Paper - Recursive partitioning

*The author of this computation has been verified*

R Software Module: /rwasp_regression_trees1.wasp (opens new window with default values)

Title produced by software: Recursive Partitioning (Regression Trees)

Date of computation: Wed, 22 Dec 2010 11:34:12 +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/Dec/22/t12930176800pcwxa9dt800i1o.htm/, Retrieved Wed, 22 Dec 2010 12:34:40 +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/Dec/22/t12930176800pcwxa9dt800i1o.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 «

10.81 -0,2643 0 0 24563400 24.45 9.12 -0,2643 0 0 14163200 23.62 11.03 -0,2643 0 0 18184800 21.90 12.74 -0,1918 0 0 20810300 27.12 9.98 -0,1918 0 0 12843000 27.70 11.62 -0,1918 0 0 13866700 29.23 9.40 -0,2246 0 0 15119200 26.50 9.27 -0,2246 0 0 8301600 22.84 7.76 -0,2246 0 0 14039600 20.49 8.78 0,3654 0 0 12139700 23.28 10.65 0,3654 0 0 9649000 25.71 10.95 0,3654 0 0 8513600 26.52 12.36 0,0447 0 0 15278600 25.51 10.85 0,0447 0 0 15590900 23.36 11.84 0,0447 0 0 9691100 24.15 12.14 -0,0312 0 0 10882700 20.92 11.65 -0,0312 0 0 10294800 20.38 8.86 -0,0312 0 0 16031900 21.90 7.63 -0,0048 0 0 13683600 19.21 7.38 -0,0048 0 0 8677200 19.65 7.25 -0,0048 0 0 9874100 17.51 8.03 0,0705 0 0 10725500 21.41 7.75 0,0705 0 0 8348400 23.09 7.16 0,0705 0 0 8046200 20.70 7.18 -0,0134 0 0 10862300 19.00 7.51 -0,0134 0 0 8100300 19.04 7.07 -0,0134 0 0 7287500 19.45 7.11 0,0812 0 0 14002500 20.54 8.98 0,0812 0 0 19037900 19.77 9.53 0,0812 0 0 10774600 20.60 10.54 0,1885 0 0 8960600 21.21 11.31 0,1885 etc...

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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Goodness of Fit Correlation 0.9625 R-squared 0.9264 RMSE 20.5257 Actuals, Predictions, and Residuals # Actuals Forecasts Residuals 1 10.81 49.5305263157895 -38.7205263157895 2 9.12 10.1563157894737 -1.03631578947368 3 11.03 10.1563157894737 0.873684210526315 4 12.74 10.1563157894737 2.58368421052632 5 9.98 10.1563157894737 -0.176315789473684 6 11.62 10.1563157894737 1.46368421052632 7 9.4 10.1563157894737 -0.756315789473684 8 9.27 10.1563157894737 -0.886315789473684 9 7.76 10.1563157894737 -2.39631578947368 10 8.78 23.2811111111111 -14.5011111111111 11 10.65 23.2811111111111 -12.6311111111111 12 10.95 23.2811111111111 -12.3311111111111 13 12.36 10.1563157894737 2.20368421052632 14 10.85 10.1563157894737 0.693684210526316 15 11.84 10.1563157894737 1.68368421052632 16 12.14 10.1563157894737 1.98368421052632 17 11.65 10.1563157894737 1.49368421052632 18 8.86 10.1563157894737 -1.29631578947368 19 7.63 10.1563157894737 -2.52631578947368 20 7.38 10.1563157894737 -2.77631578947368 21 7.25 10.1563157894737 -2.90631578947368 22 8.03 10.1563157894737 -2.12631578947368 23 7.75 10.1563157894737 -2.40631578947368 24 7.16 10.1563157894737 -2.99631578947368 25 7.18 10.1563157894737 -2.97631578947368 26 7.51 10.1563157894737 -2.64631578947368 27 7.07 10.1563157894737 -3.08631578947368 28 7.11 10.1563157894737 -3.04631578947368 29 8.98 10.1563157894737 -1.17631578947368 30 9.53 10.1563157894737 -0.626315789473685 31 10.54 10.1563157894737 0.383684210526315 32 11.31 10.1563157894737 1.15368421052632 33 10.36 10.1563157894737 0.203684210526315 34 11.44 10.1563157894737 1.28368421052632 35 10.45 10.1563157894737 0.293684210526315 36 10.69 10.1563157894737 0.533684210526316 37 11.28 10.1563157894737 1.12368421052632 38 11.96 10.1563157894737 1.80368421052632 39 13.52 10.1563157894737 3.36368421052632 40 12.89 10.1563157894737 2.73368421052632 41 14.03 10.1563157894737 3.87368421052632 42 16.27 10.1563157894737 6.11368421052632 43 16.17 23.2811111111111 -7.11111111111111 44 17.25 23.2811111111111 -6.03111111111111 45 19.38 23.2811111111111 -3.90111111111111 46 26.2 49.5305263157895 -23.3305263157895 47 33.53 49.5305263157895 -16.0005263157895 48 32.2 49.5305263157895 -17.3305263157895 49 38.45 49.5305263157895 -11.0805263157895 50 44.86 49.5305263157895 -4.67052631578947 51 41.67 49.5305263157895 -7.86052631578947 52 36.06 49.5305263157895 -13.4705263157895 53 39.76 49.5305263157895 -9.77052631578947 54 36.81 23.2811111111111 13.5288888888889 55 42.65 23.2811111111111 19.3688888888889 56 46.89 23.2811111111111 23.6088888888889 57 53.61 49.5305263157895 4.07947368421053 58 57.59 49.5305263157895 8.05947368421053 59 67.82 87.4663636363636 -19.6463636363636 60 71.89 49.5305263157895 22.3594736842105 61 75.51 87.4663636363636 -11.9563636363636 62 68.49 49.5305263157895 18.9594736842105 63 62.72 49.5305263157895 13.1894736842105 64 70.39 49.5305263157895 20.8594736842105 65 59.77 49.5305263157895 10.2394736842105 66 57.27 49.5305263157895 7.73947368421053 67 67.96 49.5305263157895 18.4294736842105 68 67.85 49.5305263157895 18.3194736842105 69 76.98 87.4663636363636 -10.4863636363636 70 81.08 87.4663636363636 -6.38636363636364 71 91.66 87.4663636363636 4.19363636363636 72 84.84 87.4663636363636 -2.62636363636364 73 85.73 87.4663636363636 -1.73636363636363 74 84.61 87.4663636363636 -2.85636363636364 75 92.91 87.4663636363636 5.44363636363636 76 99.8 87.4663636363636 12.3336363636364 77 121.19 87.4663636363636 33.7236363636364 78 122.04 124.094615384615 -2.05461538461537 79 131.76 150.437272727273 -18.6772727272727 80 138.48 150.437272727273 -11.9572727272727 81 153.47 150.437272727273 3.03272727272727 82 189.95 150.437272727273 39.5127272727273 83 182.22 150.437272727273 31.7827272727273 84 198.08 218.733125 -20.653125 85 135.36 150.437272727273 -15.0772727272727 86 125.02 150.437272727273 -25.4172727272727 87 143.5 150.437272727273 -6.93727272727273 88 173.95 150.437272727273 23.5127272727273 89 188.75 218.733125 -29.983125 90 167.44 150.437272727273 17.0027272727273 91 158.95 218.733125 -59.783125 92 169.53 218.733125 -49.203125 93 113.66 150.437272727273 -36.7772727272727 94 107.59 124.094615384615 -16.5046153846154 95 92.67 124.094615384615 -31.4246153846154 96 85.35 124.094615384615 -38.7446153846154 97 90.13 124.094615384615 -33.9646153846154 98 89.31 124.094615384615 -34.7846153846154 99 105.12 124.094615384615 -18.9746153846154 100 125.83 124.094615384615 1.73538461538462 101 135.81 124.094615384615 11.7153846153846 102 142.43 124.094615384615 18.3353846153846 103 163.39 124.094615384615 39.2953846153846 104 168.21 124.094615384615 44.1153846153846 105 185.35 124.094615384615 61.2553846153846 106 188.5 218.733125 -30.233125 107 199.91 218.733125 -18.823125 108 210.73 218.733125 -8.00312500000001 109 192.06 218.733125 -26.673125 110 204.62 218.733125 -14.113125 111 235 218.733125 16.266875 112 261.09 218.733125 42.356875 113 256.88 218.733125 38.146875 114 251.53 218.733125 32.796875 115 257.25 218.733125 38.516875 116 243.1 218.733125 24.366875 117 283.75 218.733125 65.016875

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/22/t12930176800pcwxa9dt800i1o/2anzo1293017642.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930176800pcwxa9dt800i1o/2anzo1293017642.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930176800pcwxa9dt800i1o/3anzo1293017642.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930176800pcwxa9dt800i1o/3anzo1293017642.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930176800pcwxa9dt800i1o/4lwhr1293017642.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/22/t12930176800pcwxa9dt800i1o/4lwhr1293017642.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = none ; par3 = 3 ; par4 = no ;

Parameters (R input):

par1 = 1 ; par2 = none ; par3 = 3 ; par4 = no ;

R code (references can be found in the software module):

library(party) library(Hmisc) par1 <- as.numeric(par1) par3 <- as.numeric(par3) x <- data.frame(t(y)) is.data.frame(x) x <- x[!is.na(x[,par1]),] k <- length(x[1,]) n <- length(x[,1]) colnames(x)[par1] x[,par1] if (par2 == 'kmeans') { cl <- kmeans(x[,par1], par3) print(cl) clm <- matrix(cbind(cl$centers,1:par3),ncol=2) clm <- clm[sort.list(clm[,1]),] for (i in 1:par3) { cl$cluster[cl$cluster==clm[i,2]] <- paste('C',i,sep='') } cl$cluster <- as.factor(cl$cluster) print(cl$cluster) x[,par1] <- cl$cluster } if (par2 == 'quantiles') { x[,par1] <- cut2(x[,par1],g=par3) } if (par2 == 'hclust') { hc <- hclust(dist(x[,par1])^2, 'cen') print(hc) memb <- cutree(hc, k = par3) dum <- c(mean(x[memb==1,par1])) for (i in 2:par3) { dum <- c(dum, mean(x[memb==i,par1])) } hcm <- matrix(cbind(dum,1:par3),ncol=2) hcm <- hcm[sort.list(hcm[,1]),] for (i in 1:par3) { memb[memb==hcm[i,2]] <- paste('C',i,sep='') } memb <- as.factor(memb) print(memb) x[,par1] <- memb } if (par2=='equal') { ed <- cut(as.numeric(x[,par1]),par3,labels=paste('C',1:par3,sep='')) x[,par1] <- as.factor(ed) } table(x[,par1]) colnames(x) colnames(x)[par1] x[,par1] if (par2 == 'none') { m <- ctree(as.formula(paste(colnames(x)[par1],' ~ .',sep='')),data = x) } load(file='createtable') if (par2 != 'none') { m <- ctree(as.formula(paste('as.factor(',colnames(x)[par1],') ~ .',sep='')),data = x) if (par4=='yes') { a<-table.start() a<-table.row.start(a) a<-table.element(a,'10-Fold Cross Validation',3+2*par3,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'',1,TRUE) a<-table.element(a,'Prediction (training)',par3+1,TRUE) a<-table.element(a,'Prediction (testing)',par3+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Actual',1,TRUE) for (jjj in 1:par3) a<-table.element(a,paste('C',jjj,sep=''),1,TRUE) a<-table.element(a,'CV',1,TRUE) for (jjj in 1:par3) a<-table.element(a,paste('C',jjj,sep=''),1,TRUE) a<-table.element(a,'CV',1,TRUE) a<-table.row.end(a) for (i in 1:10) { ind <- sample(2, nrow(x), replace=T, prob=c(0.9,0.1)) m.ct <- ctree(as.formula(paste('as.factor(',colnames(x)[par1],') ~ .',sep='')),data =x[ind==1,]) if (i==1) { m.ct.i.pred <- predict(m.ct, newdata=x[ind==1,]) m.ct.i.actu <- x[ind==1,par1] m.ct.x.pred <- predict(m.ct, newdata=x[ind==2,]) m.ct.x.actu <- x[ind==2,par1] } else { m.ct.i.pred <- c(m.ct.i.pred,predict(m.ct, newdata=x[ind==1,])) m.ct.i.actu <- c(m.ct.i.actu,x[ind==1,par1]) m.ct.x.pred <- c(m.ct.x.pred,predict(m.ct, newdata=x[ind==2,])) m.ct.x.actu <- c(m.ct.x.actu,x[ind==2,par1]) } } print(m.ct.i.tab <- table(m.ct.i.actu,m.ct.i.pred)) numer <- 0 for (i in 1:par3) { print(m.ct.i.tab[i,i] / sum(m.ct.i.tab[i,])) numer <- numer + m.ct.i.tab[i,i] } print(m.ct.i.cp <- numer / sum(m.ct.i.tab)) print(m.ct.x.tab <- table(m.ct.x.actu,m.ct.x.pred)) numer <- 0 for (i in 1:par3) { print(m.ct.x.tab[i,i] / sum(m.ct.x.tab[i,])) numer <- numer + m.ct.x.tab[i,i] } print(m.ct.x.cp <- numer / sum(m.ct.x.tab)) for (i in 1:par3) { a<-table.row.start(a) a<-table.element(a,paste('C',i,sep=''),1,TRUE) for (jjj in 1:par3) a<-table.element(a,m.ct.i.tab[i,jjj]) a<-table.element(a,round(m.ct.i.tab[i,i]/sum(m.ct.i.tab[i,]),4)) for (jjj in 1:par3) a<-table.element(a,m.ct.x.tab[i,jjj]) a<-table.element(a,round(m.ct.x.tab[i,i]/sum(m.ct.x.tab[i,]),4)) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,'Overall',1,TRUE) for (jjj in 1:par3) a<-table.element(a,'-') a<-table.element(a,round(m.ct.i.cp,4)) for (jjj in 1:par3) a<-table.element(a,'-') a<-table.element(a,round(m.ct.x.cp,4)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') } } m bitmap(file='test1.png') plot(m) dev.off() bitmap(file='test1a.png') plot(x[,par1] ~ as.factor(where(m)),main='Response by Terminal Node',xlab='Terminal Node',ylab='Response') dev.off() if (par2 == 'none') { forec <- predict(m) result <- as.data.frame(cbind(x[,par1],forec,x[,par1]-forec)) colnames(result) <- c('Actuals','Forecasts','Residuals') print(result) } if (par2 != 'none') { print(cbind(as.factor(x[,par1]),predict(m))) myt <- table(as.factor(x[,par1]),predict(m)) print(myt) } bitmap(file='test2.png') if(par2=='none') { op <- par(mfrow=c(2,2)) plot(density(result$Actuals),main='Kernel Density Plot of Actuals') plot(density(result$Residuals),main='Kernel Density Plot of Residuals') plot(result$Forecasts,result$Actuals,main='Actuals versus Predictions',xlab='Predictions',ylab='Actuals') plot(density(result$Forecasts),main='Kernel Density Plot of Predictions') par(op) } if(par2!='none') { plot(myt,main='Confusion Matrix',xlab='Actual',ylab='Predicted') } dev.off() if (par2 == 'none') { detcoef <- cor(result$Forecasts,result$Actuals) a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goodness of Fit',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Correlation',1,TRUE) a<-table.element(a,round(detcoef,4)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'R-squared',1,TRUE) a<-table.element(a,round(detcoef*detcoef,4)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'RMSE',1,TRUE) a<-table.element(a,round(sqrt(mean((result$Residuals)^2)),4)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Actuals, Predictions, and Residuals',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'#',header=TRUE) a<-table.element(a,'Actuals',header=TRUE) a<-table.element(a,'Forecasts',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:length(result$Actuals)) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,result$Actuals[i]) a<-table.element(a,result$Forecasts[i]) a<-table.element(a,result$Residuals[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') } if (par2 != 'none') { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Confusion Matrix (predicted in columns / actuals in rows)',par3+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'',1,TRUE) for (i in 1:par3) { a<-table.element(a,paste('C',i,sep=''),1,TRUE) } a<-table.row.end(a) for (i in 1:par3) { a<-table.row.start(a) a<-table.element(a,paste('C',i,sep=''),1,TRUE) for (j in 1:par3) { a<-table.element(a,myt[i,j]) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.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

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