{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Receiver Operating Characteristic" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": true }, "outputs": [], "source": [ "suppressPackageStartupMessages(library(tidyverse))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Logistic regression concept\n", "\n", "In logistic regression, we want to relate some predictor variable (e..g gene expression value) to the **probability** of a binary outcome. We would like a linear model since that is mathematically and computationally tractable, but run into the issue that probabilities are restricted to [0,1]. Logistic regression solves this by transforming the output of a linear model into the [0, 1] range." ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n <- 50\n", "x <- seq(-4, 4, length.out = n)\n", "a = 0\n", "b = 1\n", "\n", "lx <- a + b*x\n", "px <- exp(lx)/(1 + exp(lx))\n", "y <- rbinom(n, 1, px)\n", "\n", "df <- data.frame(y=y, x=x, lx=lx, px=px)" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width=4, repr.plot.height=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A linear model cannot be directly interpreted as a probability" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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kLADQJvvRXL/jm2Q8xIJQjj+8knUZzsxswjj6l8Tz+pJCW/+OKsGF83uHprE91z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\nIQIUwPnwofOWiQARIAJEIHgE/g+92E3Vbc1e9AAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(df, aes(x=x, y=lx)) + \n", "geom_point(color='blue') +\n", "labs(x=\"Gene expression value\", \n", " y=\"Linear model relating gene\\nexpression to probability of outcome\")" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": {}, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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39Mhw4dossuu0zqlJCQYHX2m2++oe+++05OG7rlllvoiiuusN47cuSI1AlT5K68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\nrkx5R11gWiId/vvss4+M+uPSpU6kq4eEpwGl4xt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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ggplot(df, aes(x=x, y=y)) + \n", "geom_point() +\n", "geom_line(aes(y=px), color='red') +\n", "labs(x=\"Gene expression value\", y=\"Binary outcome\", \n", " title=\"Probability of outcome given value\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation from logistic model" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sim.binomial <- function(n, b0, b1, b2, b3) { \n", " x1 <- rnorm(n)\n", " x2 <- rnorm(n)\n", " x3 <- rnorm(n)\n", " lx <- b0 + b1 * x1 + b2 * x2 + b3 * x3 \n", " px <- exp(lx)/(1 + exp(lx))\n", " y <- rbinom(n, 1, px)\n", " data.frame(y, px, x1, x2, x3)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LOOCV" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": true }, "outputs": [], "source": [ "set.seed(31219)\n", "data <- sim.binomial(100, 0.1, 0, 1, 0)" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
ypxx1x2x3
0 0.5830298 1.2472628 0.23522348 1.4787281
1 0.4546145 0.5804904 -0.28204321-0.8217013
1 0.5417889 0.3065363 0.06754626 1.3946841
1 0.8080377 0.4604304 1.33730956 0.6502840
0 0.5436883 1.2094387 0.07519995 0.6585957
1 0.4011430 0.2338796 -0.50070506-0.8225897
\n" ], "text/latex": [ "\\begin{tabular}{r|lllll}\n", " y & px & x1 & x2 & x3\\\\\n", "\\hline\n", "\t 0 & 0.5830298 & 1.2472628 & 0.23522348 & 1.4787281 \\\\\n", "\t 1 & 0.4546145 & 0.5804904 & -0.28204321 & -0.8217013 \\\\\n", "\t 1 & 0.5417889 & 0.3065363 & 0.06754626 & 1.3946841 \\\\\n", "\t 1 & 0.8080377 & 0.4604304 & 1.33730956 & 0.6502840 \\\\\n", "\t 0 & 0.5436883 & 1.2094387 & 0.07519995 & 0.6585957 \\\\\n", "\t 1 & 0.4011430 & 0.2338796 & -0.50070506 & -0.8225897 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "y | px | x1 | x2 | x3 | \n", "|---|---|---|---|---|---|\n", "| 0 | 0.5830298 | 1.2472628 | 0.23522348 | 1.4787281 | \n", "| 1 | 0.4546145 | 0.5804904 | -0.28204321 | -0.8217013 | \n", "| 1 | 0.5417889 | 0.3065363 | 0.06754626 | 1.3946841 | \n", "| 1 | 0.8080377 | 0.4604304 | 1.33730956 | 0.6502840 | \n", "| 0 | 0.5436883 | 1.2094387 | 0.07519995 | 0.6585957 | \n", "| 1 | 0.4011430 | 0.2338796 | -0.50070506 | -0.8225897 | \n", "\n", "\n" ], "text/plain": [ " y px x1 x2 x3 \n", "1 0 0.5830298 1.2472628 0.23522348 1.4787281\n", "2 1 0.4546145 0.5804904 -0.28204321 -0.8217013\n", "3 1 0.5417889 0.3065363 0.06754626 1.3946841\n", "4 1 0.8080377 0.4604304 1.33730956 0.6502840\n", "5 0 0.5436883 1.2094387 0.07519995 0.6585957\n", "6 1 0.4011430 0.2338796 -0.50070506 -0.8225897" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "head(data)" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n <- nrow(data)\n", "pred <- numeric(n)\n", "for (i in 1:n) {\n", " train <- data[-i,]\n", " test <- data[i,]\n", " model <- glm(y ~ x1 + x2 + x3, data=train, family=\"binomial\")\n", " pred[i] <- predict(model, test, type=\"response\")\n", "}\n", "yhat <- ifelse(pred < 0.5, 0, 1)\n", "preddat <- data.frame(probhat=pred, yhat=yhat, y=data$y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Confusion matrix" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": true }, "outputs": [], "source": [ "suppressPackageStartupMessages(library(caret))" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Confusion Matrix and Statistics\n", "\n", " \n", "yhat 0 1\n", " 0 31 26\n", " 1 21 22\n", " \n", " Accuracy : 0.53 \n", " 95% CI : (0.4276, 0.6306)\n", " No Information Rate : 0.52 \n", " P-Value [Acc > NIR] : 0.4607 \n", " \n", " Kappa : 0.0547 \n", " Mcnemar's Test P-Value : 0.5596 \n", " \n", " Sensitivity : 0.5962 \n", " Specificity : 0.4583 \n", " Pos Pred Value : 0.5439 \n", " Neg Pred Value : 0.5116 \n", " Prevalence : 0.5200 \n", " Detection Rate : 0.3100 \n", " Detection Prevalence : 0.5700 \n", " Balanced Accuracy : 0.5272 \n", " \n", " 'Positive' Class : 0 \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tbl <- table(yhat, data$y)\n", "confusionMatrix(tbl)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ROC and AUC" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": true }, "outputs": [], "source": [ "suppressPackageStartupMessages(library(ROCR))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Helper functions" ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ROC <- function(preddat, mlab = \"probhat\", ylab = \"y\") {\n", " m <- preddat[[mlab]]\n", " y <- preddat[[ylab]]\n", " performance(prediction(m, y), measure = \"tpr\", x.measure = \"fpr\")\n", "}\n", "\n", "AUC <- function(preddat, mlab = \"probhat\", ylab = \"y\") { \n", " m <- preddat[[mlab]]\n", " y <- preddat[[ylab]]\n", " performance(prediction(m, y), \"auc\")@y.values[[1]]\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate and plot ROC and AUC" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": true }, "outputs": [], "source": [ "my.roc <- ROC(preddat)\n", "my.auc <- AUC(preddat)" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.530048076923077" ], "text/latex": [ "0.530048076923077" ], "text/markdown": [ "0.530048076923077" ], "text/plain": [ "[1] 0.5300481" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "my.auc" ] }, { "cell_type": "code", "execution_count": 128, "metadata": { "collapsed": true }, "outputs": [], "source": [ "options(repr.plot.width=4, repr.plot.height=4)" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "image/png": 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OdxmslrayTdjfCZ1hUz/NoKeIYFu/t+GihNBZxetw/DE3AopBFgVNtApSrgbrqg\nl+S8LgOT3bf3OOtzLTXpyhAp36+guTv5SV6nkk1eWyPpboG1Wlf4WgMaKJWBpcjNUbAtvA7y\nxdrQwEgZ6KYCfoCS3QabwDc7lDKV9HPh6x3WD3rxZRzwjZBr1umiSpwLO0K6qu6E5kiXdK5f\nf7p5ofMaGE8DE/k/yWDL1sj/+KWtCwf4+nkc6yTIYM98Hk3WKGC1oYFyGligy2ydQfp3wPtg\n8ZZtcyvPtyHfTH/Ssm5YLw/nwLn2ewVkYEYiXx5SMR8HK0MjNmAmlXO6s/w23bDidJwNpPJt\njPdo9sA14Fo+C4YRu3PQiyH/w7kF0soXCcZ4GEgleyNkoNL9kBbxzXAypIWZ5WW5/ktW5sYe\n/P0rpHv513AE/Hf99WNMfwe3Q/KeNLkeO+jwGvCgjXu8AgYm5vBvAaWIWeTiYMilo31KkSMz\nMQwDlboGPB2BubUnXczp/kml1SAV8PuhjAMhViRf/wn58pAWbiPPjemDLDsG/gGGEVbAw7Du\nMacwUJoKeGUyegHkC/82U2Ta1dU2MPYVcOP0pqJdA7aA/IOMSiTfq0Du+02Fm1b9sMMKeNhn\nwOO3MVCKCnhrMpaK90IYpc+ZNj5d1AcDY10BH4jAfAPN8H+jfwasgPvn0j31zcDQK+D3UpR0\nOX8DZvWtWO5olA1UqgLuZhR0Ttpu8HG4FubAkZBu3arEuynIu+Br0MtI7mXZ/iDIm6VIrFUk\nkWk0MCYGFqOcGSy5M2QMx9FgaKByBhboskT5h/gcZGTxp+A6+Am8EfLjDKMeuVa8PmRqaEAD\ngzewNofMYyQ3hheAlS8SDA00G0jFvT2kBfwXyGCm+yCtxs1gVGNYFbBd0KP6jql0vgfeBb0L\nOnN3xalQhrEZlT67I1q4SnVB9+McpLtod/gBPAKpjD8KRnEDVsDFXZlyYAYGVgFnYOT+kDsU\nDoCngaGBdgYqVQEv1K6EXS6bRfp0STfffpSBE2WNZchYHhaSPOf2o7TcHwJDAxUxMLEaBdkX\nmv8np1O2PITj/Ols2MU2ua3xWNgQdoQzwdDAWBjo9hpwQ0q+hewCJ0BuEciAiXQ9fw3+ET4P\nZYr8cx8Od8A9kGvXV8FNkEr4GjgM8nhKQwOjbuD5FOBNfShEKt/v92E/nXaRx0heDhm0mDxb\n+SLB0EAnA1uyIhVVKrF0NafLKNdrXgNpCZcxPkmmktdwA1wIp0G+dZ8Bv4BbIevvggwoG3TY\nBT1o45U+3gRfjifyP1rmeBuZy8N8vgOLgKGBIgYq1QVdpMDNaXL7USqq38NHYCUoc+xK5pLf\nVLQbTZLRXHPaGi6FpN8CBhlWwIO0XfljlboCTmV7BKTy3avyp8IC9tvAWFfAGSixeb+NzuD+\n8u063cu53lskliHRA/D1Ion7mMYKuI8y3VVpK+DZnJvL4M+QJ9EZGujWQKUq4G4HYe3bra0h\np1+f418E+bZdJO4l0ZWwSpHEptHAcA1M5AvjZyAfSs2xWvOLkszvQD6+C1fAy+BOMDQw1gam\nGoSVf/AVoFFRP7P+OssmI7cmlSFuJRMZ3DGrYGZS3lTaGaBlaKDsBtYmg+k9aR3tfCPLDi1J\n5nN55yNwOhwJLwUrXyQYGpjKQL6t5proxvWEjWvAWTYZZWkp5/7k5PMU2Aw6RT4ktoIMyMrA\nsgw2G2TYBT1I25U51gTv6Qne3xNlfQpdbvfL/14u67ymMtotyDANpLcnn+mjdCm0o69Gy7ZT\ngrNY8UdI12wig5nS8p0qfjdVggGtT5dX8nsA7AQ3w01wN+RDYUlYFlaHlSCV795wARga0MD0\nDTyPTU+CXP7J7UZXg6EBDfRgYA22TTd0p0iX9jawQacEQ1qefB8DqYDz7amZh3idLxkHw6ow\njLAFPAzrI3/M0raA0/OU/6vvweIjr9kClMlApVrA3YpNF/S+k2yUrrBUbl+dJM2wV6XVm4p2\nLUgXWRnCCrgMZ6G0eZjgQ2fiyzCnBe5nL1UX9CwUHgKPw8fA0EC/DVSqAp6qCzqV1NZNBpdg\nfiN4e9Oyxmxav42W7z2NhSWcpus5GBoYFQO5jPJeOBH+0pTpPDjm8zw6+a9Ny4Y1uzIHPh6e\nA9vDz8HQgAZ6MJDW4i3Q3GU71fyDpM/IY6O4AVvAxV2NYcqJZ9dbuqncyhj5kn4bXAipiA0N\nzJSBsWoBp6W4I6xXt8m37dp5kMEVrfE3FjwMl8ONrSt9rQENVNJAWuZfgCPgfZDuZ0MDGpgB\nA/lHe80M7Hfcd2kLeNzfAZOWv5Qt4MXI8rGQL91vmjT7rtRA/wyMVQu4VduHWhf4WgMaGDsD\na1Pi9IItDC+AK8HQgAa6NDDVIKw8GSojG++B3CObW5AWhKkityAEQwMaqJaBXSjOHDgX3gz3\ngaEBDcyAgSvYZwZdjeqTsGZAyYzs0i7oGdFalZ2Wogs6X7w/Bfki/mnI0+MMDQzawFh1QZ+F\n3Tyk4t665VF7Etag3xweTwNVNLAchcr13g0hgzLPBEMDGtBAJQzYAq7EaZypQgy1BbwJpcpd\nDbm7YTYYGhimgUq1gBfok8lcS14H7Jbqk1B3o4ESGNiDPJwPud67BVwPhgY0MEQDr+XYhzUd\nfyfm74dcK74FXg5GdwZsAXfna8xSD7wFvAiCc19vfkhhrzGTbXHLbaBSLeBuVb+aDVLR5tF3\nae3mWcoZBZmHcPwIUhHn9XPAKG7ACri4qzFMOdAKeDaCL4N0O28KhgbKZKBSFXC3XdD7ciau\ng80gFfGrIJXwwbADZJBGXqeiNjSggdEykP/hVL75Ep3HyV4ChgY0MEMGuqmAk3ZdOAYaN96/\nop6vE+rTa5n+Hjaqv3aiAQ2U30B6sz4Kp8OR8FK4EwwNaGAGDUz1II7mQy/Bi1wbuq2+MPcF\n5h81D+m4tL4sk6RJN4GhAQ2U38DSZPEo2AZeByeCoQENDMBANy3gXN9NZbtVPV8vYboM5J7A\nXANOpAv67yAtYUMDGii3gfXJ3i9hDcjtRla+SDA0UFYDXyRjufZ7DtwFqXjzzTnx/yCPn3wS\n/h6M4gYchFXc1RimnJFBWLsjMv+v34PFx1CqRR5NA+ldTR20+Whmv7dcp3v525BR0HdAfoqs\nEXlqlr+M0rDR3dQKuDtfY5a6rxXwLOQdAvnZwFz3NTQwSgbGugJunKhIyMCN5kh3Vq4TG90b\nsALu3tkYbdG3CnhlpF0AGcfR6LkaI48WtQIGKlUBdzMIq/ncPcaL1WFdWBYyYvJy+AsYGtBA\n+QxsTZaOg4zPyF0Kt4ChAQ2MmIH1yO/PIf3wzaRSzjXi1pYxi4wpDNgCnkLQeK/uuQX8Pvyl\ny/nrkC5oQwOjamCsW8CrctYugiUho59/BblpP8tzT/AHIAM6UqFkgNYoxPJkMr9z/AcYlTyP\nglfzOHwDi5GFb8JOsAccDYYGNDCiBk4k33k+7HZt8p9v1l+GtIpf2GZ9WRd9pp7ndKUPK2wB\nD8v8SBx3Wi3gtSnab+FPsP5IFNNMamBqA2PdAt4GP4fB2W08pYvrQ5Cb+beF/IrKsCMfPGkF\nTBar1FduwvSB+vyfmd5Un3eigVEzsAsZngPnwpshvVSGBjQwwgbyjOe0bt85RRnOY31aymWI\nK8hE83XqovP7DjjztoAHLHy0Dle4Bbwg5fo0PAGfAsdjIMGolIGxbQHfz2kMG0xyOiMnD+G4\nZJI0g1yVQSeHQu5fPgXynOrWeBEL8qsvX4Lc35y4YN7EvxoYGQPLkdNjYUPYETJGw9CABipk\nIP/g6WrOP3hrpJLLgI+0Mtutb00/qNfP5UC/hjwk5P3Q2irwGjBSjDIbmLIFnMsnN8LlMBsM\nDVTVQKVawN2epNXZ4F5IJZuu5rQa94cj4M+Q5cdD2WJhMnQwZJTzj6Fx3ZfZmhVwLBglNjBp\nBbwHGc/AyKMgX4INDVTZwFhXwDmxqbzOgFS2zTzE6/8HZf4QeDH5yxeFe+ANkLACnufBv6U1\n0LYCzv9Zvvim8t2rtFk3Yxror4FKVcDTeRLWzfh8OSwO68KKcB1cA/kwKHP8lMxlZHSuDed3\njXeGB8HQQEkMTHyWjKzQkplFW17P5vUJsDxsBWUZc0FWDA1ooKiBBYombJMulW2efpWBS7dB\n2Stfsjg30oX+engLvBIyAtnQQAkMTOT/8cOQL7XNkfELX4N8+d0BLoPcWvR8sPJFgqGBcTGw\nEgX9EaTCbe6CTiv4XTBKMZvM5pr1z2AJGFbkS0BcLjasDHjcMhhIBTzB+2AirdrWyODBj0Fu\nMToEFgRDA+NmoFJd0N2evI3Y4FbIYKZUwrnF59PwLci11VQiX4B8WBjFDVgBF3dV4ZQdK+Cl\nKfSp8ADsUmEBFk0DUxmoVAXc7TXgvbGTwR+57SHdYM0RMZ+HD0JalRfAqMW7yXBa8enuy3Xi\n6caybHgQxEmRWKtIItOMpYGMWTgR0uOU/7urwdCABipgoJtrwOnyehkcCK2Vb1TkenAq37SQ\nc211FCPX3vKB13oNbhTLYp5H38DuFOEiyP/bZmDliwRDA+NoYGEKnW/hu01R+AtZf8wUacq6\nelgVsF3QZX1HDDRfjS7oO7flsOlNykNvPgKGBjQwz0CluqC7PannscGPoFPLeXXWZcRmunKN\n4gasgIu7qnDKVMA3M45i6Ssp5G2wTYULa9E0MB0DY10Br42x2+F0yPWoyEjkPsWdIV1kv4Rn\nQX5jt8EzmC9LLENGZsM6kIeKlGHksRUwJ8JYiAp3xUYFvLI+NKCB+QyMdQWca1Fp4fIhMZcn\nmd7f9LqxvHW6D2mGGRty8MPhDmjNW17nISKHwfIwjLACHob1ch3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GUsGV4ecIF6/V1r2YCvdJ8vOmsgozXxrQwFgaqNTPEToIayzfwx0L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\nQAMaGGUD/x/EvWvPdSjoWAAAAABJRU5ErkJggg==", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(my.roc, col = \"blue\")\n", "abline(0, 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Resubstitution ROC" ] }, { "cell_type": "code", "execution_count": 134, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model.1 <- glm(y ~ x1 + x2 + x3, data=data, family=\"binomial\")\n", "pred.1 <- predict(model.1, type=\"response\")\n", "yhat.1 <- ifelse(pred.1 < 0.5, 0, 1)\n", "preddat.1 <- data.frame(probhat=pred.1, yhat=yhat.1, y=data$y)" ] }, { "cell_type": "code", "execution_count": 136, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rs.roc <- ROC(preddat.1)\n", "rs.auc <- AUC(preddat.1)" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [ { "data": { "text/html": [ "0.616987179487179" ], "text/latex": [ "0.616987179487179" ], "text/markdown": [ "0.616987179487179" ], "text/plain": [ "[1] 0.6169872" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rs.auc" ] }, { "cell_type": "code", "execution_count": 144, "metadata": {}, "outputs": [ { "data": { "image/png": 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u4f1FD3SN0rdc9sect7F/RVnKF50CloS6QZ0KPRR+hTNCvqjwag+ZGc7xHoEWQz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\nCBAgQIAAAQIECBAgQIAAAQL/WeALjyJ5LreSI70AAAAASUVORK5CYII=", "text/plain": [ "Plot with title “Resubstitution ROC is optimistic”" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(my.roc, col = \"blue\", main=\"Resubstitution ROC is optimistic\")\n", "plot(rs.roc, col = \"red\", add=TRUE)\n", "abline(0, 1)" ] } ], "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": "3.4.0" } }, "nbformat": 4, "nbformat_minor": 2 }