primary composite outcome (blanks)

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

Title produced by software: Bias-Reduced Logistic Regression

Date of computation: Fri, 10 Oct 2008 03:30:53 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/10/t1223631231zdm9zp50smizef3.htm/, Retrieved Fri, 10 Oct 2008 09:33:53 +0000

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Oct/10/t1223631231zdm9zp50smizef3.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

This computation does NOT treat blanks as missing values. When you copy/paste your data from the spreadsheet the blanks are filled with the next available value which leads to wrong results.

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This computation is private

User-defined keywords:

Dataseries X:

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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 computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 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) -0.683287288677931 0.401247919207087 -1.70290550049004 0.0906569413532652 IM 0.912557268889368 0.384607902211778 2.37269505811372 0.0189267172511209 UC -0.286581047364018 0.378550431093277 -0.75704852993128 0.450208300901998 DIA 0.0453179037750105 0.360263792342417 0.125790891947136 0.90006589398881 TEN -0.91733167182092 0.371025895592631 -2.4724195338325 0.0145371498597089 Summary of Bias-Reduced Logistic Regression Deviance 183.701358677209 Penalized deviance 172.251960034912 Residual Degrees of Freedom 150 ROC Area 0.654761904761905 Hosmer–Lemeshow test Chi-square 10.0577337204959 Degrees of Freedom 8 P(>Chi) 0.260997133227709 Fit of Logistic Regression Index Actual Fitted Error 1 0 0.174321949128263 -0.174321949128263 2 0 0.283061710881172 -0.283061710881172 3 0 0.283061710881172 -0.283061710881172 4 1 0.334464398221005 0.665535601778995 5 0 0.344626566040748 -0.344626566040748 6 0 0.557067734637987 -0.557067734637987 7 0 0.335528009182617 -0.335528009182617 8 0 0.335528009182617 -0.335528009182617 9 0 0.283061710881172 -0.283061710881172 10 0 0.174321949128263 -0.174321949128263 11 0 0.344626566040748 -0.344626566040748 12 0 0.497001745093596 -0.497001745093596 13 0 0.274906746407678 -0.274906746407678 14 0 0.497001745093596 -0.497001745093596 15 1 0.497001745093596 0.502998254906404 16 0 0.284031620348882 -0.284031620348882 17 0 0.497001745093596 -0.497001745093596 18 0 0.497001745093596 -0.497001745093596 19 1 0.485676153623096 0.514323846376904 20 1 0.485676153623096 0.514323846376904 21 1 0.497001745093596 0.502998254906404 22 1 0.497001745093596 0.502998254906404 23 1 0.568218875230518 0.431781124769482 24 1 0.273956073698742 0.726043926301258 25 0 0.273956073698742 -0.273956073698742 26 0 0.273956073698742 -0.273956073698742 27 0 0.485676153623096 -0.485676153623096 28 0 0.557067734637987 -0.557067734637987 29 0 0.274906746407678 -0.274906746407678 30 0 0.335528009182617 -0.335528009182617 31 0 0.334464398221005 -0.334464398221005 32 0 0.557067734637987 -0.557067734637987 33 1 0.344626566040748 0.655373433959252 34 1 0.345705706844236 0.654294293155764 35 1 0.334464398221005 0.665535601778995 36 1 0.345705706844236 0.654294293155764 37 1 0.345705706844236 0.654294293155764 38 0 0.174321949128263 -0.174321949128263 39 0 0.274906746407678 -0.274906746407678 40 0 0.568218875230518 -0.568218875230518 41 1 0.485676153623096 0.514323846376904 42 0 0.345705706844236 -0.345705706844236 43 0 0.335528009182617 -0.335528009182617 44 1 0.335528009182617 0.664471990817383 45 1 0.174321949128263 0.825678050871737 46 1 0.274906746407678 0.725093253592322 47 0 0.131564052511061 -0.131564052511061 48 0 0.345705706844236 -0.345705706844236 49 0 0.485676153623096 -0.485676153623096 50 0 0.274906746407678 -0.274906746407678 51 0 0.568218875230518 -0.568218875230518 52 1 0.557067734637987 0.442932265362013 53 0 0.131564052511061 -0.131564052511061 54 1 0.273956073698742 0.726043926301258 55 0 0.273956073698742 -0.273956073698742 56 0 0.283061710881172 -0.283061710881172 57 0 0.273956073698742 -0.273956073698742 58 0 0.283061710881172 -0.283061710881172 59 0 0.497001745093596 -0.497001745093596 60 0 0.344626566040748 -0.344626566040748 61 0 0.283061710881172 -0.283061710881172 62 0 0.497001745093596 -0.497001745093596 63 0 0.283061710881172 -0.283061710881172 64 0 0.335528009182617 -0.335528009182617 65 0 0.284031620348882 -0.284031620348882 66 1 0.283061710881172 0.716938289118828 67 1 0.273956073698742 0.726043926301258 68 0 0.283061710881172 -0.283061710881172 69 0 0.273956073698742 -0.273956073698742 70 0 0.283061710881172 -0.283061710881172 71 0 0.283061710881172 -0.283061710881172 72 0 0.344626566040748 -0.344626566040748 73 0 0.334464398221005 -0.334464398221005 74 0 0.136828851462236 -0.136828851462236 75 0 0.131564052511061 -0.131564052511061 76 0 0.283061710881172 -0.283061710881172 77 0 0.283061710881172 -0.283061710881172 78 0 0.274906746407678 -0.274906746407678 79 0 0.284031620348882 -0.284031620348882 80 0 0.273956073698742 -0.273956073698742 81 0 0.174321949128263 -0.174321949128263 82 0 0.136828851462236 -0.136828851462236 83 0 0.283061710881172 -0.283061710881172 84 0 0.283061710881172 -0.283061710881172 85 1 0.273956073698742 0.726043926301258 86 0 0.344626566040748 -0.344626566040748 87 0 0.283061710881172 -0.283061710881172 88 0 0.284031620348882 -0.284031620348882 89 0 0.284031620348882 -0.284031620348882 90 0 0.283061710881172 -0.283061710881172 91 0 0.283061710881172 -0.283061710881172 92 0 0.283061710881172 -0.283061710881172 93 0 0.136828851462236 -0.136828851462236 94 0 0.344626566040748 -0.344626566040748 95 1 0.485676153623096 0.514323846376904 96 0 0.131564052511061 -0.131564052511061 97 0 0.273956073698742 -0.273956073698742 98 1 0.485676153623096 0.514323846376904 99 1 0.335528009182617 0.664471990817383 100 0 0.274906746407678 -0.274906746407678 101 0 0.274906746407678 -0.274906746407678 102 0 0.167895124376798 -0.167895124376798 103 1 0.283061710881172 0.716938289118828 104 0 0.334464398221005 -0.334464398221005 105 1 0.283061710881172 0.716938289118828 106 1 0.167895124376798 0.832104875623202 107 0 0.174321949128263 -0.174321949128263 108 1 0.568218875230518 0.431781124769482 109 0 0.274906746407678 -0.274906746407678 110 1 0.136828851462236 0.863171148537764 111 0 0.335528009182617 -0.335528009182617 112 1 0.131564052511061 0.868435947488939 113 0 0.136828851462236 -0.136828851462236 114 0 0.274906746407678 -0.274906746407678 115 0 0.131564052511061 -0.131564052511061 116 0 0.274906746407678 -0.274906746407678 117 1 0.284031620348882 0.715968379651118 118 0 0.335528009182617 -0.335528009182617 119 0 0.131564052511061 -0.131564052511061 120 0 0.283061710881172 -0.283061710881172 121 0 0.131564052511061 -0.131564052511061 122 0 0.273956073698742 -0.273956073698742 123 0 0.345705706844236 -0.345705706844236 124 0 0.284031620348882 -0.284031620348882 125 1 0.283061710881172 0.716938289118828 126 0 0.174321949128263 -0.174321949128263 127 0 0.485676153623096 -0.485676153623096 128 0 0.497001745093596 -0.497001745093596 129 0 0.497001745093596 -0.497001745093596 130 0 0.167895124376798 -0.167895124376798 131 0 0.497001745093596 -0.497001745093596 132 0 0.131564052511061 -0.131564052511061 133 1 0.485676153623096 0.514323846376904 134 1 0.273956073698742 0.726043926301258 135 0 0.335528009182617 -0.335528009182617 136 0 0.334464398221005 -0.334464398221005 137 1 0.174321949128263 0.825678050871737 138 0 0.274906746407678 -0.274906746407678 139 0 0.274906746407678 -0.274906746407678 140 1 0.497001745093596 0.502998254906404 141 1 0.485676153623096 0.514323846376904 142 0 0.284031620348882 -0.284031620348882 143 1 0.497001745093596 0.502998254906404 144 1 0.284031620348882 0.715968379651118 145 1 0.284031620348882 0.715968379651118 146 1 0.497001745093596 0.502998254906404 147 1 0.557067734637987 0.442932265362013 148 1 0.497001745093596 0.502998254906404 149 1 0.557067734637987 0.442932265362013 150 1 0.568218875230518 0.431781124769482 151 0 0.284031620348882 -0.284031620348882 152 1 0.497001745093596 0.502998254906404 153 1 0.283061710881172 0.716938289118828 154 1 0.345705706844236 0.654294293155764 155 1 0.284031620348882 0.715968379651118 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 1 0.06 0 1 0.07 0 1 0.08 0 1 0.09 0 1 0.1 0 1 0.11 0 1 0.12 0 1 0.13 0 1 0.14 0.04 0.885714285714286 0.15 0.04 0.885714285714286 0.16 0.04 0.885714285714286 0.17 0.06 0.866666666666667 0.18 0.1 0.80952380952381 0.19 0.1 0.80952380952381 0.2 0.1 0.80952380952381 0.21 0.1 0.80952380952381 0.22 0.1 0.80952380952381 0.23 0.1 0.80952380952381 0.24 0.1 0.80952380952381 0.25 0.1 0.80952380952381 0.26 0.1 0.80952380952381 0.27 0.1 0.80952380952381 0.28 0.22 0.619047619047619 0.29 0.4 0.361904761904762 0.3 0.4 0.361904761904762 0.31 0.4 0.361904761904762 0.32 0.4 0.361904761904762 0.33 0.4 0.361904761904762 0.34 0.48 0.247619047619048 0.35 0.58 0.161904761904762 0.36 0.58 0.161904761904762 0.37 0.58 0.161904761904762 0.38 0.58 0.161904761904762 0.39 0.58 0.161904761904762 0.4 0.58 0.161904761904762 0.41 0.58 0.161904761904762 0.42 0.58 0.161904761904762 0.43 0.58 0.161904761904762 0.44 0.58 0.161904761904762 0.45 0.58 0.161904761904762 0.46 0.58 0.161904761904762 0.47 0.58 0.161904761904762 0.48 0.58 0.161904761904762 0.49 0.72 0.133333333333333 0.5 0.88 0.0476190476190476 0.51 0.88 0.0476190476190476 0.52 0.88 0.0476190476190476 0.53 0.88 0.0476190476190476 0.54 0.88 0.0476190476190476 0.55 0.88 0.0476190476190476 0.56 0.94 0.0190476190476190 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/Oct/10/t1223631231zdm9zp50smizef3/18aco1223631050.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/10/t1223631231zdm9zp50smizef3/18aco1223631050.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/10/t1223631231zdm9zp50smizef3/2w4ww1223631050.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/10/t1223631231zdm9zp50smizef3/2w4ww1223631050.ps (open in new window)

Parameters (Session):

Parameters (R input):

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

library(brglm) 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 <- brglm(x) summary(r) rc <- summary(r)$coeff try(hm <- hosmerlem(y[1,],r$fitted.values),silent=T) try(hm,silent=T) 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) phm <- array('NA',dim=3) for (i in 1:3) { try(phm[i] <- hm[i],silent=T) } a<-table.element(a,phm[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Degrees of Freedom',1,TRUE) a<-table.element(a,phm[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'P(>Chi)',1,TRUE) a<-table.element(a,phm[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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