Binghnetty Logistic Regression 5 (females)

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 05:03:28 -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/t1201694703zbogz9we59dzn24.htm/, Retrieved Wed, 30 Jan 2008 13:05:03 +0100

User-defined keywords:

Dataseries X:

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1 68.7 1 5.29 1 67.5 1 4.6 1 68.9 1 5.86 1 70.5 1 6.4 1 73.5 1 4.48 1 68.1 1 3.1 1 66.7 1 3.79 1 69.3 1 5.73 1 67.5 1 3.57 1 67.8 1 3.63 1 69.4 1 6.07 1 68.8 1 5.33 1 71.7 1 4.28 1 67 1 6.45 1 70.5 1 6.23 1 76.5 1 6.9 1 73.8 1 7.21 1 71.2 1 6.55 1 82.3 1 5.73 1 72.5 1 6.81 1 67.3 1 2.18 1 72.7 1 2.17 1 69.6 1 4.05 1 74.8 1 5.23 1 71.2 1 5.76 1 72.4 1 5.17 1 83.2 1 5.58 1 65.6 1 5.7 1 79.6 1 4.35 1 66.2 1 5.44 1 68.6 1 6.08 1 65.8 1 6.48 1 82.9 1 4.65 1 88 1 6.75 1 76.6 1 6.28 1 70.7 1 3.76 1 77.3 1 3.06 1 65.5 1 6.49 1 68.5 1 7.1 1 77.1 1 1.01 1 82.3 0 4.92 1 80.7 0 5.75 1 74.4 0 5.55 1 71.2 0 4.86 1 71.1 0 5.24 1 69.5 0 6.99 0 65 1 5 0 65 1 8 0 65 0 6 0 65 1 5 0 65 1 8 0 65 0 10 0 65 1 1 0 65 1 7 0 65 1 6 0 65 1 4 0 65 0 6 0 65 0 6 0 65 1 8 0 65 0 7 0 65 0 6 0 65 1 7 0 65 1 6 0 65 1 6 0 65 0 6 0 65 1 5 0 65 1 6 0 65 1 7 0 65 1 6 0 65 1 3 0 65 1 6 0 65 1 3 0 65 1 7 0 65 1 5 0 65 1 7 0 65 1 5 0 65 1 7 0 65 1 7 0 65 1 6 0 65 1 7 0 65 1 5 0 65 1 6 0 65 1 6 0 65 1 6 0 65 1 5 0 65 1 8 0 65 0 3 0 65 0 5 0 65 0 6 0 65 0 6 0 65 1 6 0 65 0 9 0 65 1 8 0 65 1 8 0 65 0 4 0 65 1 9 0 65 1 5 0 65 0 6 0 65 1 9 0 65 1 6 0 65 1 6 0 65 1 7 0 65 1 5 0 65 0 9 0 65 1 6 0 65 1 6 0 65 0 6 0 65 1 7 0 65 0 8 0 65 0 7 0 65 1 6 0 65 2 6 0 65 1 5 0 65 1 7 0 65 1 6 0 65 0 7 0 65 1 9 0 65 1 6 0 65 1 7 0 65 1 6 0 65 1 7 0 65 1 7 0 65 0 8 0 65 1 4 0 65 0 5 0 65 1 6 0 65 1 6 0 65 1 6 0 65 1 7

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 5 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) -221.286978777820 77.7326521514536 -2.84676995642277 0.00516414207316163 age 3.35632421108479 1.18996786413708 2.82051668136322 0.00557808145767424 snoring 0.48254407892995 1.24732555360282 0.386862978583379 0.699515465804962 sleep_time -0.0426530743771127 0.342438817520885 -0.124556773925057 0.901074534645852 Summary of Bias-Reduced Logistic Regression Deviance 15.8555945340391 Penalized deviance 12.9260558629309 Residual Degrees of Freedom 125 ROC Area 1 Fit of Logistic Regression Index Actual Fitted Error 1 1 0.999928761352181 7.12386478189941e-05 2 1 0.996132397635824 0.00386760236417627 3 1 0.999962695393277 3.73046067229099e-05 4 1 0.999999822348609 1.77651391042311e-07 5 1 0.999999999993064 6.93589630174074e-12 6 1 0.99951409895434 0.000485901045659376 7 1 0.94788276004892 0.05211723995108 8 1 0.999990310238089 9.68976191140225e-06 9 1 0.996298017992705 0.00370198200729477 10 1 0.9986408234679 0.00135917653210027 11 1 0.999992971719082 7.028280917587e-06 12 1 0.99994898450532 5.10154946808949e-05 13 1 0.9999999971084 2.89159929334204e-09 14 1 0.977993714242478 0.0220062857575221 15 1 0.999999823632104 1.76367895954321e-07 16 1 1 3.33066907387547e-16 17 1 0.999999999997153 2.84694490204629e-12 18 1 0.999999982939014 1.70609858463067e-08 19 1 1 0 20 1 0.999999999780266 2.19734008766181e-10 21 1 0.993194537836476 0.00680546216352351 22 1 0.999999999907866 9.2133856099963e-11 23 1 0.9999967046189 3.29538109944405e-06 24 1 0.999999999999909 9.12603326241879e-14 25 1 0.999999983504322 1.64956778236913e-08 26 1 0.999999999713397 2.86603407673169e-10 27 1 1 0 28 1 0.294695090310946 0.705304909689054 29 1 1 0 30 1 0.759911678167803 0.240088321832197 31 1 0.999896937870933 0.000103062129067411 32 1 0.441594457912379 0.558405542087621 33 1 1 0 34 1 1 0 35 1 1 2.22044604925031e-16 36 1 0.999999918877992 8.11220077778785e-08 37 1 1 0 38 1 0.224085036233934 0.775914963766066 39 1 0.999849430759968 0.000150569240031651 40 1 1 0 41 1 1 0 42 1 1 0 43 1 0.999999999999426 5.73652236823818e-13 44 1 0.999999974280365 2.57196348663058e-08 45 1 0.999999963434862 3.65651382505661e-08 46 1 0.999991533703288 8.46629671191756e-06 47 0 0.0543398017565514 -0.0543398017565514 48 0 0.0481271236411846 -0.0481271236411846 49 0 0.0328683797745128 -0.0328683797745128 50 0 0.0543398017565514 -0.0543398017565514 51 0 0.0481271236411846 -0.0481271236411846 52 0 0.0278565350397756 -0.0278565350397756 53 0 0.0638036965089954 -0.0638036965089954 54 0 0.0501191921834295 -0.0501191921834295 55 0 0.0521891951873008 -0.0521891951873008 56 0 0.05657374053984 -0.05657374053984 57 0 0.0328683797745128 -0.0328683797745128 58 0 0.0328683797745128 -0.0328683797745128 59 0 0.0481271236411846 -0.0481271236411846 60 0 0.0315392064913704 -0.0315392064913704 61 0 0.0328683797745128 -0.0328683797745128 62 0 0.0501191921834295 -0.0501191921834295 63 0 0.0521891951873008 -0.0521891951873008 64 0 0.0521891951873008 -0.0521891951873008 65 0 0.0328683797745128 -0.0328683797745128 66 0 0.0543398017565514 -0.0543398017565514 67 0 0.0521891951873008 -0.0521891951873008 68 0 0.0501191921834295 -0.0501191921834295 69 0 0.0521891951873008 -0.0521891951873008 70 0 0.0588937982490979 -0.0588937982490979 71 0 0.0521891951873008 -0.0521891951873008 72 0 0.0588937982490979 -0.0588937982490979 73 0 0.0501191921834295 -0.0501191921834295 74 0 0.0543398017565514 -0.0543398017565514 75 0 0.0501191921834295 -0.0501191921834295 76 0 0.0543398017565514 -0.0543398017565514 77 0 0.0501191921834295 -0.0501191921834295 78 0 0.0501191921834295 -0.0501191921834295 79 0 0.0521891951873008 -0.0521891951873008 80 0 0.0501191921834295 -0.0501191921834295 81 0 0.0543398017565514 -0.0543398017565514 82 0 0.0521891951873008 -0.0521891951873008 83 0 0.0521891951873008 -0.0521891951873008 84 0 0.0521891951873008 -0.0521891951873008 85 0 0.0543398017565514 -0.0543398017565514 86 0 0.0481271236411846 -0.0481271236411846 87 0 0.0371882778641705 -0.0371882778641705 88 0 0.0342515879813616 -0.0342515879813616 89 0 0.0328683797745128 -0.0328683797745128 90 0 0.0328683797745128 -0.0328683797745128 91 0 0.0521891951873008 -0.0521891951873008 92 0 0.0290351606044783 -0.0290351606044783 93 0 0.0481271236411846 -0.0481271236411846 94 0 0.0481271236411846 -0.0481271236411846 95 0 0.0356908579155549 -0.0356908579155549 96 0 0.0462103811931719 -0.0462103811931719 97 0 0.0543398017565514 -0.0543398017565514 98 0 0.0328683797745128 -0.0328683797745128 99 0 0.0462103811931719 -0.0462103811931719 100 0 0.0521891951873008 -0.0521891951873008 101 0 0.0521891951873008 -0.0521891951873008 102 0 0.0501191921834295 -0.0501191921834295 103 0 0.0543398017565514 -0.0543398017565514 104 0 0.0290351606044783 -0.0290351606044783 105 0 0.0521891951873008 -0.0521891951873008 106 0 0.0521891951873008 -0.0521891951873008 107 0 0.0328683797745128 -0.0328683797745128 108 0 0.0501191921834295 -0.0501191921834295 109 0 0.0302621021122409 -0.0302621021122409 110 0 0.0315392064913704 -0.0315392064913704 111 0 0.0521891951873008 -0.0521891951873008 112 0 0.0819054125547117 -0.0819054125547117 113 0 0.0543398017565514 -0.0543398017565514 114 0 0.0501191921834295 -0.0501191921834295 115 0 0.0521891951873008 -0.0521891951873008 116 0 0.0315392064913704 -0.0315392064913704 117 0 0.0462103811931719 -0.0462103811931719 118 0 0.0521891951873008 -0.0521891951873008 119 0 0.0501191921834295 -0.0501191921834295 120 0 0.0521891951873008 -0.0521891951873008 121 0 0.0501191921834295 -0.0501191921834295 122 0 0.0501191921834295 -0.0501191921834295 123 0 0.0302621021122409 -0.0302621021122409 124 0 0.05657374053984 -0.05657374053984 125 0 0.0342515879813616 -0.0342515879813616 126 0 0.0521891951873008 -0.0521891951873008 127 0 0.0521891951873008 -0.0521891951873008 128 0 0.0521891951873008 -0.0521891951873008 129 0 0.0501191921834295 -0.0501191921834295 Type I & II errors for various threshold values Threshold Type I Type II 0.01 0 1 0.02 0 1 0.03 0 0.963855421686747 0.04 0 0.746987951807229 0.05 0 0.63855421686747 0.06 0 0.0240963855421687 0.07 0 0.0120481927710843 0.08 0 0.0120481927710843 0.09 0 0 0.1 0 0 0.11 0 0 0.12 0 0 0.13 0 0 0.14 0 0 0.15 0 0 0.16 0 0 0.17 0 0 0.18 0 0 0.19 0 0 0.2 0 0 0.21 0 0 0.22 0 0 0.23 0.0217391304347826 0 0.24 0.0217391304347826 0 0.25 0.0217391304347826 0 0.26 0.0217391304347826 0 0.27 0.0217391304347826 0 0.28 0.0217391304347826 0 0.29 0.0217391304347826 0 0.3 0.0434782608695652 0 0.31 0.0434782608695652 0 0.32 0.0434782608695652 0 0.33 0.0434782608695652 0 0.34 0.0434782608695652 0 0.35 0.0434782608695652 0 0.36 0.0434782608695652 0 0.37 0.0434782608695652 0 0.38 0.0434782608695652 0 0.39 0.0434782608695652 0 0.4 0.0434782608695652 0 0.41 0.0434782608695652 0 0.42 0.0434782608695652 0 0.43 0.0434782608695652 0 0.44 0.0434782608695652 0 0.45 0.0652173913043478 0 0.46 0.0652173913043478 0 0.47 0.0652173913043478 0 0.48 0.0652173913043478 0 0.49 0.0652173913043478 0 0.5 0.0652173913043478 0 0.51 0.0652173913043478 0 0.52 0.0652173913043478 0 0.53 0.0652173913043478 0 0.54 0.0652173913043478 0 0.55 0.0652173913043478 0 0.56 0.0652173913043478 0 0.57 0.0652173913043478 0 0.58 0.0652173913043478 0 0.59 0.0652173913043478 0 0.6 0.0652173913043478 0 0.61 0.0652173913043478 0 0.62 0.0652173913043478 0 0.63 0.0652173913043478 0 0.64 0.0652173913043478 0 0.65 0.0652173913043478 0 0.66 0.0652173913043478 0 0.67 0.0652173913043478 0 0.68 0.0652173913043478 0 0.69 0.0652173913043478 0 0.7 0.0652173913043478 0 0.71 0.0652173913043478 0 0.72 0.0652173913043478 0 0.73 0.0652173913043478 0 0.74 0.0652173913043478 0 0.75 0.0652173913043478 0 0.76 0.0869565217391304 0 0.77 0.0869565217391304 0 0.78 0.0869565217391304 0 0.79 0.0869565217391304 0 0.8 0.0869565217391304 0 0.81 0.0869565217391304 0 0.82 0.0869565217391304 0 0.83 0.0869565217391304 0 0.84 0.0869565217391304 0 0.85 0.0869565217391304 0 0.86 0.0869565217391304 0 0.87 0.0869565217391304 0 0.88 0.0869565217391304 0 0.89 0.0869565217391304 0 0.9 0.0869565217391304 0 0.91 0.0869565217391304 0 0.92 0.0869565217391304 0 0.93 0.0869565217391304 0 0.94 0.0869565217391304 0 0.95 0.108695652173913 0 0.96 0.108695652173913 0 0.97 0.108695652173913 0 0.98 0.130434782608696 0 0.99 0.130434782608696 0

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201694703zbogz9we59dzn24/1vwlo1201694600.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201694703zbogz9we59dzn24/1vwlo1201694600.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201694703zbogz9we59dzn24/2s4ev1201694600.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/30/t1201694703zbogz9we59dzn24/2s4ev1201694600.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)$coeff bitmap(file='test0.png') ra <- roc.analysis(r) dev.off() te <- array(0,dim=c(2,99)) for (i in 1:99) { threshold <- i / 100 numcorr1 <- 0 numfaul1 <- 0 numcorr0 <- 0 numfaul0 <- 0 for (j in 1:length(r$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$area) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Fit of Logistic Regression',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Index',1,TRUE) a<-table.element(a,'Actual',1,TRUE) a<-table.element(a,'Fitted',1,TRUE) a<-table.element(a,'Error',1,TRUE) a<-table.row.end(a) for (i in 1:length(r$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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