Binghnetty Logistic Regression 1

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 01:49:31 -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/t1201683126on2c5tyr0czo91k.htm/, Retrieved Wed, 30 Jan 2008 09:52:09 +0100

User-defined keywords:

Dataseries X:

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1 1 5.3 1 1 4.6 1 1 5.9 1 1 6.4 1 1 4.5 1 1 3.1 1 1 3.8 1 1 5.7 1 1 3.6 1 1 3.6 1 1 6.1 1 1 5.3 1 1 4.3 1 1 6.5 1 1 6.2 1 1 6.9 1 1 7.2 1 1 6.6 1 1 5.7 1 1 6.8 1 1 2.2 1 1 2.2 1 1 4.1 1 1 5.2 1 1 5.8 1 1 5.2 1 1 5.6 1 1 5.7 1 1 4.4 1 1 5.4 1 1 6.1 1 1 6.5 1 1 4.7 1 1 6.8 1 1 6.3 1 1 3.8 1 1 3.1 1 1 6.5 1 1 7.1 1 1 1.0 1 0 4.9 1 0 5.8 1 0 5.6 1 0 4.9 1 0 5.2 1 0 7.0 0 1 5.0 0 1 8.0 0 0 6.0 0 1 5.0 0 1 8.0 0 0 10.0 0 1 1.0 0 1 7.0 0 1 6.0 0 1 4.0 0 0 6.0 0 0 6.0 0 1 8.0 0 0 7.0 0 0 6.0 0 1 7.0 0 1 6.0 0 1 6.0 0 0 6.0 0 1 5.0 0 1 6.0 0 1 7.0 0 1 6.0 0 1 3.0 0 1 6.0 0 1 3.0 0 1 7.0 0 1 5.0 0 1 7.0 0 1 5.0 0 1 7.0 0 1 7.0 0 1 6.0 0 1 7.0 0 1 5.0 0 1 6.0 0 1 6.0 0 1 6.0 0 1 5.0 0 1 8.0 0 0 3.0 0 0 5.0 0 0 6.0 0 0 6.0 0 1 6.0 0 0 99.0 0 1 8.0 0 1 8.0 0 0 4.0 0 1 9.0 0 1 5.0 0 0 6.0 0 1 99.0 0 1 6.0 0 1 6.0 0 1 7.0 0 1 5.0 0 0 99.0 0 1 6.0 0 1 6.0 0 0 6.0 0 1 7.0 0 0 8.0 0 0 7.0 0 1 6.0 0 2 6.0 0 1 5.0 0 1 7.0 0 1 6.0 0 0 7.0 0 1 9.0 0 1 6.0 0 1 7.0 0 1 6.0 0 1 7.0 0 1 7.0 0 0 8.0 0 1 4.0 0 0 5.0 0 1 6.0 0 1 6.0 0 1 6.0 0 1 7.0

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 28 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Coefficients of Bias-Reduced Logistic Regression Variable Parameter S.E. t-stat 2-sided p-value (Intercept) -0.825890022943728 0.480135282129261 -1.72011941984589 0.0878658393608114 snoring 0.518923897826726 0.471739707655631 1.10002166322946 0.273419900430739 sleep_time -0.0231428624222981 0.0275856292428259 -0.838946330300468 0.403088263277221 Summary of Bias-Reduced Logistic Regression Deviance 162.926225935245 Penalized deviance 150.860973421723 Residual Degrees of Freedom 126 ROC Area 0.685699319015191 Hosmer–Lemeshow test Chi-square 70.5399502271576 Degrees of Freedom 8 P(>Chi) 3.83659770619715e-12 Fit of Logistic Regression Index Actual Fitted Error 1 1 0.394216288602478 0.605783711397522 2 1 0.398091564643848 0.601908435356152 3 1 0.390905159967589 0.609094840032411 4 1 0.388153526004179 0.611846473995821 5 1 0.39864623214808 0.60135376785192 6 1 0.406438308596170 0.59356169140383 7 1 0.402536118992557 0.597463881007444 8 1 0.392007770079260 0.607992229920741 9 1 0.40364979475207 0.59635020524793 10 1 0.40364979475207 0.59635020524793 11 1 0.389803662825327 0.610196337174673 12 1 0.394216288602478 0.605783711397522 13 1 0.399756346657742 0.600243653342258 14 1 0.387604047791694 0.612395952208306 15 1 0.38925333477472 0.61074666522528 16 1 0.385409005215578 0.614590994784422 17 1 0.383765771818281 0.616234228181719 18 1 0.387054855361341 0.612945144638659 19 1 0.392007770079260 0.607992229920741 20 1 0.385957332830875 0.614042667169125 21 1 0.411472752558004 0.588527247441996 22 1 0.411472752558004 0.588527247441996 23 1 0.400867491796758 0.599132508203242 24 1 0.394769097940561 0.605230902059439 25 1 0.391456326535033 0.608543673464967 26 1 0.394769097940561 0.605230902059439 27 1 0.39255948933125 0.60744051066875 28 1 0.392007770079260 0.607992229920741 29 1 0.399201159920673 0.600798840079327 30 1 0.393663749868724 0.606336250131276 31 1 0.389803662825327 0.610196337174673 32 1 0.387604047791694 0.612395952208306 33 1 0.397537158709246 0.602462841290754 34 1 0.385957332830875 0.614042667169125 35 1 0.388703288749294 0.611296711250706 36 1 0.402536118992557 0.597463881007444 37 1 0.406438308596170 0.59356169140383 38 1 0.387604047791694 0.612395952208306 39 1 0.384313223475466 0.615686776524534 40 1 0.418214105047298 0.581785894952702 41 1 0.281043771719492 0.718956228280508 42 1 0.276854444804339 0.72314555519566 43 1 0.277782069507206 0.722217930492794 44 1 0.281043771719492 0.718956228280508 45 1 0.279643045375763 0.720356954624237 46 1 0.271329031711626 0.728670968288374 47 0 0.395875523296432 -0.395875523296432 48 0 0.379396861385598 -0.379396861385598 49 0 0.275928734306748 -0.275928734306748 50 0 0.395875523296432 -0.395875523296432 51 0 0.379396861385598 -0.379396861385598 52 0 0.257822198062316 -0.257822198062316 53 0 0.418214105047298 -0.418214105047298 54 0 0.384860968352024 -0.384860968352024 55 0 0.390354271643189 -0.390354271643189 56 0 0.401423447577954 -0.401423447577954 57 0 0.275928734306748 -0.275928734306748 58 0 0.275928734306748 -0.275928734306748 59 0 0.379396861385598 -0.379396861385598 60 0 0.271329031711626 -0.271329031711626 61 0 0.275928734306748 -0.275928734306748 62 0 0.384860968352024 -0.384860968352024 63 0 0.390354271643189 -0.390354271643189 64 0 0.390354271643189 -0.390354271643189 65 0 0.275928734306748 -0.275928734306748 66 0 0.395875523296432 -0.395875523296432 67 0 0.390354271643189 -0.390354271643189 68 0 0.384860968352024 -0.384860968352024 69 0 0.390354271643189 -0.390354271643189 70 0 0.406996742048269 -0.406996742048269 71 0 0.390354271643189 -0.390354271643189 72 0 0.406996742048269 -0.406996742048269 73 0 0.384860968352024 -0.384860968352024 74 0 0.395875523296432 -0.395875523296432 75 0 0.384860968352024 -0.384860968352024 76 0 0.395875523296432 -0.395875523296432 77 0 0.384860968352024 -0.384860968352024 78 0 0.384860968352024 -0.384860968352024 79 0 0.390354271643189 -0.390354271643189 80 0 0.384860968352024 -0.384860968352024 81 0 0.395875523296432 -0.395875523296432 82 0 0.390354271643189 -0.390354271643189 83 0 0.390354271643189 -0.390354271643189 84 0 0.390354271643189 -0.390354271643189 85 0 0.395875523296432 -0.395875523296432 86 0 0.379396861385598 -0.379396861385598 87 0 0.290013473631371 -0.290013473631371 88 0 0.280576388320880 -0.280576388320880 89 0 0.275928734306748 -0.275928734306748 90 0 0.275928734306748 -0.275928734306748 91 0 0.390354271643189 -0.390354271643189 92 0 0.0424100863065165 -0.0424100863065165 93 0 0.379396861385598 -0.379396861385598 94 0 0.379396861385598 -0.379396861385598 95 0 0.285271483543346 -0.285271483543346 96 0 0.373963169926946 -0.373963169926946 97 0 0.395875523296432 -0.395875523296432 98 0 0.275928734306748 -0.275928734306748 99 0 0.0692601885400124 -0.0692601885400124 100 0 0.390354271643189 -0.390354271643189 101 0 0.390354271643189 -0.390354271643189 102 0 0.384860968352024 -0.384860968352024 103 0 0.395875523296432 -0.395875523296432 104 0 0.0424100863065165 -0.0424100863065165 105 0 0.390354271643189 -0.390354271643189 106 0 0.390354271643189 -0.390354271643189 107 0 0.275928734306748 -0.275928734306748 108 0 0.384860968352024 -0.384860968352024 109 0 0.266777754860427 -0.266777754860427 110 0 0.271329031711626 -0.271329031711626 111 0 0.390354271643189 -0.390354271643189 112 0 0.518267015817867 -0.518267015817867 113 0 0.395875523296432 -0.395875523296432 114 0 0.384860968352024 -0.384860968352024 115 0 0.390354271643189 -0.390354271643189 116 0 0.271329031711626 -0.271329031711626 117 0 0.373963169926946 -0.373963169926946 118 0 0.390354271643189 -0.390354271643189 119 0 0.384860968352024 -0.384860968352024 120 0 0.390354271643189 -0.390354271643189 121 0 0.384860968352024 -0.384860968352024 122 0 0.384860968352024 -0.384860968352024 123 0 0.266777754860427 -0.266777754860427 124 0 0.401423447577954 -0.401423447577954 125 0 0.280576388320880 -0.280576388320880 126 0 0.390354271643189 -0.390354271643189 127 0 0.390354271643189 -0.390354271643189 128 0 0.390354271643189 -0.390354271643189 129 0 0.384860968352024 -0.384860968352024 Type I & II errors for various threshold values Threshold Type I Type II 0.01 0 1 0.02 0 1 0.03 0 1 0.04 0 1 0.05 0 0.975903614457831 0.06 0 0.975903614457831 0.07 0 0.963855421686747 0.08 0 0.963855421686747 0.09 0 0.963855421686747 0.1 0 0.963855421686747 0.11 0 0.963855421686747 0.12 0 0.963855421686747 0.13 0 0.963855421686747 0.14 0 0.963855421686747 0.15 0 0.963855421686747 0.16 0 0.963855421686747 0.17 0 0.963855421686747 0.18 0 0.963855421686747 0.19 0 0.963855421686747 0.2 0 0.963855421686747 0.21 0 0.963855421686747 0.22 0 0.963855421686747 0.23 0 0.963855421686747 0.24 0 0.963855421686747 0.25 0 0.963855421686747 0.26 0 0.951807228915663 0.27 0 0.927710843373494 0.28 0.0869565217391304 0.783132530120482 0.29 0.130434782608696 0.746987951807229 0.3 0.130434782608696 0.734939759036145 0.31 0.130434782608696 0.734939759036145 0.32 0.130434782608696 0.734939759036145 0.33 0.130434782608696 0.734939759036145 0.34 0.130434782608696 0.734939759036145 0.35 0.130434782608696 0.734939759036145 0.36 0.130434782608696 0.734939759036145 0.37 0.130434782608696 0.734939759036145 0.38 0.130434782608696 0.63855421686747 0.39 0.434782608695652 0.457831325301205 0.4 0.782608695652174 0.072289156626506 0.41 0.934782608695652 0.0240963855421687 0.42 1 0.0120481927710843 0.43 1 0.0120481927710843 0.44 1 0.0120481927710843 0.45 1 0.0120481927710843 0.46 1 0.0120481927710843 0.47 1 0.0120481927710843 0.48 1 0.0120481927710843 0.49 1 0.0120481927710843 0.5 1 0.0120481927710843 0.51 1 0.0120481927710843 0.52 1 0 0.53 1 0 0.54 1 0 0.55 1 0 0.56 1 0 0.57 1 0 0.58 1 0 0.59 1 0 0.6 1 0 0.61 1 0 0.62 1 0 0.63 1 0 0.64 1 0 0.65 1 0 0.66 1 0 0.67 1 0 0.68 1 0 0.69 1 0 0.7 1 0 0.71 1 0 0.72 1 0 0.73 1 0 0.74 1 0 0.75 1 0 0.76 1 0 0.77 1 0 0.78 1 0 0.79 1 0 0.8 1 0 0.81 1 0 0.82 1 0 0.83 1 0 0.84 1 0 0.85 1 0 0.86 1 0 0.87 1 0 0.88 1 0 0.89 1 0 0.9 1 0 0.91 1 0 0.92 1 0 0.93 1 0 0.94 1 0 0.95 1 0 0.96 1 0 0.97 1 0 0.98 1 0 0.99 1 0

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201683126on2c5tyr0czo91k/1qlfa1201682941.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201683126on2c5tyr0czo91k/1qlfa1201682941.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201683126on2c5tyr0czo91k/2igvy1201682941.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201683126on2c5tyr0czo91k/2igvy1201682941.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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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