Binghnetty Logistic Regression 4 (males)

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 04:57:29 -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/t1201694416qocyfa271e5fls3.htm/, Retrieved Wed, 30 Jan 2008 13:00:19 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1 70.6 1 7.8 1 71.3 1 6.0 1 67.5 1 6.0 1 73.2 1 7.1 1 81.2 1 5.9 1 75.5 1 3.6 1 66.7 1 6.9 1 68.7 1 8.0 1 73.0 1 5.6 1 78.4 1 6.1 1 76.1 1 5.1 1 65.7 1 5.0 1 66.7 1 5.2 1 72.3 1 2.9 1 66.2 1 4.9 1 67.7 1 4.7 1 64.9 1 6.5 1 72.2 1 7.5 1 69.4 1 3.9 1 72.8 1 3.2 1 75.4 1 4.5 1 74.7 1 6.5 1 77.4 1 7.4 1 68.8 1 3.3 1 75.3 1 5.9 1 72.4 1 4.8 1 72.7 1 4.4 1 65.3 1 5.4 1 67.0 1 5.9 1 66.7 1 6.1 1 67.0 1 5.4 1 67.5 1 6.0 1 69.9 1 4.9 1 72.5 1 5.3 1 73.8 1 6.0 1 71.9 1 3.2 1 69.9 1 6.5 1 71.4 1 3.6 1 64.9 1 5.9 1 70.2 1 5.2 1 65.3 1 7.3 1 67.5 1 8.9 1 68.1 1 1.8 1 82.9 1 6.5 1 66.2 1 3.0 1 74.0 1 7.0 1 69.8 1 7.0 1 81.3 1 5.9 1 76.9 1 6.3 1 76.6 1 3.8 1 72.7 1 7.6 1 78.6 1 6.3 1 70.2 1 5.6 1 69.5 1 6.4 1 73.8 1 7.5 1 66.1 1 7.0 1 77.8 1 1.1 1 73.2 1 6.0 1 72.8 1 6.5 1 74.8 1 5.7 1 67.2 1 5.5 1 80.7 1 6.4 1 67.2 1 6.5 1 75.4 1 1.9 1 75.3 1 3.4 1 73.2 1 6.4 1 65.3 1 1.6 1 71.8 1 6.8 1 67.3 1 6.1 1 73.7 1 6.3 1 80.6 0 5.1 1 75.7 0 4.7 1 73.0 0 4.1 1 71.3 0 3.0 1 70.8 0 6.5 1 69.6 0 5.3 1 66.1 0 6.4 1 65.6 0 6.8 0 65.0 1 12.0 0 65.0 1 7.0 0 65.0 0 6.0 0 65.0 1 5.0 0 65.0 1 7.0 0 65.0 1 8.0 0 65.0 0 5.0 0 65.0 1 8.0 0 65.0 1 5.0 0 65.0 1 6.0 0 65.0 1 9.0 0 65.0 0 7.0 0 65.0 1 6.0 0 65.0 0 6.0 0 65.0 0 7.0 0 65.0 0 6.0 0 65.0 0 6.0 0 65.0 0 8.0 0 65.0 0 7.0 0 65.0 0 5.0 0 65.0 0 7.0 0 65.0 0 7.0 0 65.0 1 6.0 0 65.0 1 5.0 0 65.0 1 7.0 0 65.0 0 8.0 0 65.0 1 8.0 0 65.0 0 9.0 0 65.0 0 99.0 0 65.0 0 8.0 0 65.0 0 6.0 0 65.0 1 5.0 0 65.0 1 9.0 0 65.0 1 7.0 0 65.0 1 6.0 0 65.0 1 7.0 0 65.0 0 6.0 0 65.0 0 6.0 0 65.0 1 7.0 0 65.0 1 7.0 0 65.0 0 6.0 0 65.0 1 6.0 0 65.0 0 6.0 0 65.0 0 8.0 0 65.0 1 6.0 0 65.0 0 7.0 0 65.0 1 7.0 0 65.0 1 5.0 0 65.0 0 8.0 0 65.0 1 4.0 0 65.0 1 7.0 0 65.0 1 8.0 0 65.0 1 10.0 0 65.0 1 6.0 0 65.0 0 7.0 0 65.0 1 5.0 0 65.0 0 6.0 0 65.0 0 6.0 0 65.0 0 10.0 0 65.0 0 7.0 0 65.0 0 6.0

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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Coefficients of Bias-Reduced Logistic Regression Variable Parameter S.E. t-stat 2-sided p-value (Intercept) -254.669757167595 85.1818396820186 -2.98971891330675 0.00331920749560477 age 3.90024229882397 1.30254874216756 2.99431581526356 0.00327270654856004 snoring 1.07161664801122 0.916160978774116 1.16968160927910 0.244190073162315 sleep_time -0.277556136210037 0.273565258291474 -1.01458839453331 0.312116999755588 Summary of Bias-Reduced Logistic Regression Deviance 29.5179828359480 Penalized deviance 25.3731748071590 Residual Degrees of Freedom 135 ROC Area 0.990332072299285 Fit of Logistic Regression Index Actual Fitted Error 1 1 0.999999996906702 3.0932982841847e-09 2 1 0.99999999987761 1.22391208279282e-10 3 1 0.999665613241877 0.000334386758123029 4 1 0.9999999999999 1.00364161426114e-13 5 1 1 0 6 1 1 0 7 1 0.990367024751051 0.00963297524894868 8 1 0.999994594327677 5.40567232254485e-06 9 1 0.999999999999855 1.44551037806195e-13 10 1 1 0 11 1 1 0 12 1 0.77902573458791 0.220974265412090 13 1 0.993968614647771 0.00603138535222902 14 1 0.999999999998952 1.04760644603630e-12 15 1 0.962234950554555 0.0377650494454449 16 1 0.999893125589951 0.000106874410048863 17 1 0.0930854613304026 0.906914538669597 18 1 0.999999999994452 5.54756240944698e-12 19 1 0.999999887037078 1.12962921572368e-07 20 1 0.999999999999838 1.61870516990348e-13 21 1 1 0 22 1 1 2.22044604925031e-16 23 1 1 0 24 1 0.999999007059787 9.92940213162541e-07 25 1 1 0 26 1 0.999999999998798 1.20192744645919e-12 27 1 0.999999999999666 3.33733041202322e-13 28 1 0.398643226954229 0.601356773045771 29 1 0.997718213731127 0.00228178626887288 30 1 0.992270322113214 0.00772967788678602 31 1 0.998013297489842 0.00198670251015809 32 1 0.999665613241877 0.000334386758123029 33 1 0.999999978789535 2.12104653840584e-08 34 1 0.999999999999065 9.34807786734382e-13 35 1 0.999999999999993 7.105427357601e-15 36 1 0.999999999994581 5.41899858319539e-12 37 1 0.99999996693139 3.30686109606404e-08 38 1 0.999999999957434 4.25663948533384e-11 39 1 0.108129001442059 0.89187099855794 40 1 0.999999992845877 7.1541232937733e-09 41 1 0.281207841417195 0.718792158582805 42 1 0.999252452616717 0.000747547383282643 43 1 0.99998995834912 1.00416508808099e-05 44 1 1 0 45 1 0.977362089801144 0.0226379101988561 46 1 0.999999999999996 4.21884749357559e-15 47 1 0.999999943885918 5.61140820476425e-08 48 1 1 0 49 1 1 0 50 1 1 0 51 1 0.999999999999189 8.11350986396064e-13 52 1 1 0 53 1 0.99999999200584 7.99416033370193e-09 54 1 0.99999984692535 1.53074649289486e-07 55 1 0.99999999999999 1.08801856413265e-14 56 1 0.905935081154805 0.0940649188451953 57 1 1 0 58 1 0.999999999999926 7.39408534400354e-14 59 1 0.999999999999595 4.04787314778332e-13 60 1 1 2.22044604925031e-16 61 1 0.99906271291837 0.000937287081629656 62 1 1 0 63 1 0.998763245409384 0.00123675459061612 64 1 1 0 65 1 1 0 66 1 0.999999999999917 8.28226376370367e-14 67 1 0.655564934486218 0.344435065513782 68 1 0.99999999997826 2.17399431790000e-11 69 1 0.999250289744306 0.00074971025569448 70 1 0.999999999999988 1.15463194561016e-14 71 1 1 0 72 1 1 0 73 1 0.999999999999722 2.78443934575989e-13 74 1 0.999999999844574 1.55426116421609e-10 75 1 0.999999997113678 2.88632229228369e-09 76 1 0.999999776992299 2.23007701194433e-07 77 1 0.795743365448061 0.204256634551939 78 1 0.331536454586766 0.668463545413233 79 0 0.0318896451354848 -0.0318896451354848 80 0 0.116573713341479 -0.116573713341479 81 0 0.0562877399798279 -0.0562877399798279 82 0 0.186916506102960 -0.186916506102960 83 0 0.116573713341479 -0.116573713341479 84 0 0.0908880110667426 -0.0908880110667426 85 0 0.0729800868819681 -0.0729800868819681 86 0 0.0908880110667426 -0.0908880110667426 87 0 0.186916506102960 -0.186916506102960 88 0 0.148334003794352 -0.148334003794352 89 0 0.0704107859750647 -0.0704107859750647 90 0 0.0432352793163922 -0.0432352793163922 91 0 0.148334003794352 -0.148334003794352 92 0 0.0562877399798279 -0.0562877399798279 93 0 0.0432352793163922 -0.0432352793163922 94 0 0.0562877399798279 -0.0562877399798279 95 0 0.0562877399798279 -0.0562877399798279 96 0 0.0331033593898801 -0.0331033593898801 97 0 0.0432352793163922 -0.0432352793163922 98 0 0.0729800868819681 -0.0729800868819681 99 0 0.0432352793163922 -0.0432352793163922 100 0 0.0432352793163922 -0.0432352793163922 101 0 0.148334003794352 -0.148334003794352 102 0 0.186916506102960 -0.186916506102960 103 0 0.116573713341479 -0.116573713341479 104 0 0.0331033593898801 -0.0331033593898801 105 0 0.0908880110667426 -0.0908880110667426 106 0 0.0252830485335928 -0.0252830485335928 107 0 3.67495533956679e-13 -3.67495533956679e-13 108 0 0.0331033593898801 -0.0331033593898801 109 0 0.0562877399798279 -0.0562877399798279 110 0 0.186916506102960 -0.186916506102960 111 0 0.0704107859750647 -0.0704107859750647 112 0 0.116573713341479 -0.116573713341479 113 0 0.148334003794352 -0.148334003794352 114 0 0.116573713341479 -0.116573713341479 115 0 0.0562877399798279 -0.0562877399798279 116 0 0.0562877399798279 -0.0562877399798279 117 0 0.116573713341479 -0.116573713341479 118 0 0.116573713341479 -0.116573713341479 119 0 0.0562877399798279 -0.0562877399798279 120 0 0.148334003794352 -0.148334003794352 121 0 0.0562877399798279 -0.0562877399798279 122 0 0.0331033593898801 -0.0331033593898801 123 0 0.148334003794352 -0.148334003794352 124 0 0.0432352793163922 -0.0432352793163922 125 0 0.116573713341479 -0.116573713341479 126 0 0.186916506102960 -0.186916506102960 127 0 0.0331033593898801 -0.0331033593898801 128 0 0.232791456908998 -0.232791456908998 129 0 0.116573713341479 -0.116573713341479 130 0 0.0908880110667426 -0.0908880110667426 131 0 0.0542716973274171 -0.0542716973274171 132 0 0.148334003794352 -0.148334003794352 133 0 0.0432352793163922 -0.0432352793163922 134 0 0.186916506102960 -0.186916506102960 135 0 0.0562877399798279 -0.0562877399798279 136 0 0.0562877399798279 -0.0562877399798279 137 0 0.0192733756628649 -0.0192733756628649 138 0 0.0432352793163922 -0.0432352793163922 139 0 0.0562877399798279 -0.0562877399798279 Type I & II errors for various threshold values Threshold Type I Type II 0.01 0 0.98360655737705 0.02 0 0.967213114754098 0.03 0 0.950819672131147 0.04 0 0.852459016393443 0.05 0 0.721311475409836 0.06 0 0.508196721311475 0.07 0 0.508196721311475 0.08 0 0.442622950819672 0.09 0 0.442622950819672 0.1 0.0128205128205128 0.377049180327869 0.11 0.0256410256410256 0.377049180327869 0.12 0.0256410256410256 0.229508196721311 0.13 0.0256410256410256 0.229508196721311 0.14 0.0256410256410256 0.229508196721311 0.15 0.0256410256410256 0.114754098360656 0.16 0.0256410256410256 0.114754098360656 0.17 0.0256410256410256 0.114754098360656 0.18 0.0256410256410256 0.114754098360656 0.19 0.0256410256410256 0.0163934426229508 0.2 0.0256410256410256 0.0163934426229508 0.21 0.0256410256410256 0.0163934426229508 0.22 0.0256410256410256 0.0163934426229508 0.23 0.0256410256410256 0.0163934426229508 0.24 0.0256410256410256 0 0.25 0.0256410256410256 0 0.26 0.0256410256410256 0 0.27 0.0256410256410256 0 0.28 0.0256410256410256 0 0.29 0.0384615384615385 0 0.3 0.0384615384615385 0 0.31 0.0384615384615385 0 0.32 0.0384615384615385 0 0.33 0.0384615384615385 0 0.34 0.0512820512820513 0 0.35 0.0512820512820513 0 0.36 0.0512820512820513 0 0.37 0.0512820512820513 0 0.38 0.0512820512820513 0 0.39 0.0512820512820513 0 0.4 0.0641025641025641 0 0.41 0.0641025641025641 0 0.42 0.0641025641025641 0 0.43 0.0641025641025641 0 0.44 0.0641025641025641 0 0.45 0.0641025641025641 0 0.46 0.0641025641025641 0 0.47 0.0641025641025641 0 0.48 0.0641025641025641 0 0.49 0.0641025641025641 0 0.5 0.0641025641025641 0 0.51 0.0641025641025641 0 0.52 0.0641025641025641 0 0.53 0.0641025641025641 0 0.54 0.0641025641025641 0 0.55 0.0641025641025641 0 0.56 0.0641025641025641 0 0.57 0.0641025641025641 0 0.58 0.0641025641025641 0 0.59 0.0641025641025641 0 0.6 0.0641025641025641 0 0.61 0.0641025641025641 0 0.62 0.0641025641025641 0 0.63 0.0641025641025641 0 0.64 0.0641025641025641 0 0.65 0.0641025641025641 0 0.66 0.0769230769230769 0 0.67 0.0769230769230769 0 0.68 0.0769230769230769 0 0.69 0.0769230769230769 0 0.7 0.0769230769230769 0 0.71 0.0769230769230769 0 0.72 0.0769230769230769 0 0.73 0.0769230769230769 0 0.74 0.0769230769230769 0 0.75 0.0769230769230769 0 0.76 0.0769230769230769 0 0.77 0.0769230769230769 0 0.78 0.0897435897435897 0 0.79 0.0897435897435897 0 0.8 0.102564102564103 0 0.81 0.102564102564103 0 0.82 0.102564102564103 0 0.83 0.102564102564103 0 0.84 0.102564102564103 0 0.85 0.102564102564103 0 0.86 0.102564102564103 0 0.87 0.102564102564103 0 0.88 0.102564102564103 0 0.89 0.102564102564103 0 0.9 0.102564102564103 0 0.91 0.115384615384615 0 0.92 0.115384615384615 0 0.93 0.115384615384615 0 0.94 0.115384615384615 0 0.95 0.115384615384615 0 0.96 0.115384615384615 0 0.97 0.128205128205128 0 0.98 0.141025641025641 0 0.99 0.141025641025641 0

Charts produced by software:

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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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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.

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