Binghnetty Logistic Regression 2

R Software Module: rwasp_logisticregression.wasp (opens new window with default values)

Title produced by software: Bias-Reduced Logistic Regression

Date of computation: Wed, 30 Jan 2008 01:56:09 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/30/t120168343090cb6m99ccho5r4.htm/, Retrieved Wed, 30 Jan 2008 09:57:11 +0100

User-defined keywords:

Dataseries X:

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1 1 7.8 1 1 6.0 1 1 6.0 1 1 7.1 1 1 5.9 1 1 3.6 1 1 6.9 1 1 8.0 1 1 5.6 1 1 6.1 1 1 5.1 1 1 5.0 1 1 5.2 1 1 2.9 1 1 4.9 1 1 4.7 1 1 6.5 1 1 7.5 1 1 3.9 1 1 3.2 1 1 4.5 1 1 6.5 1 1 7.4 1 1 3.3 1 1 5.9 1 1 4.8 1 1 4.4 1 1 5.4 1 1 5.9 1 1 6.1 1 1 5.4 1 1 6.0 1 1 4.9 1 1 5.3 1 1 6.0 1 1 3.2 1 1 6.5 1 1 3.6 1 1 5.9 1 1 5.2 1 1 7.3 1 1 8.9 1 1 1.8 1 1 6.5 1 1 3.0 1 1 7.0 1 1 7.0 1 1 5.9 1 1 6.3 1 1 3.8 1 1 7.6 1 1 6.3 1 1 5.6 1 1 6.4 1 1 7.5 1 1 7.0 1 1 1.1 1 1 6.0 1 1 6.5 1 1 5.7 1 1 5.5 1 1 6.4 1 1 6.5 1 1 1.9 1 1 3.4 1 1 6.4 1 1 1.6 1 1 6.8 1 1 6.1 1 1 6.3 1 0 5.1 1 0 4.7 1 0 4.1 1 0 3.0 1 0 6.5 1 0 5.3 1 0 6.4 1 0 6.8 0 1 12.0 0 1 7.0 0 0 6.0 0 1 5.0 0 1 7.0 0 1 8.0 0 0 5.0 0 1 8.0 0 1 5.0 0 1 6.0 0 1 9.0 0 0 7.0 0 1 6.0 0 0 6.0 0 0 7.0 0 0 6.0 0 0 6.0 0 0 8.0 0 0 7.0 0 0 5.0 0 0 7.0 0 0 7.0 0 1 6.0 0 1 5.0 0 1 7.0 0 0 8.0 0 1 8.0 0 0 9.0 0 0 99.0 0 0 8.0 0 0 6.0 0 1 5.0 0 1 9.0 0 1 7.0 0 1 6.0 0 1 7.0 0 0 6.0 0 0 6.0 0 1 7.0 0 1 7.0 0 0 6.0 0 1 6.0 0 0 6.0 0 0 8.0 0 1 6.0 0 0 7.0 0 1 7.0 0 1 5.0 0 0 8.0 0 1 4.0 0 1 7.0 0 1 8.0 0 1 10.0 0 1 6.0 0 0 7.0 0 1 5.0 0 0 6.0 0 0 6.0 0 0 10.0 0 0 7.0 0 0 6.0

Text written by user:

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Coefficients of Bias-Reduced Logistic Regression Variable Parameter S.E. t-stat 2-sided p-value (Intercept) 2.64677019469518 1.07629665754013 2.45914560465547 0.0151824790131359 snoring 2.04491203101559 0.481290539368603 4.24880994689461 3.96266638371667e-05 sleep_time -0.628209641732441 0.165475458149953 -3.79639161453877 0.000220352198996299 Summary of Bias-Reduced Logistic Regression Deviance 141.784547049377 Penalized deviance 133.528184042251 Residual Degrees of Freedom 136 ROC Area 0.805800756620429 Hosmer–Lemeshow test Chi-square 28.7664346279777 Degrees of Freedom 8 P(>Chi) 0.000348453628294165 Fit of Logistic Regression Index Actual Fitted Error 1 1 0.448099374030784 0.551900625969216 2 1 0.715535831240259 0.284464168759741 3 1 0.715535831240259 0.284464168759741 4 1 0.557591701635861 0.442408298364139 5 1 0.728147765592221 0.271852234407779 6 1 0.91909601515448 0.08090398484552 7 1 0.58832267115294 0.41167732884706 8 1 0.417268919138258 0.582731080861742 9 1 0.763814641903368 0.236185358096632 10 1 0.702577788907515 0.297422211092485 11 1 0.815749796862538 0.184250203137462 12 1 0.825005284731655 0.174994715268345 13 1 0.806119825717223 0.193880174282777 14 1 0.94633696309509 0.05366303690491 15 1 0.833890512728604 0.166109487271396 16 1 0.850572319870626 0.149427680129374 17 1 0.647557374500253 0.352442625499747 18 1 0.495027642106805 0.504972357893195 19 1 0.903929113494106 0.0960708865058936 20 1 0.93592081996753 0.0640791800324692 21 1 0.865848342638196 0.134151657361804 22 1 0.647557374500253 0.352442625499747 23 1 0.510731071105808 0.489268928894192 24 1 0.932048485524623 0.0679515144753774 25 1 0.728147765592221 0.271852234407779 26 1 0.84241077494936 0.157589225050640 27 1 0.872979080796478 0.127020919203522 28 1 0.785725595780042 0.214274404219958 29 1 0.728147765592221 0.271852234407779 30 1 0.702577788907515 0.297422211092485 31 1 0.785725595780042 0.214274404219958 32 1 0.715535831240259 0.284464168759741 33 1 0.833890512728604 0.166109487271396 34 1 0.79611233575954 0.203887664240460 35 1 0.715535831240259 0.284464168759741 36 1 0.93592081996753 0.0640791800324692 37 1 0.647557374500253 0.352442625499747 38 1 0.91909601515448 0.08090398484552 39 1 0.728147765592221 0.271852234407779 40 1 0.806119825717223 0.193880174282777 41 1 0.526413348818329 0.473586651181671 42 1 0.289177187171216 0.710822812828784 43 1 0.972371897229638 0.027628102770362 44 1 0.647557374500253 0.352442625499747 45 1 0.943055783232344 0.056944216767656 46 1 0.573027654958788 0.426972345041212 47 1 0.573027654958788 0.426972345041212 48 1 0.728147765592221 0.271852234407779 49 1 0.675673990001272 0.324326009998728 50 1 0.909247852654858 0.0907521473451425 51 1 0.479334017328521 0.520665982671479 52 1 0.675673990001272 0.324326009998728 53 1 0.763814641903368 0.236185358096632 54 1 0.661758493343508 0.338241506656492 55 1 0.495027642106805 0.504972357893195 56 1 0.573027654958788 0.426972345041212 57 1 0.982025295792842 0.0179747042071580 58 1 0.715535831240259 0.284464168759741 59 1 0.647557374500253 0.352442625499747 60 1 0.75229448858394 0.247705511416060 61 1 0.774959292862254 0.225040707137746 62 1 0.661758493343508 0.338241506656492 63 1 0.647557374500253 0.352442625499747 64 1 0.970633201395172 0.0293667986048278 65 1 0.927960156143235 0.0720398438567647 66 1 0.661758493343508 0.338241506656492 67 1 0.975554188104337 0.0244458118956632 68 1 0.60344894981484 0.39655105018516 69 1 0.702577788907515 0.297422211092485 70 1 0.675673990001272 0.324326009998728 71 1 0.364218965545232 0.635781034454768 72 1 0.424136547533282 0.575863452466718 73 1 0.517770178284816 0.482229821715184 74 1 0.681818445934552 0.318181554065448 75 1 0.192073577776478 0.807926422223522 76 1 0.335649835471053 0.664350164528947 77 1 0.202011185243902 0.797988814756098 78 1 0.164508852513049 0.835491147486951 79 0 0.0548452299114503 -0.0548452299114503 80 0 0.573027654958788 -0.573027654958788 81 0 0.245550140567029 -0.245550140567029 82 0 0.825005284731655 -0.825005284731655 83 0 0.573027654958788 -0.573027654958788 84 0 0.417268919138258 -0.417268919138258 85 0 0.378886295980825 -0.378886295980825 86 0 0.417268919138258 -0.417268919138258 87 0 0.825005284731655 -0.825005284731655 88 0 0.715535831240259 -0.715535831240259 89 0 0.276437024444399 -0.276437024444399 90 0 0.147959270029361 -0.147959270029361 91 0 0.715535831240259 -0.715535831240259 92 0 0.245550140567029 -0.245550140567029 93 0 0.147959270029361 -0.147959270029361 94 0 0.245550140567029 -0.245550140567029 95 0 0.245550140567029 -0.245550140567029 96 0 0.0847953543393836 -0.0847953543393836 97 0 0.147959270029361 -0.147959270029361 98 0 0.378886295980825 -0.378886295980825 99 0 0.147959270029361 -0.147959270029361 100 0 0.147959270029361 -0.147959270029361 101 0 0.715535831240259 -0.715535831240259 102 0 0.825005284731655 -0.825005284731655 103 0 0.573027654958788 -0.573027654958788 104 0 0.0847953543393836 -0.0847953543393836 105 0 0.417268919138258 -0.417268919138258 106 0 0.0471054033394483 -0.0471054033394483 107 0 1.37882002772302e-26 -1.37882002772302e-26 108 0 0.0847953543393836 -0.0847953543393836 109 0 0.245550140567029 -0.245550140567029 110 0 0.825005284731655 -0.825005284731655 111 0 0.276437024444399 -0.276437024444399 112 0 0.573027654958788 -0.573027654958788 113 0 0.715535831240259 -0.715535831240259 114 0 0.573027654958788 -0.573027654958788 115 0 0.245550140567029 -0.245550140567029 116 0 0.245550140567029 -0.245550140567029 117 0 0.573027654958788 -0.573027654958788 118 0 0.573027654958788 -0.573027654958788 119 0 0.245550140567029 -0.245550140567029 120 0 0.715535831240259 -0.715535831240259 121 0 0.245550140567029 -0.245550140567029 122 0 0.0847953543393836 -0.0847953543393836 123 0 0.715535831240259 -0.715535831240259 124 0 0.147959270029361 -0.147959270029361 125 0 0.573027654958788 -0.573027654958788 126 0 0.825005284731655 -0.825005284731655 127 0 0.0847953543393836 -0.0847953543393836 128 0 0.898333511614579 -0.898333511614579 129 0 0.573027654958788 -0.573027654958788 130 0 0.417268919138258 -0.417268919138258 131 0 0.169325631056143 -0.169325631056143 132 0 0.715535831240259 -0.715535831240259 133 0 0.147959270029361 -0.147959270029361 134 0 0.825005284731655 -0.825005284731655 135 0 0.245550140567029 -0.245550140567029 136 0 0.245550140567029 -0.245550140567029 137 0 0.0256975474914539 -0.0256975474914539 138 0 0.147959270029361 -0.147959270029361 139 0 0.245550140567029 -0.245550140567029 Type I & II errors for various threshold values Threshold Type I Type II 0.01 0 0.98360655737705 0.02 0 0.98360655737705 0.03 0 0.967213114754098 0.04 0 0.967213114754098 0.05 0 0.950819672131147 0.06 0 0.934426229508197 0.07 0 0.934426229508197 0.08 0 0.934426229508197 0.09 0 0.852459016393443 0.1 0 0.852459016393443 0.11 0 0.852459016393443 0.12 0 0.852459016393443 0.13 0 0.852459016393443 0.14 0 0.852459016393443 0.15 0 0.721311475409836 0.16 0 0.721311475409836 0.17 0.0128205128205128 0.704918032786885 0.18 0.0128205128205128 0.704918032786885 0.19 0.0128205128205128 0.704918032786885 0.2 0.0256410256410256 0.704918032786885 0.21 0.0384615384615385 0.704918032786885 0.22 0.0384615384615385 0.704918032786885 0.23 0.0384615384615385 0.704918032786885 0.24 0.0384615384615385 0.704918032786885 0.25 0.0384615384615385 0.508196721311475 0.26 0.0384615384615385 0.508196721311475 0.27 0.0384615384615385 0.508196721311475 0.28 0.0384615384615385 0.475409836065574 0.29 0.0512820512820513 0.475409836065574 0.3 0.0512820512820513 0.475409836065574 0.31 0.0512820512820513 0.475409836065574 0.32 0.0512820512820513 0.475409836065574 0.33 0.0512820512820513 0.475409836065574 0.34 0.0641025641025641 0.475409836065574 0.35 0.0641025641025641 0.475409836065574 0.36 0.0641025641025641 0.475409836065574 0.37 0.076923076923077 0.475409836065574 0.38 0.076923076923077 0.442622950819672 0.39 0.076923076923077 0.442622950819672 0.4 0.076923076923077 0.442622950819672 0.41 0.076923076923077 0.442622950819672 0.42 0.0897435897435897 0.377049180327869 0.43 0.102564102564103 0.377049180327869 0.44 0.102564102564103 0.377049180327869 0.45 0.115384615384615 0.377049180327869 0.46 0.115384615384615 0.377049180327869 0.47 0.115384615384615 0.377049180327869 0.48 0.128205128205128 0.377049180327869 0.49 0.128205128205128 0.377049180327869 0.5 0.153846153846154 0.377049180327869 0.51 0.153846153846154 0.377049180327869 0.52 0.179487179487179 0.377049180327869 0.53 0.192307692307692 0.377049180327869 0.54 0.192307692307692 0.377049180327869 0.55 0.192307692307692 0.377049180327869 0.56 0.205128205128205 0.377049180327869 0.57 0.205128205128205 0.377049180327869 0.58 0.243589743589744 0.229508196721311 0.59 0.256410256410256 0.229508196721311 0.6 0.256410256410256 0.229508196721311 0.61 0.269230769230769 0.229508196721311 0.62 0.269230769230769 0.229508196721311 0.63 0.269230769230769 0.229508196721311 0.64 0.269230769230769 0.229508196721311 0.65 0.346153846153846 0.229508196721311 0.66 0.346153846153846 0.229508196721311 0.67 0.384615384615385 0.229508196721311 0.68 0.423076923076923 0.229508196721311 0.69 0.435897435897436 0.229508196721311 0.7 0.435897435897436 0.229508196721311 0.71 0.474358974358974 0.229508196721311 0.72 0.538461538461538 0.114754098360656 0.73 0.602564102564103 0.114754098360656 0.74 0.602564102564103 0.114754098360656 0.75 0.602564102564103 0.114754098360656 0.76 0.615384615384615 0.114754098360656 0.77 0.641025641025641 0.114754098360656 0.78 0.653846153846154 0.114754098360656 0.79 0.67948717948718 0.114754098360656 0.8 0.692307692307692 0.114754098360656 0.81 0.717948717948718 0.114754098360656 0.82 0.73076923076923 0.114754098360656 0.83 0.743589743589744 0.0163934426229508 0.84 0.76923076923077 0.0163934426229508 0.85 0.782051282051282 0.0163934426229508 0.86 0.794871794871795 0.0163934426229508 0.87 0.807692307692308 0.0163934426229508 0.88 0.82051282051282 0.0163934426229508 0.89 0.82051282051282 0.0163934426229508 0.9 0.82051282051282 0 0.91 0.846153846153846 0 0.92 0.871794871794872 0 0.93 0.884615384615385 0 0.94 0.923076923076923 0 0.95 0.948717948717949 0 0.96 0.948717948717949 0 0.97 0.948717948717949 0 0.98 0.987179487179487 0 0.99 1 0

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t120168343090cb6m99ccho5r4/1skdn1201683362.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t120168343090cb6m99ccho5r4/1skdn1201683362.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t120168343090cb6m99ccho5r4/286dh1201683362.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t120168343090cb6m99ccho5r4/286dh1201683362.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

library(brlr) roc.plot <- function (sd, sdc, newplot = TRUE, ...) { sall <- sort(c(sd, sdc)) sens <- 0 specc <- 0 for (i in length(sall):1) { sens <- c(sens, mean(sd >= sall[i], na.rm = T)) specc <- c(specc, mean(sdc >= sall[i], na.rm = T)) } if (newplot) { plot(specc, sens, xlim = c(0, 1), ylim = c(0, 1), type = 'l', xlab = '1-specificity', ylab = 'sensitivity', main = 'ROC plot', ...) abline(0, 1) } else lines(specc, sens, ...) npoints <- length(sens) area <- sum(0.5 * (sens[-1] + sens[-npoints]) * (specc[-1] - specc[-npoints])) lift <- (sens - specc)[-1] cutoff <- sall[lift == max(lift)][1] sensopt <- sens[-1][lift == max(lift)][1] specopt <- 1 - specc[-1][lift == max(lift)][1] list(area = area, cutoff = cutoff, sensopt = sensopt, specopt = specopt) } roc.analysis <- function (object, newdata = NULL, newplot = TRUE, ...) { if (is.null(newdata)) { sd <- object$fitted[object$y == 1] sdc <- object$fitted[object$y == 0] } else { sd <- predict(object, newdata, type = 'response')[newdata$y == 1] sdc <- predict(object, newdata, type = 'response')[newdata$y == 0] } roc.plot(sd, sdc, newplot, ...) } hosmerlem <- function (y, yhat, g = 10) { cutyhat <- cut(yhat, breaks = quantile(yhat, probs = seq(0, 1, 1/g)), include.lowest = T) obs <- xtabs(cbind(1 - y, y) ~ cutyhat) expect <- xtabs(cbind(1 - yhat, yhat) ~ cutyhat) chisq <- sum((obs - expect)^2/expect) P <- 1 - pchisq(chisq, g - 2) c('X^2' = chisq, Df = g - 2, 'P(>Chi)' = P) } x <- as.data.frame(t(y)) r <- brlr(x) summary(r) rc <- summary(r)$coeff hm <- hosmerlem(y[1,],r$fitted.values) hm bitmap(file='test0.png') ra <- roc.analysis(r) dev.off() te <- array(0,dim=c(2,99)) for (i in 1:99) { threshold <- i / 100 numcorr1 <- 0 numfaul1 <- 0 numcorr0 <- 0 numfaul0 <- 0 for (j in 1:length(r$fitted.values)) { if (y[1,j] > 0.99) { if (r$fitted.values[j] >= threshold) numcorr1 = numcorr1 + 1 else numfaul1 = numfaul1 + 1 } else { if (r$fitted.values[j] < threshold) numcorr0 = numcorr0 + 1 else numfaul0 = numfaul0 + 1 } } te[1,i] <- numfaul1 / (numfaul1 + numcorr1) te[2,i] <- numfaul0 / (numfaul0 + numcorr0) } bitmap(file='test1.png') op <- par(mfrow=c(2,2)) plot((1:99)/100,te[1,],xlab='Threshold',ylab='Type I error', main='1 - Specificity') plot((1:99)/100,te[2,],xlab='Threshold',ylab='Type II error', main='1 - Sensitivity') plot(te[1,],te[2,],xlab='Type I error',ylab='Type II error', main='(1-Sens.) vs (1-Spec.)') plot((1:99)/100,te[1,]+te[2,],xlab='Threshold',ylab='Sum of Type I & II error', main='(1-Sens.) + (1-Spec.)') par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Coefficients of Bias-Reduced Logistic Regression',5,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'t-stat',header=TRUE) a<-table.element(a,'2-sided p-value',header=TRUE) a<-table.row.end(a) for (i in 1:length(rc[,1])) { a<-table.row.start(a) a<-table.element(a,labels(rc)[[1]][i],header=TRUE) a<-table.element(a,rc[i,1]) a<-table.element(a,rc[i,2]) a<-table.element(a,rc[i,3]) a<-table.element(a,2*(1-pt(abs(rc[i,3]),r$df.residual))) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Summary of Bias-Reduced Logistic Regression',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Deviance',1,TRUE) a<-table.element(a,r$deviance) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Penalized deviance',1,TRUE) a<-table.element(a,r$penalized.deviance) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Residual Degrees of Freedom',1,TRUE) a<-table.element(a,r$df.residual) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'ROC Area',1,TRUE) a<-table.element(a,ra$area) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Hosmer–Lemeshow test',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Chi-square',1,TRUE) a<-table.element(a,hm[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Degrees of Freedom',1,TRUE) a<-table.element(a,hm[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'P(>Chi)',1,TRUE) a<-table.element(a,hm[3]) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Fit of Logistic Regression',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Index',1,TRUE) a<-table.element(a,'Actual',1,TRUE) a<-table.element(a,'Fitted',1,TRUE) a<-table.element(a,'Error',1,TRUE) a<-table.row.end(a) for (i in 1:length(r$fitted.values)) { a<-table.row.start(a) a<-table.element(a,i,1,TRUE) a<-table.element(a,y[1,i]) a<-table.element(a,r$fitted.values[i]) a<-table.element(a,y[1,i]-r$fitted.values[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Type I & II errors for various threshold values',3,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Threshold',1,TRUE) a<-table.element(a,'Type I',1,TRUE) a<-table.element(a,'Type II',1,TRUE) a<-table.row.end(a) for (i in 1:99) { a<-table.row.start(a) a<-table.element(a,i/100,1,TRUE) a<-table.element(a,te[1,i]) a<-table.element(a,te[2,i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable3.tab')

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