{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "# Linear models with a categorical (factor) explanatory variable\n", "\n", "本节需要的包：\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [ "hide-output" ], "vscode": { "languageId": "r" } }, "outputs": [], "source": [ "require(s20x)\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Using categorical variables as explanatory variables by using indicator variables\n", "\n", "使用指标变量将分类变量用作解释变量\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/html": [ "\n", "
  1. Yes
  2. Yes
  3. Yes
  4. Yes
  5. No
  6. Yes
  7. Yes
  8. No
  9. Yes
  10. Yes
  11. No
  12. Yes
  13. No
  14. No
  15. No
  16. Yes
  17. Yes
  18. No
  19. Yes
  20. Yes
\n", "\n", "
\n", "\t\n", "\t\tLevels:\n", "\t\n", "\t\n", "\t
  1. 'No'
  2. 'Yes'
\n", "
" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item Yes\n", "\\item Yes\n", "\\item Yes\n", "\\item Yes\n", "\\item No\n", "\\item Yes\n", "\\item Yes\n", "\\item No\n", "\\item Yes\n", "\\item Yes\n", "\\item No\n", "\\item Yes\n", "\\item No\n", "\\item No\n", "\\item No\n", "\\item Yes\n", "\\item Yes\n", "\\item No\n", "\\item Yes\n", "\\item Yes\n", "\\end{enumerate*}\n", "\n", "\\emph{Levels}: \\begin{enumerate*}\n", "\\item 'No'\n", "\\item 'Yes'\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. Yes\n", "2. Yes\n", "3. Yes\n", "4. Yes\n", "5. No\n", "6. Yes\n", "7. Yes\n", "8. No\n", "9. Yes\n", "10. Yes\n", "11. No\n", "12. Yes\n", "13. No\n", "14. No\n", "15. No\n", "16. Yes\n", "17. Yes\n", "18. No\n", "19. Yes\n", "20. Yes\n", "\n", "\n", "\n", "**Levels**: 1. 'No'\n", "2. 'Yes'\n", "\n", "\n" ], "text/plain": [ " [1] Yes Yes Yes Yes No Yes Yes No Yes Yes No Yes No No No Yes Yes No Yes\n", "[20] Yes\n", "Levels: No Yes" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "library(s20x)\n", "## Importing data into R\n", "Stats20x.df <- read.table(\"../data/STATS20x.txt\", header = T)\n", "## Change Attend from a character variable to a factor variable\n", "Stats20x.df$Attend <- as.factor(Stats20x.df$Attend)\n", "## Examine the data\n", "Stats20x.df$Attend[1:20]\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "简要分析数据集，确保有你需要的可能的关系：\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Sample Size Mean Median Std Dev Midspread\n", "No 46 42.21739 40.5 16.34206 20.50\n", "Yes 100 57.78000 58.0 17.67757 28.25\n" ] }, { "data": { "image/png": "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", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "summaryStats(Stats20x.df$Exam, Stats20x.df$Attend)\n", "plot(Exam ~ Attend, data = Stats20x.df)\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "缺勤的确会让学生成绩变低，在数据分布上的确有一定的关系。\n", "\n", "为了在后面进行更好的分析，我们将缺勤的 Yes 和 No 转换为 1 和 0：\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ " Attend2\n", "Attend 0 1\n", " No 46 0\n", " Yes 0 100" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make a new variable Attend2 which is 1 if Attend = \"Yes\" and 0 otherwise\n", "\n", "# Note how we use two equal signs, ==, to test equality\n", "Stats20x.df$Attend2 <- as.numeric(Stats20x.df$Attend == \"Yes\")\n", "with(Stats20x.df, table(Attend, Attend2))\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Plot with title \"Plot of Exam vs. Attend2 (lowess+/-sd)\"" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "trendscatter(Exam ~ Attend2, data = Stats20x.df)\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "The linear model for the expected value of is\n", "\n", "$$\n", "E[Exam|Attend2] = \\beta_0 + \\beta_1 Attend2\n", "$$\n", "\n", "其中 $\\beta_0$ 是截距，即所有缺勤的均值；$\\beta_1$ 是考试成绩和缺勤的关系，由缺勤和出勤的成绩关系共同决定。\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = Exam ~ Attend2, data = Stats20x.df)\n", "\n", "Residuals:\n", " Min 1Q Median 3Q Max \n", "-46.780 -13.108 -0.217 12.642 46.783 \n", "\n", "Coefficients:\n", " Estimate Std. Error t value Pr(>|t|) \n", "(Intercept) 42.217 2.547 16.578 < 2e-16 ***\n", "Attend2 15.563 3.077 5.058 1.27e-06 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Residual standard error: 17.27 on 144 degrees of freedom\n", "Multiple R-squared: 0.1508,\tAdjusted R-squared: 0.145 \n", "F-statistic: 25.58 on 1 and 144 DF, p-value: 1.271e-06\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "examattend2.fit <- lm(Exam ~ Attend2, data = Stats20x.df)\n", "summary(examattend2.fit)\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "上述拟合代表 x 为 Attend2（0 和 1） 时，y 的期望值，即考试成绩的期望值。\n", "\n", "但注意事实上，直接使用 lm() 函数进行拟合，也能得出正确的结果，因为 lm() 函数会自动将分类变量转换为指标变量（AttendYes）：\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = Exam ~ Attend, data = Stats20x.df)\n", "\n", "Residuals:\n", " Min 1Q Median 3Q Max \n", "-46.780 -13.108 -0.217 12.642 46.783 \n", "\n", "Coefficients:\n", " Estimate Std. Error t value Pr(>|t|) \n", "(Intercept) 42.217 2.547 16.578 < 2e-16 ***\n", "AttendYes 15.563 3.077 5.058 1.27e-06 ***\n", "---\n", "Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n", "\n", "Residual standard error: 17.27 on 144 degrees of freedom\n", "Multiple R-squared: 0.1508,\tAdjusted R-squared: 0.145 \n", "F-statistic: 25.58 on 1 and 144 DF, p-value: 1.271e-06\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "examattend.fit <- lm(Exam ~ Attend, data = Stats20x.df)\n", "summary(examattend.fit)\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "让我们将拟合模型可视化。在这里，我们将使用虚拟变量拟合我们的模型得到的\"最佳\"估计直线绘制出来。\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(Exam ~ Attend2, data = Stats20x.df)\n", "## Add the lm estimated line to this plot where a=intercept, b=slope\n", "abline(coef(examattend.fit), lty = 2, col = \"blue\")\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "模型建立好了，接下来就是我们经典的模型检验三步走了：\n", "\n", "1. 残差均值接近于 0\n", "2. 残差满足正态分布\n", "3. 没有或排除了异常点\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "Plot with title \"\"" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "Plot with title \"\"" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "Plot with title \"Cook's Distance plot\"" ] }, "metadata": { "image/png": { "height": 420, "width": 420 } }, "output_type": "display_data" } ], "source": [ "plot(examattend.fit, which = 1)\n", "normcheck(examattend.fit)\n", "cooks20x(examattend.fit)\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "vscode": { "languageId": "r" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\n", "
A matrix: 2 × 3 of type dbl
fitlwrupr
142.2173937.1840147.25077
257.7800054.3661961.19381
\n" ], "text/latex": [ "A matrix: 2 × 3 of type dbl\n", "\\begin{tabular}{r|lll}\n", " & fit & lwr & upr\\\\\n", "\\hline\n", "\t1 & 42.21739 & 37.18401 & 47.25077\\\\\n", "\t2 & 57.78000 & 54.36619 & 61.19381\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A matrix: 2 × 3 of type dbl\n", "\n", "| | fit | lwr | upr |\n", "|---|---|---|---|\n", "| 1 | 42.21739 | 37.18401 | 47.25077 |\n", "| 2 | 57.78000 | 54.36619 | 61.19381 |\n", "\n" ], "text/plain": [ " fit lwr upr \n", "1 42.21739 37.18401 47.25077\n", "2 57.78000 54.36619 61.19381" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\n", "
A matrix: 2 × 3 of type dbl
fitlwrupr
142.21739 7.71025976.72452
257.7800023.47167392.08833
\n" ], "text/latex": [ "A matrix: 2 × 3 of type dbl\n", "\\begin{tabular}{r|lll}\n", " & fit & lwr & upr\\\\\n", "\\hline\n", "\t1 & 42.21739 & 7.710259 & 76.72452\\\\\n", "\t2 & 57.78000 & 23.471673 & 92.08833\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A matrix: 2 × 3 of type dbl\n", "\n", "| | fit | lwr | upr |\n", "|---|---|---|---|\n", "| 1 | 42.21739 | 7.710259 | 76.72452 |\n", "| 2 | 57.78000 | 23.471673 | 92.08833 |\n", "\n" ], "text/plain": [ " fit lwr upr \n", "1 42.21739 7.710259 76.72452\n", "2 57.78000 23.471673 92.08833" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Create data frame of values of interest: Attend==\"Yes\" and \"No\"\n", "## Make sure that the names of vars are exactly the same as in the data frame\n", "preds.df <- data.frame(Attend = c(\"No\", \"Yes\"))\n", "predict(examattend.fit, preds.df, interval = \"confidence\")\n", "predict(examattend.fit, preds.df, interval = \"prediction\")\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "再次强调：“confidence”是代表均值预测范围，而“prediction”是代表个体预测范围。\n" ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.2.2" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }