R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- array(list(1,99.2,96.7,101,1,99,98.1,100.1,1,100,100,100,1,111.6,104.9,90.6,1,122.2,104.9,86.5,1,117.6,109.5,89.7,1,121.1,110.8,90.6,1,136,112.3,82.8,1,154.2,109.3,70.1,1,153.6,105.3,65.4,1,158.5,101.7,61.3,0,140.6,95.4,62.5,0,136.2,96.4,63.6,0,168,97.6,52.6,0,154.3,102.4,59.7,0,149,101.6,59.5,0,165.5,103.8,61.3),dim=c(4,17),dimnames=list(c('Y','X1','X2','X3'),1:17))
>  y <- array(NA,dim=c(4,17),dimnames=list(c('Y','X1','X2','X3'),1:17))
>  for (i in 1:dim(x)[1])
+  {
+  	for (j in 1:dim(x)[2])
+  	{
+  		y[i,j] <- as.numeric(x[i,j])
+  	}
+  }
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: 
> library(brglm)
Loading required package: profileModel
> roc.plot <- function (sd, sdc, newplot = TRUE, ...)
+ {
+ sall <- sort(c(sd, sdc))
+ sens <- 0
+ specc <- 0
+ for (i in length(sall):1) {
+ sens <- c(sens, mean(sd >= sall[i], na.rm = T))
+ specc <- c(specc, mean(sdc >= sall[i], na.rm = T))
+ }
+ if (newplot) {
+ plot(specc, sens, xlim = c(0, 1), ylim = c(0, 1), type = 'l',
+ xlab = '1-specificity', ylab = 'sensitivity', main = 'ROC plot', ...)
+ abline(0, 1)
+ }
+ else lines(specc, sens, ...)
+ npoints <- length(sens)
+ area <- sum(0.5 * (sens[-1] + sens[-npoints]) * (specc[-1] -
+ specc[-npoints]))
+ lift <- (sens - specc)[-1]
+ cutoff <- sall[lift == max(lift)][1]
+ sensopt <- sens[-1][lift == max(lift)][1]
+ specopt <- 1 - specc[-1][lift == max(lift)][1]
+ list(area = area, cutoff = cutoff, sensopt = sensopt, specopt = specopt)
+ }
> roc.analysis <- function (object, newdata = NULL, newplot = TRUE, ...)
+ {
+ if (is.null(newdata)) {
+ sd <- object$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)

Call:
brglm(formula = x)


Coefficients:
             Estimate Std. Error z value Pr(>|z|)
(Intercept) -34.09869   23.66813  -1.441    0.150
X1            0.04522    0.13123   0.345    0.730
X2            0.16801    0.24554   0.684    0.494
X3            0.15228    0.18704   0.814    0.416

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 14.9479  on 16  degrees of freedom
Residual deviance:  7.8685  on 13  degrees of freedom
Penalized deviance: -6.46293 
AIC:  15.869 

> rc <- summary(r)$coeff
> try(hm <- hosmerlem(y[1,],r$fitted.values),silent=T)
> try(hm,silent=T)
      X^2        Df   P(>Chi) 
2.4065271 8.0000000 0.9659472 
> postscript(file="/var/wessaorg/rcomp/tmp/1nufo1321382098.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> ra <- roc.analysis(r)
> dev.off()
null device 
          1 
> 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$fitted.values[j] < threshold) numcorr0 = numcorr0 + 1 else numfaul0 = numfaul0 + 1
+ }
+ }
+ te[1,i] <- numfaul1 / (numfaul1 + numcorr1)
+ te[2,i] <- numfaul0 / (numfaul0 + numcorr0)
+ }
> postscript(file="/var/wessaorg/rcomp/tmp/2b3zg1321382098.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> op <- par(mfrow=c(2,2))
> plot((1:99)/100,te[1,],xlab='Threshold',ylab='Type I error', main='1 - Specificity')
> plot((1:99)/100,te[2,],xlab='Threshold',ylab='Type II error', main='1 - Sensitivity')
> plot(te[1,],te[2,],xlab='Type I error',ylab='Type II error', main='(1-Sens.) vs (1-Spec.)')
> plot((1:99)/100,te[1,]+te[2,],xlab='Threshold',ylab='Sum of Type I & II error', main='(1-Sens.) + (1-Spec.)')
> par(op)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Coefficients of Bias-Reduced Logistic Regression',5,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Variable',header=TRUE)
> a<-table.element(a,'Parameter',header=TRUE)
> a<-table.element(a,'S.E.',header=TRUE)
> a<-table.element(a,'t-stat',header=TRUE)
> a<-table.element(a,'2-sided p-value',header=TRUE)
> a<-table.row.end(a)
> for (i in 1:length(rc[,1])) {
+ a<-table.row.start(a)
+ a<-table.element(a,labels(rc)[[1]][i],header=TRUE)
+ a<-table.element(a,rc[i,1])
+ a<-table.element(a,rc[i,2])
+ a<-table.element(a,rc[i,3])
+ a<-table.element(a,2*(1-pt(abs(rc[i,3]),r$df.residual)))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/3iktz1321382098.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="/var/wessaorg/rcomp/tmp/49df41321382098.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="/var/wessaorg/rcomp/tmp/572kj1321382098.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="/var/wessaorg/rcomp/tmp/6k9581321382098.tab") 
> 
> try(system("convert tmp/1nufo1321382098.ps tmp/1nufo1321382098.png",intern=TRUE))
character(0)
> try(system("convert tmp/2b3zg1321382098.ps tmp/2b3zg1321382098.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.909   0.160   1.184