\n",
      "Df Residuals:                    2482   BIC:                             1113.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0510      0.024      2.098      0.036       0.003       0.099\n",
      "to_China       0.0145      0.016      0.924      0.355      -0.016       0.045\n",
      "last_phd      -0.0714      0.014     -4.947      0.000      -0.100      -0.043\n",
      "total_pub     -0.0018      0.000     -4.975      0.000      -0.002      -0.001\n",
      "age            0.0053      0.002      2.581      0.010       0.001       0.009\n",
      "conn           0.0247      0.008      3.156      0.002       0.009       0.040\n",
      "is_Chinese     0.0035      0.019      0.182      0.856      -0.035       0.042\n",
      "==============================================================================\n",
      "Omnibus:                     1068.585   Durbin-Watson:                   1.986\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            36759.279\n",
      "Skew:                           1.372   Prob(JB):                         0.00\n",
      "Kurtosis:                      21.626   Cond. No.                         126.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\\n数据结果分析说明：\\n模型一：简单的多元线性回归\\n（1） R2=0.035；调整R2=0.032 （依据自变量数目调整），说明模型整体拟合效果较差。\\n不过模型通过了F检验，说明模型优于直接预测y为数据中y的均值 （手动狗头）\\n（2） 关注核心自变量to_china的系数预测，其/beta值为0.0145，标准误为0.924，p值为0.355，故无法拒绝其系数为0的原假设\\n系数的含义（若显著可以这么解释）：由于to_china是二值变量，所以系数可以解释为，控制其他因素后，选择回到中国（x为1）的人，观测到的work_diff(y)的期望会增加0.0145。\\n（3）其他自变量\\nconst 常数项，意义是其他所有自变量都为0时，观察到的work_diff的期望，该值的意义不大，因为不少连续变量取0时没有什么现实意义\\nlast_phd 也是二值变量，其系数显著。该系数说明在控制了其他变量的情况下，流动前已经博士毕业的人的平均work_diff比流动前未博士毕业的人低0.0714\\ntotal_pub 是数值变量，其系数显著。在控制了其他变量的情况下，流动前发表的论文数量每多1篇，流动后work_diff的期望就减少0.0018\\n\\n（4）结论\\n这个模型并不支持流入中国使科学家的业绩变好的假设。\\n'"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# statsmodels建模\n",
    "\n",
    "# 模型一，简单多元线性回归\n",
    "y = df['work_diff'] \n",
    "Xdf = df[['to_China', 'last_phd', 'total_pub', 'age', 'conn', 'is_Chinese']]\n",
    "X = sm.add_constant(Xdf)\n",
    "\n",
    "mod = sm.OLS(y, X)\n",
    "res = mod.fit()\n",
    "print(res.summary())\n",
    "\n",
    "'''\n",
    "数据结果分析说明：\n",
    "模型一：简单的多元线性回归\n",
    "（1） R2=0.035；调整R2=0.032 （依据自变量数目调整），说明模型整体拟合效果较差。\n",
    "不过模型通过了F检验，说明模型优于直接预测y为数据中y的均值 （手动狗头）\n",
    "（2） 关注核心自变量to_china的系数预测，其/beta值为0.0145，标准误为0.924，p值为0.355，故无法拒绝其系数为0的原假设\n",
    "系数的含义（若显著可以这么解释）：由于to_china是二值变量，所以系数可以解释为，控制其他因素后，选择回到中国（x为1）的人，观测到的work_diff(y)的期望会增加0.0145。\n",
    "（3）其他自变量\n",
    "const 常数项，意义是其他所有自变量都为0时，观察到的work_diff的期望，该值的意义不大，因为不少连续变量取0时没有什么现实意义\n",
    "last_phd 也是二值变量，其系数显著。该系数说明在控制了其他变量的情况下，流动前已经博士毕业的人的平均work_diff比流动前未博士毕业的人低0.0714\n",
    "total_pub 是数值变量，其系数显著。在控制了其他变量的情况下，流动前发表的论文数量每多1篇，流动后work_diff的期望就减少0.0018\n",
    "\n",
    "（4）结论\n",
    "这个模型并不支持流入中国使科学家的业绩变好的假设。\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1742 253 494\n",
      "model1\n",
      "coefficients: [ 0.01729388 -0.07338427 -0.00042955  0.00024032  0.02283009  0.00415078]\n",
      "intercept: 0.059802556651392405\n",
      "model2\n",
      "coefficients: [-2.77722760e-02 -5.24165688e-02 -3.98727611e-05  1.71164832e-03\n",
      " -2.66121503e-02  1.75537748e-02  1.06242357e-01  4.72599515e-03\n",
      " -8.72996903e-03  2.49431155e-02 -1.02185012e-02 -6.47620797e-03\n",
      "  4.58568893e-04 -2.61871031e-02 -2.06896255e-02 -5.07466508e-05\n",
      "  1.43919641e-03 -3.35382025e-03 -4.48058160e-03  8.27793201e-03\n",
      "  3.21184745e-02]\n",
      "intercept: 0.06406449888191747\n",
      "model3\n",
      "coefficients: [-0.00000000e+00 -0.00000000e+00 -0.00000000e+00  0.00000000e+00\n",
      "  0.00000000e+00  0.00000000e+00  0.00000000e+00  1.60225905e-03\n",
      " -0.00000000e+00  0.00000000e+00  0.00000000e+00 -7.42965591e-03\n",
      " -0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -4.65468411e-05\n",
      "  1.14172259e-03 -4.82775760e-04 -0.00000000e+00  0.00000000e+00\n",
      "  0.00000000e+00]\n",
      "intercept: 0.06335678401553732\n",
      "调参(模型选择)\n",
      "        MSE       MAE        R2\n",
      "0  0.089807  0.174928  0.023160\n",
      "1  0.089224  0.163381  0.007278\n",
      "2  0.085530  0.172244  0.061565\n",
      "3  0.084462  0.155712 -0.000759\n",
      "4  0.086990  0.172156  0.045540\n",
      "5  0.085611  0.155325 -0.014373\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\\n        MSE       MAE        R2\\n0  0.090463  0.174077  0.034179\\n1  0.068104  0.159262  0.017061\\n2  0.083340  0.169030  0.102470\\n3  0.061953  0.154945  0.047781\\n4  0.085253  0.170492  0.081868\\n5  0.063665  0.155830  0.021459'"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sklearn建模\n",
    "# 和前面一样加载数据\n",
    "y = df['work_diff']\n",
    "Xdf = df[['to_China', 'last_phd', 'total_pub', 'age', 'conn', 'is_Chinese']]\n",
    "randSeed = 65 # 固定随机种子\n",
    "\n",
    "# 原始数据分割\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_else, y_train, y_else = train_test_split(Xdf, y, test_size=0.3,  # 先划分出训练集\n",
    "                                                 shuffle=True, \n",
    "                                                 random_state=randSeed)\n",
    "X_valid, X_test, y_valid, y_test = train_test_split(X_else, y_else, test_size=0.66,  # 再划分验证集和测试集\n",
    "                                                 shuffle=True, \n",
    "                                                 random_state=randSeed)\n",
    "print(len(X_train), len(X_valid), len(X_test)) # 划分的三个集合的长度\n",
    "\n",
    "# 加载模型\n",
    "from sklearn import linear_model\n",
    "\n",
    "# 模型一，基础多元线性回归\n",
    "model1 = linear_model.LinearRegression()\n",
    "model1.fit(X_train, y_train)\n",
    "# 系数\n",
    "print('model1')\n",
    "print(\"coefficients:\",model1.coef_)\n",
    "# 截距 \n",
    "print(\"intercept:\",model1.intercept_)\n",
    "# 查看后和前面的大差不差\n",
    "\n",
    "\n",
    "# 模型二，加入二项式交互\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly = PolynomialFeatures(interaction_only=True, include_bias=False)\n",
    "extendedX = poly.fit_transform(X_train) # shape (1742, 21) 即 6 + C_2_6 个特征\n",
    "model2 = linear_model.LinearRegression()\n",
    "model2.fit(extendedX, y_train)\n",
    "# 系数 \n",
    "print('model2')\n",
    "print(\"coefficients:\",model2.coef_)\n",
    "# 截距\n",
    "print(\"intercept:\",model2.intercept_)\n",
    "\n",
    "# 模型三，在所有二次项式交互的基础上，采用Lasso回归（即 L1 正则，正则项会让一些不显著的系数更趋近于0 ）\n",
    "# 原因是模型二加入的不少交互系数不一定相关，除了Lasso回归外，也可以采用大概模型搜索的思路，一个一个做F检验？？\n",
    "model3 = linear_model.Lasso(alpha=0.05)\n",
    "model3.fit(extendedX, y_train)\n",
    "print('model3')\n",
    "# 系数 \n",
    "print(\"coefficients:\",model3.coef_)\n",
    "# 截距\n",
    "print(\"intercept:\",model3.intercept_)\n",
    "\n",
    "\n",
    "# 利用validSet调整模型超参数\n",
    "print('调参(模型选择)')\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error\n",
    "stats_dic = {'MSE':[], 'MAE':[], 'R2':[]}\n",
    "# MSE 均方误差\n",
    "stats_dic['MSE'].append(mean_squared_error(y_train, model1.predict(X_train)))\n",
    "stats_dic['MSE'].append(mean_squared_error(y_valid, model1.predict(X_valid)))\n",
    "stats_dic['MSE'].append(mean_squared_error(y_train, model2.predict(poly.fit_transform(X_train))))\n",
    "stats_dic['MSE'].append(mean_squared_error(y_valid, model2.predict(poly.fit_transform(X_valid))))\n",
    "stats_dic['MSE'].append(mean_squared_error(y_train, model3.predict(poly.fit_transform(X_train))))\n",
    "stats_dic['MSE'].append(mean_squared_error(y_valid, model3.predict(poly.fit_transform(X_valid))))\n",
    "# RMSE就是开个方，不算了\n",
    "# MAE \n",
    "stats_dic['MAE'].append(mean_absolute_error(y_train, model1.predict(X_train)))\n",
    "stats_dic['MAE'].append(mean_absolute_error(y_valid, model1.predict(X_valid)))\n",
    "stats_dic['MAE'].append(mean_absolute_error(y_train, model2.predict(poly.fit_transform(X_train))))\n",
    "stats_dic['MAE'].append(mean_absolute_error(y_valid, model2.predict(poly.fit_transform(X_valid))))\n",
    "stats_dic['MAE'].append(mean_absolute_error(y_train, model3.predict(poly.fit_transform(X_train))))\n",
    "stats_dic['MAE'].append(mean_absolute_error(y_valid, model3.predict(poly.fit_transform(X_valid))))\n",
    "# 调整R2\n",
    "stats_dic['R2'].append(1 - (1 - model1.score(X_train, y_train)) * (len(y_train)-1) / (len(y_train) - X_train.shape[1] - 1))\n",
    "stats_dic['R2'].append(1 - (1 - model1.score(X_valid, y_valid)) * (len(y_valid)-1) / (len(y_valid) - X_valid.shape[1] - 1))\n",
    "stats_dic['R2'].append(1 - (1 - model2.score(poly.fit_transform(X_train), y_train)) * (len(y_train)-1) / (len(y_train) - 21 - 1)) # 21就是extended的特征数\n",
    "stats_dic['R2'].append(1 - (1 - model2.score(poly.fit_transform(X_valid), y_valid)) * (len(y_valid)-1) / (len(y_valid) - 21 - 1))\n",
    "stats_dic['R2'].append(1 - (1 - model3.score(poly.fit_transform(X_train), y_train)) * (len(y_train)-1) / (len(y_train) - 21 - 1))\n",
    "stats_dic['R2'].append(1 - (1 - model3.score(poly.fit_transform(X_valid), y_valid)) * (len(y_valid)-1) / (len(y_valid) - 21 - 1))\n",
    "\n",
    "#print(pd.DataFrame(stats_dic))\n",
    "indices = ['Model1train', 'Model1valid', 'Model2train', 'Model2valid', 'Model3train', 'Model3valid'] \n",
    "# 从上到下的数据如下所示\n",
    "print(pd.DataFrame(stats_dic))\n",
    "'''\n",
    "        MSE       MAE        R2\n",
    "0  0.090463  0.174077  0.034179\n",
    "1  0.068104  0.159262  0.017061\n",
    "2  0.083340  0.169030  0.102470\n",
    "3  0.061953  0.154945  0.047781\n",
    "4  0.085253  0.170492  0.081868\n",
    "5  0.063665  0.155830  0.021459'''\n",
    "# 模型三的系数显示，X2与x3， x3与x4，x3与x5， x3与x6，x4与x5，x4与x6的交互项的系数的预测效果更好\n",
    "# 模型二的拟合效果最好（尤其在验证集上），最终采用模型二"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Evaluation\n",
    "- Main assessment contents of econometrics and statistics\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; 'Hypothesis testing of the estimated parameters' is its (traditional) core!\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp; 系Coefficient of significance : $H_{0} : \\beta_{k} = \\overline{\\beta_{k}}$ here we set $\\overline{\\beta_{i}}=0$ \n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp; a.k.a 'null hypothesis holds' <=>' There is no linear correlation between X and Y '\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp; Metrics : $t_{k} = \\frac{b_{k} - \\beta_{k}}{SE(b_{k})}$ \n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp; where $SE(b_{k})=\\sqrt{s^2(\\boldsymbol{X^{T}}\\boldsymbol{X})^{-1}}$ is called estimated standard error, or standard error\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp; Derived Merics : p-value $p_{k} = 2 · P(t > |t_{k}|)$\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp; Derived Merics : confidence interval upper/lower bound \n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp;$bound(\\alpha) = b_{k} ± T(\\frac{\\alpha}{2})·SE(b_{k})$ 注 : $T(·)$ is student-t distribution function\n",
    "\n",
    "> In a general empirical study, we often want to demonstrate that X is linearly correlated with Y, and so we want to reject the null hypothesis(but don't do p-hacking!)\n",
    "\n",
    "> if $|t_{k}|↑$(i.e.$p_{k}↓$)，it suggests that the original hypothesis $H_{0}$ is not credible so we tend to ` refused ` original hypothesis\n",
    "\n",
    "> So there were lots of bad papers that were 'p-hacking' for publication\n",
    "\n",
    "> The intuitive meaning of the confidence interval here is: if the confidence level is $1-\\alpha$, and the same 'sampling' runs $n$ times to get $n$ confidence intervals, then approximately $(1-\\alpha)n$ confidence intervals cover the true parameter $\\beta_{k}$\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; `Confidence intervals and prediction intervals of predicted values` are also issues of concern, but the formula is complex.\n",
    "\n",
    "- Main evaluation in the field of artificial intelligence and data mining\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; `How good it fits' is its focus!\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; `Regression Prediction`Evaluation Metrics : $MSE$、$RMSE$、$MAE$、$R^2$\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp;  $↓MSE = \\frac{1}{m}\\sum^{m}_{i=1}(y_{i}-\\hat{y_{i}})^2$\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp;  $↓RMSE = \\sqrt{\\frac{1}{m}\\sum^{m}_{i=1}(y_{i}-\\hat{y_{i}})^2}$ ` artificial intelligence and data mining`\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp;  $↓MAE = \\sqrt{\\frac{1}{m}\\sum^{m}_{i=1}|y_{i}-\\hat{y_{i}}|}$ ` artificial intelligence and data mining`\n",
    "\n",
    "&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp;  $↑R^2 = 1-\\frac{\\sum^{m}_{i=1}(y_{i}-\\hat{y_{i}})^2}{\\sum^{m}_{i=1}(y_{i}-\\overline{y_{i}})^2}$ ` artificial intelligence and data mining`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "评估结果：\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:              work_diff   R-squared:                       0.035\n",
      "Model:                            OLS   Adj. R-squared:                  0.032\n",
      "Method:                 Least Squares   F-statistic:                     14.86\n",
      "Date:                Mon, 16 Oct 2023   Prob (F-statistic):           9.17e-17\n",
      "Time:                        20:29:20   Log-Likelihood:                -529.04\n",
      "No. Observations:                2489   AIC:                             1072.\n",
      "Df Residuals:                    2482   BIC:                             1113.\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.0510      0.024      2.098      0.036       0.003       0.099\n",
      "to_China       0.0145      0.016      0.924      0.355      -0.016       0.045\n",
      "last_phd      -0.0714      0.014     -4.947      0.000      -0.100      -0.043\n",
      "total_pub     -0.0018      0.000     -4.975      0.000      -0.002      -0.001\n",
      "age            0.0053      0.002      2.581      0.010       0.001       0.009\n",
      "conn           0.0247      0.008      3.156      0.002       0.009       0.040\n",
      "is_Chinese     0.0035      0.019      0.182      0.856      -0.035       0.042\n",
      "==============================================================================\n",
      "Omnibus:                     1068.585   Durbin-Watson:                   1.986\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            36759.279\n",
      "Skew:                           1.372   Prob(JB):                         0.00\n",
      "Kurtosis:                      21.626   Cond. No.                         126.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\\n数据结果分析说明：\\n模型一：简单的多元线性回归\\n（1） R2=0.035；调整R2=0.032 （依据自变量数目调整），说明模型整体拟合效果较差。\\n不过模型通过了F检验，说明模型优于直接预测y为数据中y的均值 （手动狗头）\\n（2） 关注核心自变量to_china的系数预测，其/beta值为0.0145，标准误为0.924，p值为0.355，故无法拒绝其系数为0的原假设\\n系数的含义（若显著可以这么解释）：由于to_china是二值变量，所以系数可以解释为，控制其他因素后，选择回到中国（x为1）的人，观测到的work_diff(y)的期望会增加0.0145。\\n（3）其他自变量\\nconst 常数项，意义是其他所有自变量都为0时，观察到的work_diff的期望，该值的意义不大，因为不少连续变量取0时没有什么现实意义\\nlast_phd 也是二值变量，其系数显著。该系数说明在控制了其他变量的情况下，流动前已经博士毕业的人的平均work_diff比流动前未博士毕业的人低0.0714\\ntotal_pub 是数值变量，其系数显著。在控制了其他变量的情况下，流动前发表的论文数量每多1篇，流动后work_diff的期望就减少0.0018\\n\\n（4）结论\\n这个模型并不支持流入中国使科学家的业绩变好的假设。\\n'"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# statsmodels评估\n",
    "\n",
    "# 模型一，简单多元线性回归\n",
    "y = df['work_diff']\n",
    "Xdf = df[['to_China', 'last_phd', 'total_pub', 'age', 'conn', 'is_Chinese']]\n",
    "X = sm.add_constant(Xdf)\n",
    "\n",
    "mod = sm.OLS(y, X)\n",
    "res = mod.fit()\n",
    "print('评估结果：')\n",
    "print(res.summary())\n",
    "\n",
    "'''\n",
    "数据结果分析说明：\n",
    "模型一：简单的多元线性回归\n",
    "（1） R2=0.035；调整R2=0.032 （依据自变量数目调整），说明模型整体拟合效果较差。\n",
    "不过模型通过了F检验，说明模型优于直接预测y为数据中y的均值 （手动狗头）\n",
    "（2） 关注核心自变量to_china的系数预测，其/beta值为0.0145，标准误为0.924，p值为0.355，故无法拒绝其系数为0的原假设\n",
    "系数的含义（若显著可以这么解释）：由于to_china是二值变量，所以系数可以解释为，控制其他因素后，选择回到中国（x为1）的人，观测到的work_diff(y)的期望会增加0.0145。\n",
    "（3）其他自变量\n",
    "const 常数项，意义是其他所有自变量都为0时，观察到的work_diff的期望，该值的意义不大，因为不少连续变量取0时没有什么现实意义\n",
    "last_phd 也是二值变量，其系数显著。该系数说明在控制了其他变量的情况下，流动前已经博士毕业的人的平均work_diff比流动前未博士毕业的人低0.0714\n",
    "total_pub 是数值变量，其系数显著。在控制了其他变量的情况下，流动前发表的论文数量每多1篇，流动后work_diff的期望就减少0.0018\n",
    "\n",
    "（4）结论\n",
    "这个模型并不支持流入中国使科学家的业绩变好的假设。\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        MSE       MAE        R2\n",
      "0  0.085530  0.172244  0.072884\n",
      "1  0.091817  0.171779  0.033123\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\\n        MSE       MAE        R2\\n0  0.083340  0.169030  0.113296\\n1  0.098915  0.183462  0.006348\\n'"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sklearn评估\n",
    "\n",
    "# 模型评估\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score\n",
    "stats_dic = {}\n",
    "stats_dic = {'MSE':[], 'MAE':[], 'R2':[]}\n",
    "# MSE 均方误差\n",
    "stats_dic['MSE'].append(mean_squared_error(y_train, model2.predict(poly.fit_transform(X_train))))\n",
    "stats_dic['MSE'].append(mean_squared_error(y_test, model2.predict(poly.fit_transform(X_test))))\n",
    "# RMSE就是开个方，不算了\n",
    "# MAE \n",
    "stats_dic['MAE'].append(mean_absolute_error(y_train, model2.predict(poly.fit_transform(X_train))))\n",
    "stats_dic['MAE'].append(mean_absolute_error(y_test, model2.predict(poly.fit_transform(X_test))))\n",
    "# R2\n",
    "stats_dic['R2'].append(model2.score(poly.fit_transform(X_train), y_train)) # 21就是extended的特征数\n",
    "stats_dic['R2'].append(model2.score(poly.fit_transform(X_test), y_test))\n",
    "print(pd.DataFrame(stats_dic))\n",
    "'''\n",
    "        MSE       MAE        R2\n",
    "0  0.083340  0.169030  0.113296\n",
    "1  0.098915  0.183462  0.006348\n",
    "'''\n",
    "# 0为训练集，1为测试集。测试集上的R方偏低，\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x1200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 计算残差\n",
    "residual_train = model2.predict(poly.fit_transform(X_train)) - y_train\n",
    "residual_test = model2.predict(poly.fit_transform(X_test)) - y_test\n",
    "# 进行核密度估计，需要导入库计算经验分布函数，进而得到经验概率密度\n",
    "from statsmodels.distributions.empirical_distribution import ECDF \n",
    "residual_train_e_d = ECDF(residual_train)\n",
    "residual_test_e_d = ECDF(residual_test)\n",
    "# 计算经验概率密度函数\n",
    "x = np.linspace(-3, 3, 40)\n",
    "delta = 6/40\n",
    "residual_train_e_prop = residual_train_e_d(x) - residual_train_e_d(x-delta)\n",
    "residual_test_e_prop = residual_test_e_d(x) - residual_test_e_d(x-delta)\n",
    "\n",
    "# 核密度估计参数\n",
    "from sklearn.neighbors import KernelDensity\n",
    "kernel = \"gaussian\"\n",
    "bandwidths = [0.01, 0.05, 0.1]\n",
    "lw = 2\n",
    "colors = [\"navy\", \"cornflowerblue\", \"darkorange\"]\n",
    "\n",
    "\n",
    "# 绘图\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "figs, axs = plt.subplots(1, 2, figsize=(16, 12), dpi=100)\n",
    "plt.rcParams['font.sans-serif'] = ['SimHei'] # 步骤一（替换sans-serif字体）\n",
    "plt.rcParams['axes.unicode_minus'] = False   # 步骤二（解决坐标轴负数的负号显示问题）\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.hist(residual_train, bins=20, weights=np.zeros_like(residual_train) + 1 / len(residual_train))\n",
    "plt.title(\"训练集残差直方图\")\n",
    "plt.xlabel(\"residual\")\n",
    "plt.ylabel(\"rate\")\n",
    "\n",
    "for bandwidth, color in zip(bandwidths, colors): \n",
    "    kde = KernelDensity(kernel=kernel, bandwidth=bandwidth).fit(residual_train_e_prop.reshape(-1, 1))\n",
    "    log_dens = kde.score_samples(x.reshape(-1, 1))\n",
    "    axs[0].plot(\n",
    "        x,\n",
    "        np.exp(log_dens),\n",
    "        color=color,\n",
    "        lw=lw,\n",
    "        linestyle=\"-\",\n",
    "        label=f\"bandwidth = '{bandwidth}'\"\n",
    "    )\n",
    "\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.hist(residual_test, bins=20, weights=np.zeros_like(residual_test) + 1 / len(residual_test))\n",
    "plt.title(\"测试集残差直方图\")\n",
    "plt.xlabel(\"residual\")\n",
    "plt.ylabel(\"rate\")\n",
    "for bandwidth, color in zip(bandwidths, colors): \n",
    "    \n",
    "    kde = KernelDensity(kernel=kernel, bandwidth=bandwidth).fit(residual_test_e_prop.reshape(-1, 1))\n",
    "    log_dens = kde.score_samples(x.reshape(-1, 1))\n",
    "    axs[1].plot(\n",
    "        x,\n",
    "        np.exp(log_dens),\n",
    "        color=color,\n",
    "        lw=lw,\n",
    "        linestyle=\"-\",\n",
    "        label=f\"bandwidth = '{bandwidth}'\"\n",
    "    )\n",
    "plt.show()\n",
    "\n",
    "# 可以从核密度估计和直方图中看出，残差的分布有较高的峰度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 参考资料\n",
    "- 计量经济学与统计学库 : `statsmodels`\n",
    "\n",
    "- 人工智能与数据挖掘库 : `sklearn`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "d2l",
   "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": "3.11.5"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}