Home » date » 2008 » Feb » 02 » attachments

OOF brlr 1

R Software Module: rwasp_logisticregression.wasp (opens new window with default values)

Title produced by software: Bias-Reduced Logistic Regression

Date of computation: Sat, 02 Feb 2008 04:01:18 -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/Feb/02/t1201950411vwntoxlf914gcb0.htm/, Retrieved Sat, 02 Feb 2008 12:06:51 +0100

User-defined keywords:

schakel, brlr

Dataseries X:

» Textbox « » Textfile « » CSV «

0 780.8 93 1 699.1 193 1 598.5 112 0 735.3 71 0 700.5 105 0 706.9 119 0 656.3 162 1 1025.1 277 0 639.4 96 0 637.2 24 1 1065.6 231 0 576.1 99 0 525.6 27 1 377.5 112 0 627.8 96 0 646 95 1 999.31 143 1 168.3 13 0 219.5 22 0 507.4 27 1 227.1 56 1 821.6 278 0 144.7 10 0 761.6 55 1 817.7 61 0 547.8 44 0 313.4 10 0 291.8 28 0 650.3 53 0 679.4 41 1 736.5 135 0 842.6 85 0 904.9 14 0 263.7 12 1 446.5 93 0 511.8 22 1 645.6 101 1 873.9 201 0 871.6 2 0 287.3 9 0 505.7 49 1 597.7 112 1 791 27 0 725.8 93 0 919.4 49 0 114.7 1 0 866.8 69 0 870.7 108 0 700.2 108 0 636.5 70 1 890.3 165 0 879.1 208 0 100.5 4 0 782.8 153 0 738.1 67 1 762.3 163 1 857 75 1 712.5 238 1 609.9 90 0 940.1 137 0 586.7 133 1 49.3 17 0 9.7 0 0 786.7 33 1 755.7 123 1 749.2 153 1 630.1 126 0 835.6 164 0 1024.3 14 1 896.2 102 1 410.7 16 0 120.2 6 1 700.7 140 0 704.8 120 0 1042.4 124 1 831.8 49 1 854.1 99 1 547 23 0 999.4 80 0 532.6 56 0 826.4 152 0 670.9 78 1 837.1 105 0 1032.8 229 1 639.9 80 1 850.4 144 1 845 54 1 984.4 52 1 993.2 187 1 958.3 117 0 832.5 144 1 880.9 147 1 1020.9 182 1 764.8 117 1 601.6 104 1 686.2 46 1 821.2 138 0 836.9 89 0 985.5 120 1 973.2 314 1 702.9 111 1 929.2 80 0 747.2 187 1 654.3 166 1 628.8 70 0 564.6 91 0 981 202 1 705.3 112 0 397.9 40 0 56.3 2 1 929.7 69 0 559.7 75 1 669.2 78 0 923.5 128 1 539.8 38 1 401.7 19 0 923.5 171 1 688.3 124 0 324.5 4 1 613 27 0 930.5 255 0 348.6 6 1 582.9 143 1 919.7 113 0 786.5 87 1 637 85 1 917.1 110

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	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)	-0.929438286901469	0.566357930375745	-1.64107931937113	0.103315046769471
ws	8.48316892050935e-05	0.000964791483071943	0.0879274855691982	0.930076152681868
pe	0.00796165833057662	0.00368328430376561	2.16156497135912	0.0325729358755396

Summary of Bias-Reduced Logistic Regression
Deviance	166.660374217898
Penalized deviance	137.745270895628
Residual Degrees of Freedom	124
ROC Area	0.657213930348259
Hosmer–Lemeshow test
Chi-square	6.19362066324741
Degrees of Freedom	8
P(>Chi)	0.625553436536364

Fit of Logistic Regression
Index	Actual	Fitted	Error
1	0	0.469346620796885	-0.469346620796885
2	1	0.660711746154738	0.339288253845262
3	1	0.503259756842614	0.496740243157386
4	0	0.425121475400066	-0.425121475400066
5	0	0.491490930624266	-0.491490930624266
6	0	0.519481776086645	-0.519481776086645
7	0	0.602531772965839	-0.602531772965839
8	1	0.796230949675818	0.203769050324182
9	0	0.472308937100362	-0.472308937100362
10	0	0.335301431513776	-0.335301431513776
11	1	0.731078521588136	0.268921478411864
12	0	0.476925757228949	-0.476925757228949
13	0	0.338522373119333	-0.338522373119333
14	1	0.498572856075156	0.501427143924844
15	0	0.472063686467112	-0.472063686467112
16	0	0.470464556894217	-0.470464556894217
17	1	0.572938906060953	0.427061093939047
18	1	0.307536967312889	0.692463032687111
19	0	0.323953637063134	-0.323953637063134
20	0	0.338176733361602	-0.338176733361602
21	1	0.385961467397986	0.614038532602014
22	1	0.794717633537687	0.205282366462313
23	0	0.302051758671776	-0.302051758671776
24	0	0.394857443357395	-0.394857443357395
25	1	0.407475779518553	0.592524220481447
26	0	0.369897976244151	-0.369897976244151
27	0	0.305077295132243	-0.305077295132243
28	0	0.335869055642874	-0.335869055642874
29	0	0.388813026582237	-0.388813026582237
30	0	0.366937958530794	-0.366937958530794
31	1	0.551779726471134	0.448220273528866
32	0	0.454819040797021	-0.454819040797021
33	0	0.322739415570033	-0.322739415570033
34	0	0.307564926169421	-0.307564926169421
35	1	0.462290066783286	0.537709933216714
36	0	0.32940774712041	-0.32940774712041
37	1	0.482371445684229	0.517628554315771
38	1	0.678085946806729	0.321914053193271
39	0	0.30162416034027	-0.30162416034027
40	0	0.302924269646613	-0.302924269646613
41	0	0.378382904462766	-0.378382904462766
42	1	0.503242791222164	0.496757208777836
43	1	0.343582075122205	0.656417924877795
44	0	0.468184737421961	-0.468184737421961
45	0	0.386672072132718	-0.386672072132718
46	0	0.286642595851246	-0.286642595851246
47	0	0.423956638998722	-0.423956638998722
48	0	0.501070939510219	-0.501070939510219
49	0	0.497455012374279	-0.497455012374279
50	0	0.421132320568926	-0.421132320568926
51	1	0.61295747492131	0.38704252507869
52	0	0.690223028616242	-0.690223028616242
53	0	0.291302595638712	-0.291302595638712
54	0	0.58785417486599	-0.58785417486599
55	0	0.417415305881618	-0.417415305881618
56	1	0.606584853252275	0.393415146747725
57	1	0.435458805776039	0.56454119422396
58	1	0.736116169380234	0.263883830619766
59	1	0.459799413596834	0.540200586403166
60	0	0.559974649864694	-0.559974649864694
61	0	0.544688686395893	-0.544688686395893
62	1	0.31218844691745	0.68781155308255
63	0	0.283205700277772	-0.283205700277772
64	0	0.354351364467991	-0.354351364467991
65	1	0.528457461464415	0.471542538535585
66	1	0.587163416143886	0.412836583856114
67	1	0.531752987245562	0.468247012754438
68	0	0.60996355804703	-0.60996355804703
69	0	0.324957341245778	-0.324957341245778
70	1	0.489670725474735	0.510329274525265
71	1	0.317082649501417	0.682917350498583
72	0	0.294948191622305	-0.294948191622305
73	1	0.560855663419938	0.439144336580062
74	0	0.521424395501767	-0.521424395501767
75	0	0.536493962802357	-0.536493962802357
76	1	0.384911190451985	0.615088809548015
77	1	0.482811933683747	0.517188066316253
78	1	0.331830583407291	0.668169416592709
79	0	0.44825472444424	-0.44825472444424
80	0	0.39212131479393	-0.39212131479393
81	0	0.586820943618734	-0.586820943618734
82	0	0.437450553361287	-0.437450553361287
83	1	0.494387346973941	0.505612653026059
84	0	0.727385053914676	-0.727385053914676
85	1	0.440724601035345	0.559275398964655
86	1	0.571795709694692	0.428204290305308
87	1	0.394645591639646	0.605354408360354
88	1	0.393667054176293	0.606332945823707
89	1	0.655577326022475	0.344422673977525
90	1	0.520830422545411	0.479169577454589
91	0	0.571423874649817	-0.571423874649817
92	1	0.578264667428593	0.421735332571407
93	1	0.647070789580369	0.352929210419631
94	1	0.516732502939241	0.483267497060759
95	1	0.487404896000865	0.512595103999135
96	1	0.376368601831714	0.623631398168286
97	1	0.559451018877196	0.440548981122804
98	0	0.462606188088298	-0.462606188088298
99	0	0.527363218966757	-0.527363218966757
100	1	0.839306971658747	0.160693028341253
101	1	0.503483439173038	0.496516560826962
102	1	0.446782331816519	0.553217668183481
103	0	0.650850110774755	-0.650850110774755
104	1	0.610092813218604	0.389907186781396
105	1	0.420973090777195	0.579026909222806
106	0	0.460822620960866	-0.460822620960866
107	0	0.681795734595339	-0.681795734595339
108	1	0.505524584292048	0.494475415707952
109	0	0.359573115252250	-0.359573115252250
110	0	0.287257957171120	-0.287257957171120
111	1	0.425260287774601	0.574739712225399
112	0	0.429269151314273	-0.429269151314273
113	1	0.437415064440714	0.562584935559286
114	0	0.541900512057102	-0.541900512057102
115	1	0.358678804249841	0.641321195750159
116	1	0.322110445817804	0.677889554182196
117	0	0.624887898497627	-0.624887898497627
118	1	0.529016608888891	0.470983391111109
119	0	0.295241032874722	-0.295241032874722
120	1	0.340184600221689	0.659815399778311
121	0	0.764897540559039	-0.764897540559039
122	0	0.298993356504975	-0.298993356504975
123	1	0.564274221849562	0.435725778150438
124	1	0.512059862783981	0.487940137216019
125	0	0.457588683980164	-0.457588683980164
126	1	0.450497810179948	0.549502189820052
127	1	0.506035524736446	0.493964475263554

Type I & II errors for various threshold values
Threshold	Type I	Type II
0.01	0	1
0.02	0	1
0.03	0	1
0.04	0	1
0.05	0	1
0.06	0	1
0.07	0	1
0.08	0	1
0.09	0	1
0.1	0	1
0.11	0	1
0.12	0	1
0.13	0	1
0.14	0	1
0.15	0	1
0.16	0	1
0.17	0	1
0.18	0	1
0.19	0	1
0.2	0	1
0.21	0	1
0.22	0	1
0.23	0	1
0.24	0	1
0.25	0	1
0.26	0	1
0.27	0	1
0.28	0	1
0.29	0	0.955223880597015
0.3	0	0.895522388059702
0.31	0.0166666666666667	0.82089552238806
0.32	0.05	0.82089552238806
0.33	0.0666666666666667	0.761194029850746
0.34	0.0833333333333333	0.701492537313433
0.35	0.116666666666667	0.701492537313433
0.36	0.133333333333333	0.671641791044776
0.37	0.133333333333333	0.64179104477612
0.38	0.15	0.626865671641791
0.39	0.183333333333333	0.597014925373134
0.4	0.216666666666667	0.567164179104478
0.41	0.233333333333333	0.567164179104478
0.42	0.233333333333333	0.552238805970149
0.43	0.266666666666667	0.492537313432836
0.44	0.3	0.477611940298507
0.45	0.333333333333333	0.462686567164179
0.46	0.366666666666667	0.432835820895522
0.47	0.383333333333333	0.373134328358209
0.48	0.383333333333333	0.313432835820896
0.49	0.45	0.313432835820896
0.5	0.483333333333333	0.283582089552239
0.51	0.566666666666667	0.268656716417910
0.52	0.6	0.253731343283582
0.53	0.65	0.223880597014925
0.54	0.666666666666667	0.208955223880597
0.55	0.666666666666667	0.179104477611940
0.56	0.7	0.164179104477612
0.57	0.733333333333333	0.164179104477612
0.58	0.783333333333333	0.149253731343284
0.59	0.8	0.119402985074627
0.6	0.8	0.119402985074627
0.61	0.816666666666667	0.0895522388059701
0.62	0.85	0.0895522388059701
0.63	0.85	0.0746268656716418
0.64	0.85	0.0746268656716418
0.65	0.866666666666667	0.0746268656716418
0.66	0.883333333333333	0.0597014925373134
0.67	0.9	0.0597014925373134
0.68	0.916666666666667	0.0597014925373134
0.69	0.916666666666667	0.0447761194029851
0.7	0.916666666666667	0.0298507462686567
0.71	0.916666666666667	0.0298507462686567
0.72	0.916666666666667	0.0298507462686567
0.73	0.916666666666667	0.0149253731343284
0.74	0.95	0.0149253731343284
0.75	0.95	0.0149253731343284
0.76	0.95	0.0149253731343284
0.77	0.95	0
0.78	0.95	0
0.79	0.95	0
0.8	0.983333333333333	0
0.81	0.983333333333333	0
0.82	0.983333333333333	0
0.83	0.983333333333333	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/Feb/02/t1201950411vwntoxlf914gcb0/1y4kt1201950070.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Feb/02/t1201950411vwntoxlf914gcb0/1y4kt1201950070.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Feb/02/t1201950411vwntoxlf914gcb0/21vjy1201950070.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Feb/02/t1201950411vwntoxlf914gcb0/21vjy1201950070.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

hm <- hosmerlem(y[1,],r$fitted.values)

hm

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)

a<-table.element(a,hm[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Degrees of Freedom',1,TRUE)

a<-table.element(a,hm[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'P(>Chi)',1,TRUE)

a<-table.element(a,hm[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')

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.

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