primary composite outcome (missing are treated as zeroes)

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 03:36:26 -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/t12236315636r81irw44sqtfke.htm/, Retrieved Fri, 10 Oct 2008 09:39:23 +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/t12236315636r81irw44sqtfke.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:

In this computation every blank is replaced by a zero. This may not be adequate - it is just displayed for the purpose of comparison.

IsPrivate?

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 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) -4.37666921379609 1.42342617716857 -3.07474267650606 0.00250393711862484 IM 2.80704667331724 1.40171144166732 2.00258526104223 0.0470238850659515 UC 0.476338359925393 0.650416538761874 0.732358929298055 0.465092308533444 DIA -0.756429649213741 0.591866215441167 -1.27804160717285 0.203208965567862 TEN -0.393687983725064 0.585322062053738 -0.672600623225645 0.502236211100646 Summary of Bias-Reduced Logistic Regression Deviance 73.0449861485117 Penalized deviance 68.2164597781075 Residual Degrees of Freedom 150 ROC Area 0.765151515151515 Hosmer–Lemeshow test Chi-square NA Degrees of Freedom NA P(>Chi) NA Fit of Logistic Regression Index Actual Fitted Error 1 0 0.00396298517614339 -0.00396298517614339 2 0 0.0959201324934114 -0.0959201324934114 3 0 0.0959201324934114 -0.0959201324934114 4 1 0.123109219284500 0.8768907807155 5 0 0.0618185337110289 -0.0618185337110289 6 0 0.172270208230679 -0.172270208230679 7 0 0.0124111744099204 -0.0124111744099204 8 0 0.0124111744099204 -0.0124111744099204 9 0 0.0959201324934114 -0.0959201324934114 10 0 0.00396298517614339 -0.00396298517614339 11 0 0.0618185337110289 -0.0618185337110289 12 0 0.135906500173194 -0.135906500173194 13 0 0.0198338727507165 -0.0198338727507165 14 0 0.135906500173194 -0.135906500173194 15 1 0.135906500173194 0.864093499826806 16 0 0.00940783085246568 -0.00940783085246568 17 0 0.135906500173194 -0.135906500173194 18 0 0.184376623989256 -0.184376623989256 19 0 0.135906500173194 -0.135906500173194 20 0 0.135906500173194 -0.135906500173194 21 0 0.0959201324934114 -0.0959201324934114 22 0 0.0959201324934114 -0.0959201324934114 23 0 0.184376623989256 -0.184376623989256 24 0 0.184376623989256 -0.184376623989256 25 0 0.0618185337110289 -0.0618185337110289 26 0 0.0618185337110289 -0.0618185337110289 27 0 0.0618185337110289 -0.0618185337110289 28 0 0.00586366883261908 -0.00586366883261908 29 0 0.00840609014893699 -0.00840609014893699 30 0 0.0124111744099204 -0.0124111744099204 31 0 0.00586366883261908 -0.00586366883261908 32 0 0.0889881905643604 -0.0889881905643604 33 0 0.00940783085246568 -0.00940783085246568 34 1 0.251000350398710 0.74899964960129 35 0 0.0618185337110289 -0.0618185337110289 36 0 0.00940783085246568 -0.00940783085246568 37 0 0.0889881905643604 -0.0889881905643604 38 0 0.172270208230679 -0.172270208230679 39 0 0.0134661456330231 -0.0134661456330231 40 0 0.0198338727507165 -0.0198338727507165 41 0 0.123109219284500 -0.123109219284500 42 0 0.135906500173194 -0.135906500173194 43 0 0.00840609014893699 -0.00840609014893699 44 0 0.0124111744099204 -0.0124111744099204 45 0 0.172270208230679 -0.172270208230679 46 0 0.0198338727507165 -0.0198338727507165 47 0 0.184376623989256 -0.184376623989256 48 0 0.172270208230679 -0.172270208230679 49 0 0.0889881905643604 -0.0889881905643604 50 0 0.0198338727507165 -0.0198338727507165 51 0 0.251000350398710 -0.251000350398710 52 0 0.00840609014893699 -0.00840609014893699 53 0 0.00840609014893699 -0.00840609014893699 54 0 0.0618185337110289 -0.0618185337110289 55 0 0.0124111744099204 -0.0124111744099204 56 0 0.0618185337110289 -0.0618185337110289 57 1 0.123109219284500 0.8768907807155 58 0 0.184376623989256 -0.184376623989256 59 0 0.0959201324934114 -0.0959201324934114 60 0 0.184376623989256 -0.184376623989256 61 0 0.0959201324934114 -0.0959201324934114 62 0 0.135906500173194 -0.135906500173194 63 0 0.0618185337110289 -0.0618185337110289 64 0 0.0959201324934114 -0.0959201324934114 65 0 0.135906500173194 -0.135906500173194 66 0 0.0959201324934114 -0.0959201324934114 67 0 0.0124111744099204 -0.0124111744099204 68 0 0.00940783085246568 -0.00940783085246568 69 1 0.0959201324934114 0.904079867506589 70 1 0.184376623989256 0.815623376010744 71 0 0.0959201324934114 -0.0959201324934114 72 0 0.184376623989256 -0.184376623989256 73 0 0.0959201324934114 -0.0959201324934114 74 0 0.0959201324934114 -0.0959201324934114 75 0 0.0618185337110289 -0.0618185337110289 76 0 0.123109219284500 -0.123109219284500 77 0 0.00636567812954466 -0.00636567812954466 78 0 0.0134661456330231 -0.0134661456330231 79 0 0.0959201324934114 -0.0959201324934114 80 0 0.0959201324934114 -0.0959201324934114 81 0 0.0198338727507165 -0.0198338727507165 82 0 0.00940783085246568 -0.00940783085246568 83 0 0.184376623989256 -0.184376623989256 84 0 0.00396298517614339 -0.00396298517614339 85 0 0.00636567812954466 -0.00636567812954466 86 0 0.0959201324934114 -0.0959201324934114 87 0 0.0959201324934114 -0.0959201324934114 88 1 0.184376623989256 0.815623376010744 89 0 0.0618185337110289 -0.0618185337110289 90 0 0.0959201324934114 -0.0959201324934114 91 0 0.00940783085246568 -0.00940783085246568 92 0 0.00940783085246568 -0.00940783085246568 93 0 0.0959201324934114 -0.0959201324934114 94 0 0.0959201324934114 -0.0959201324934114 95 0 0.0959201324934114 -0.0959201324934114 96 0 0.00636567812954466 -0.00636567812954466 97 0 0.0618185337110289 -0.0618185337110289 98 1 0.251000350398710 0.74899964960129 99 0 0.00840609014893699 -0.00840609014893699 100 0 0.0618185337110289 -0.0618185337110289 101 0 0.0959201324934114 -0.0959201324934114 102 0 0.0198338727507165 -0.0198338727507165 103 0 0.00840609014893699 -0.00840609014893699 104 0 0.00840609014893699 -0.00840609014893699 105 0 0.0124111744099204 -0.0124111744099204 106 0 0.0959201324934114 -0.0959201324934114 107 1 0.0889881905643604 0.91101180943564 108 0 0.135906500173194 -0.135906500173194 109 1 0.135906500173194 0.864093499826806 110 0 0.0198338727507165 -0.0198338727507165 111 0 0.0959201324934114 -0.0959201324934114 112 0 0.172270208230679 -0.172270208230679 113 0 0.123109219284500 -0.123109219284500 114 0 0.135906500173194 -0.135906500173194 115 0 0.00840609014893699 -0.00840609014893699 116 0 0.0889881905643604 -0.0889881905643604 117 0 0.135906500173194 -0.135906500173194 118 0 0.172270208230679 -0.172270208230679 119 0 0.0889881905643604 -0.0889881905643604 120 0 0.123109219284500 -0.123109219284500 121 0 0.251000350398710 -0.251000350398710 122 0 0.0124111744099204 -0.0124111744099204 123 0 0.0134661456330231 -0.0134661456330231 124 0 0.0959201324934114 -0.0959201324934114 125 0 0.0134661456330231 -0.0134661456330231 126 0 0.184376623989256 -0.184376623989256 127 0 0.00586366883261908 -0.00586366883261908 128 0 0.00940783085246568 -0.00940783085246568 129 1 0.0959201324934114 0.904079867506589 130 0 0.00396298517614339 -0.00396298517614339 131 0 0.251000350398710 -0.251000350398710 132 0 0.135906500173194 -0.135906500173194 133 0 0.135906500173194 -0.135906500173194 134 0 0.00840609014893699 -0.00840609014893699 135 0 0.135906500173194 -0.135906500173194 136 0 0.0198338727507165 -0.0198338727507165 137 1 0.135906500173194 0.864093499826806 138 0 0.00636567812954466 -0.00636567812954466 139 0 0.172270208230679 -0.172270208230679 140 0 0.00586366883261908 -0.00586366883261908 141 0 0.251000350398710 -0.251000350398710 142 0 0.251000350398710 -0.251000350398710 143 0 0.172270208230679 -0.172270208230679 144 0 0.0198338727507165 -0.0198338727507165 145 0 0.0959201324934114 -0.0959201324934114 146 0 0.135906500173194 -0.135906500173194 147 0 0.00396298517614339 -0.00396298517614339 148 0 0.0959201324934114 -0.0959201324934114 149 0 0.0618185337110289 -0.0618185337110289 150 0 0.0618185337110289 -0.0618185337110289 151 0 0.0959201324934114 -0.0959201324934114 152 0 0.251000350398710 -0.251000350398710 153 0 0.0959201324934114 -0.0959201324934114 154 0 0.251000350398710 -0.251000350398710 155 0 0.184376623989256 -0.184376623989256 Type I & II errors for various threshold values Threshold Type I Type II 0.01 0 0.79020979020979 0.02 0 0.643356643356643 0.03 0 0.643356643356643 0.04 0 0.643356643356643 0.05 0 0.643356643356643 0.06 0 0.643356643356643 0.07 0 0.538461538461538 0.08 0 0.538461538461538 0.09 0.0833333333333333 0.503496503496504 0.1 0.25 0.307692307692308 0.11 0.25 0.307692307692308 0.12 0.25 0.307692307692308 0.13 0.416666666666667 0.27972027972028 0.14 0.666666666666667 0.174825174825175 0.15 0.666666666666667 0.174825174825175 0.16 0.666666666666667 0.174825174825175 0.17 0.666666666666667 0.174825174825175 0.18 0.666666666666667 0.118881118881119 0.19 0.833333333333333 0.048951048951049 0.2 0.833333333333333 0.048951048951049 0.21 0.833333333333333 0.048951048951049 0.22 0.833333333333333 0.048951048951049 0.23 0.833333333333333 0.048951048951049 0.24 0.833333333333333 0.048951048951049 0.25 0.833333333333333 0.048951048951049 0.26 1 0 0.27 1 0 0.28 1 0 0.29 1 0 0.3 1 0 0.31 1 0 0.32 1 0 0.33 1 0 0.34 1 0 0.35 1 0 0.36 1 0 0.37 1 0 0.38 1 0 0.39 1 0 0.4 1 0 0.41 1 0 0.42 1 0 0.43 1 0 0.44 1 0 0.45 1 0 0.46 1 0 0.47 1 0 0.48 1 0 0.49 1 0 0.5 1 0 0.51 1 0 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/Oct/10/t12236315636r81irw44sqtfke/14zul1223631377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/10/t12236315636r81irw44sqtfke/14zul1223631377.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/10/t12236315636r81irw44sqtfke/2ytjf1223631377.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/10/t12236315636r81irw44sqtfke/2ytjf1223631377.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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