Home » date » 2010 » Nov » 30 »

*The author of this computation has been verified*
R Software Module: /rwasp_logisticregression.wasp (opens new window with default values)
Title produced by software: Bias-Reduced Logistic Regression
Date of computation: Tue, 30 Nov 2010 14:56:19 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/30/t1291129001epuq2l9or3su95f.htm/, Retrieved Tue, 30 Nov 2010 15:56:43 +0100
 
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/2010/Nov/30/t1291129001epuq2l9or3su95f.htm/},
    year = {2010},
}
@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 = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1 0.841400 1 0.197000 1 0.000000 1 0.254200 1 0.582400 1 0.756600 1 0.660000 1 0.447200 1 0.003000 1 0.944200 0 0.010400 0 0.002000 0 0.015000 0 0.004000 0 0.003200 0 0.002400 0 0.005000 0 0.002200 0 0.003200 0 0.056200
 
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Coefficients of Bias-Reduced Logistic Regression
VariableParameterS.E.t-stat2-sided p-value
(Intercept)-1.329477202244730.699616878327928-1.900293208222980.0735337626023451
P9.02543994238355.074843573992971.778466628732390.0922226035616822


Summary of Bias-Reduced Logistic Regression
Deviance13.1878373939968
Penalized deviance15.4780628985594
Residual Degrees of Freedom18
ROC Area0.83
Hosmer–Lemeshow test
Chi-square4.47748980314667
Degrees of Freedom8
P(>Chi)0.811680935800227


Fit of Logistic Regression
IndexActualFittedError
110.9981010017504170.00189899824958328
210.6102907337605510.389709266239449
310.2092458552405820.790754144759418
410.7240797435156560.275920256484344
510.9806768477760570.0193231522239428
610.995926499104440.00407350089556091
710.9903137375462610.00968626245373894
810.9374208129196730.0625791870803267
910.2137612296735640.786238770326436
1010.9992482413522830.000751758647717038
1100.225200594719172-0.225200594719172
1200.212248266657792-0.212248266657792
1300.232527240787173-0.232527240787173
1400.215282030154283-0.215282030154283
1500.214064762806792-0.214064762806792
1600.21285251130805-0.21285251130805
1700.216810666735283-0.216810666735283
1800.212550232220111-0.212550232220111
1900.214064762806792-0.214064762806792
2000.305286791176809-0.305286791176809


Type I & II errors for various threshold values
ThresholdType IType II
0.0101
0.0201
0.0301
0.0401
0.0501
0.0601
0.0701
0.0801
0.0901
0.101
0.1101
0.1201
0.1301
0.1401
0.1501
0.1601
0.1701
0.1801
0.1901
0.201
0.210.11
0.220.20.3
0.230.20.2
0.240.20.1
0.250.20.1
0.260.20.1
0.270.20.1
0.280.20.1
0.290.20.1
0.30.20.1
0.310.20
0.320.20
0.330.20
0.340.20
0.350.20
0.360.20
0.370.20
0.380.20
0.390.20
0.40.20
0.410.20
0.420.20
0.430.20
0.440.20
0.450.20
0.460.20
0.470.20
0.480.20
0.490.20
0.50.20
0.510.20
0.520.20
0.530.20
0.540.20
0.550.20
0.560.20
0.570.20
0.580.20
0.590.20
0.60.20
0.610.20
0.620.30
0.630.30
0.640.30
0.650.30
0.660.30
0.670.30
0.680.30
0.690.30
0.70.30
0.710.30
0.720.30
0.730.40
0.740.40
0.750.40
0.760.40
0.770.40
0.780.40
0.790.40
0.80.40
0.810.40
0.820.40
0.830.40
0.840.40
0.850.40
0.860.40
0.870.40
0.880.40
0.890.40
0.90.40
0.910.40
0.920.40
0.930.40
0.940.50
0.950.50
0.960.50
0.970.50
0.980.50
0.990.60
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291129001epuq2l9or3su95f/11pzs1291128976.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291129001epuq2l9or3su95f/11pzs1291128976.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291129001epuq2l9or3su95f/2uhhv1291128976.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291129001epuq2l9or3su95f/2uhhv1291128976.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')
 




Copyright

Creative Commons License

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

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

  • personalize online software applications according to your needs
  • enforce strict security rules with respect to the data that you upload (e.g. statistical data)
  • manage user sessions of online applications
  • alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by