::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes Path Models with Latent Variables by the Partial Least Squares Approach. There is a maximum of 8 latent variables that can be defined. The relationship between the latent variables is defined through a lower triangular matrix (column variables have an impact on row variables). Load the default data set to see a working example of the PLS-PM.

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!

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Source code of R module

library(plspm) library(diagram) y <- as.data.frame(t(y)) is.data.frame(y) head(y) trim <- function(char) { return(sub("s+$", "", sub("^s+", "", char))) } (latnames <- strsplit(par1," ")[[1]]) (n <- length(latnames)) (L1 <- as.numeric(strsplit(par3," ")[[1]])) (L2 <- as.numeric(strsplit(par4," ")[[1]])) (L3 <- as.numeric(strsplit(par5," ")[[1]])) (L4 <- as.numeric(strsplit(par6," ")[[1]])) (L5 <- as.numeric(strsplit(par7," ")[[1]])) (L6 <- as.numeric(strsplit(par8," ")[[1]])) (L7 <- as.numeric(strsplit(par9," ")[[1]])) (L8 <- as.numeric(strsplit(par10," ")[[1]])) (S1 <- as.numeric(strsplit(par11," ")[[1]])) (S2 <- as.numeric(strsplit(par12," ")[[1]])) (S3 <- as.numeric(strsplit(par13," ")[[1]])) (S4 <- as.numeric(strsplit(par14," ")[[1]])) (S5 <- as.numeric(strsplit(par15," ")[[1]])) (S6 <- as.numeric(strsplit(par16," ")[[1]])) (S7 <- as.numeric(strsplit(par17," ")[[1]])) (S8 <- as.numeric(strsplit(par18," ")[[1]])) if (n==1) sat.mat <- rbind(S1) if (n==2) sat.mat <- rbind(S1,S2) if (n==3) sat.mat <- rbind(S1,S2,S3) if (n==4) sat.mat <- rbind(S1,S2,S3,S4) if (n==5) sat.mat <- rbind(S1,S2,S3,S4,S5) if (n==6) sat.mat <- rbind(S1,S2,S3,S4,S5,S6) if (n==7) sat.mat <- rbind(S1,S2,S3,S4,S5,S6,S7) if (n==8) sat.mat <- rbind(S1,S2,S3,S4,S5,S6,S7,S8) sat.mat if (n==1) sat.sets <- list(L1) if (n==2) sat.sets <- list(L1,L2) if (n==3) sat.sets <- list(L1,L2,L3) if (n==4) sat.sets <- list(L1,L2,L3,L4) if (n==5) sat.sets <- list(L1,L2,L3,L4,L5) if (n==6) sat.sets <- list(L1,L2,L3,L4,L5,L6) if (n==7) sat.sets <- list(L1,L2,L3,L4,L5,L6,L7) if (n==8) sat.sets <- list(L1,L2,L3,L4,L5,L6,L7,L8) sat.sets (sat.mod <- strsplit(par2," ")[[1]]) res <- plspm(y, sat.mat, sat.sets, sat.mod, scheme="centroid", scaled=TRUE, boot.val=TRUE) (r <- summary(res)) (myr <- res$path_coefs) myind <- 1 for (j in 1:(length(sat.mat[1,])-1)) { for (i in 1:length(sat.mat[,1])) { if (sat.mat[i,j] == 1) { if ((res$boot$path[myind,"perc.025"] < 0) && (res$boot$path[myind,"perc.975"] > 0)) { myr[i,j] = 0 } myind = myind + 1 } } } bitmap(file="test1.png") plotmat(round(myr,4), pos = NULL, curve = 0, name = latnames, lwd = 1, box.lwd = 1, cex.txt = 1, box.type = "circle", box.prop = 0.5, box.cex = 1, arr.type = "triangle", arr.pos = 0.5, shadow.size = 0.01, prefix = "", arr.lcol = "blue", arr.col = "blue", arr.width = 0.2, main = c("Inner Model", "Path Coefficients")) dev.off() (myr <- res$path_coefs) myind <- 1 myi <- 1 for (j in 1:(length(sat.mat[1,])-1)) { for (i in 1:length(sat.mat[,1])) { if (i > j) { myr[i,j] = res$boot$total.efs[myi,"Original"] myi = myi + 1 if ((res$boot$total.efs[myind,"perc.025"] < 0) && (res$boot$total.efs[myind,"perc.975"] > 0)) { myr[i,j] = 0 } myind = myind + 1 } } } bitmap(file="test2.png") plotmat(round(myr,4), pos = NULL, curve = 0, name = latnames, lwd = 1, box.lwd = 1, cex.txt = 1, box.type = "circle", box.prop = 0.5, box.cex = 1, arr.type = "triangle", arr.pos = 0.5, shadow.size = 0.01, prefix = "", arr.lcol = "blue", arr.col = "blue", arr.width = 0.2, main = c("Inner Model", "Total Effects")) dev.off() labels(r) labels(r$model) labels(r$gof) labels(r$inputs) print(r$model) print(r$gof) print(r$inputs) load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"PARTIAL LEAST SQUARES PATH MODELING (PLS-PM)",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"MODEL SPECIFICATION",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Number of Cases",header=TRUE) a<-table.element(a,r$model$gens$obs) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Latent Variables",header=TRUE) a<-table.element(a,n) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Manifest Variables",header=TRUE) a<-table.element(a,length(y[1,])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Scaled?",header=TRUE) a<-table.element(a,as.character(r$model$specs$scaled)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Weighting Scheme",header=TRUE) a<-table.element(a,r$model$specs$scheme) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Bootstrapping?",header=TRUE) a<-table.element(a,as.character(r$model$specs$boot.val)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Bootstrap samples",header=TRUE) a<-table.element(a,r$model$specs$br) 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,"BLOCKS DEFINITION",4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Block",header=TRUE) a<-table.element(a,"Type",header=TRUE) a<-table.element(a,"NMVs",header=TRUE) a<-table.element(a,"Mode",header=TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,latnames[i],header=TRUE) a<-table.element(a,r$inputs$Type[i]) a<-table.element(a,r$inputs$Size[i]) a<-table.element(a,r$inputs$Mode[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,"BLOCKS UNIDIMENSIONALITY",7,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Block",header=TRUE) a<-table.element(a,"Type.measure",header=TRUE) a<-table.element(a,"MVs",header=TRUE) a<-table.element(a,"eig.1st",header=TRUE) a<-table.element(a,"eig.2nd",header=TRUE) a<-table.element(a,"C.alpha",header=TRUE) a<-table.element(a,"DG.rho",header=TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,latnames[i],header=TRUE) a<-table.element(a,r$inputs$Type[i]) a<-table.element(a,r$unidim$MVs[i]) a<-table.element(a,r$unidim$eig.1st[i]) a<-table.element(a,r$unidim$eig.2nd[i]) a<-table.element(a,r$unidim$C.alpha[i]) a<-table.element(a,r$unidim$DG.rho[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable3.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"OUTER MODEL",6,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"MV Number",header=TRUE) a<-table.element(a,"Block",header=TRUE) a<-table.element(a,"weights",header=TRUE) a<-table.element(a,"std.loads",header=TRUE) a<-table.element(a,"communal",header=TRUE) a<-table.element(a,"redundan",header=TRUE) a<-table.row.end(a) for (i in 1:length(r$outer_model[,1])) { a<-table.row.start(a) a<-table.element(a,i,header=T) a<-table.element(a,r$outer_model[i,1]) a<-table.element(a,r$outer_model[i,3]) a<-table.element(a,r$outer_model[i,4]) a<-table.element(a,r$outer_model[i,5]) a<-table.element(a,r$outer_model[i,6]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable4.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"CORRELATIONS BETWEEN MVs AND LVs",n+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Block",header=TRUE) for (iii in 1:n) { a<-table.element(a,latnames[iii],header=TRUE) } a<-table.row.end(a) for (i in 1:length(r$crossloadings[,1])) { a<-table.row.start(a) a<-table.element(a,r$crossloadings[i,1],header=TRUE) for(j in 1:n) { a<-table.element(a,r$crossloadings[i,2+j]) } } a<-table.end(a) table.save(a,file="mytable5.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"INNER MODEL",5,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Block",header=TRUE) a<-table.element(a,"Estimate",header=TRUE) a<-table.element(a,"S.E.",header=TRUE) a<-table.element(a,"t value",header=TRUE) a<-table.element(a,"Pr(>|t|)",header=TRUE) a<-table.row.end(a) for (i in 1:(length(labels(r$inner_model)))) { a<-table.row.start(a) print (paste("i=",i,sep="")) a<-table.element(a,labels(r$inner_model)[i],3,header=TRUE) a<-table.row.end(a) for (j in 1:length(r$inner_model[[i]][,1])) { print (paste("j=",j,sep="")) a<-table.row.start(a) a<-table.element(a,rownames(r$inner_model[[i]])[j],header=T) a<-table.element(a,r$inner_model[[i]][j,1]) a<-table.element(a,r$inner_model[[i]][j,2]) a<-table.element(a,r$inner_model[[i]][j,3]) a<-table.element(a,r$inner_model[[i]][j,4]) a<-table.row.end(a) } } a<-table.end(a) table.save(a,file="mytable6.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"CORRELATIONS BETWEEN LVs",n+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"",header=TRUE) for (iii in 1:n) { a<-table.element(a,latnames[iii],header=TRUE) } a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,latnames[i],header=T) for (j in 1:n) { a<-table.element(a,r$correlations[i,j]) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable7.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"SUMMARY INNER MODEL",6,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"",header=TRUE) a<-table.element(a,"LV.Type",header=TRUE) a<-table.element(a,"R-squared",header=TRUE) a<-table.element(a,"Block Communality",header=TRUE) a<-table.element(a,"Mean Redundancy",header=TRUE) a<-table.element(a,"AVE",header=TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,latnames[i],header=T) a<-table.element(a,r$inner_summary[i,1]) a<-table.element(a,r$inner_summary[i,2]) a<-table.element(a,r$inner_summary[i,3]) a<-table.element(a,r$inner_summary[i,4]) a<-table.element(a,r$inner_summary[i,5]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable8.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"TOTAL EFFECTS",4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"relationships",header=TRUE) a<-table.element(a,"dir.effect",header=TRUE) a<-table.element(a,"ind.effect",header=TRUE) a<-table.element(a,"tot.effect",header=TRUE) a<-table.row.end(a) for (i in 1:length(r$effects[,1])) { a<-table.row.start(a) a<-table.element(a,r$effects[i,1],header=T) a<-table.element(a,r$effects[i,2]) a<-table.element(a,r$effects[i,3]) a<-table.element(a,r$effects[i,4]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable10.tab") dum <- r$boot$weights a<-table.start() a<-table.row.start(a) a<-table.element(a,"BOOTSTRAP VALIDATION - WEIGHTS",length(colnames(dum))+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"",header=TRUE) for (i in 1:length(colnames(dum))) { a<-table.element(a,colnames(dum)[i],header=TRUE) } a<-table.row.end(a) for (i in 1:length(rownames(dum))) { a<-table.row.start(a) a<-table.element(a,rownames(dum)[i],header=T) for (j in 1:length(colnames(dum))) { a<-table.element(a,dum[i,j]) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable11.tab") dum <- r$boot$loadings a<-table.start() a<-table.row.start(a) a<-table.element(a,"BOOTSTRAP VALIDATION - LOADINGS",length(colnames(dum))+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"",header=TRUE) for (i in 1:length(colnames(dum))) { a<-table.element(a,colnames(dum)[i],header=TRUE) } a<-table.row.end(a) for (i in 1:length(rownames(dum))) { a<-table.row.start(a) a<-table.element(a,rownames(dum)[i],header=T) for (j in 1:length(colnames(dum))) { a<-table.element(a,dum[i,j]) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable12.tab") dum <- r$boot$paths a<-table.start() a<-table.row.start(a) a<-table.element(a,"BOOTSTRAP VALIDATION - PATHS",length(colnames(dum))+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"",header=TRUE) for (i in 1:length(colnames(dum))) { a<-table.element(a,colnames(dum)[i],header=TRUE) } a<-table.row.end(a) for (i in 1:length(rownames(dum))) { a<-table.row.start(a) a<-table.element(a,rownames(dum)[i],header=T) for (j in 1:length(colnames(dum))) { a<-table.element(a,dum[i,j]) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable13.tab") dum <- r$boot$rsq a<-table.start() a<-table.row.start(a) a<-table.element(a,"BOOTSTRAP VALIDATION - RSQ",length(colnames(dum))+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"",header=TRUE) for (i in 1:length(colnames(dum))) { a<-table.element(a,colnames(dum)[i],header=TRUE) } a<-table.row.end(a) for (i in 1:length(rownames(dum))) { a<-table.row.start(a) a<-table.element(a,rownames(dum)[i],header=T) for (j in 1:length(colnames(dum))) { a<-table.element(a,dum[i,j]) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable14.tab") dum <- r$boot$total.efs a<-table.start() a<-table.row.start(a) a<-table.element(a,"BOOTSTRAP VALIDATION - TOTAL EFFECTS",length(colnames(dum))+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"",header=TRUE) for (i in 1:length(colnames(dum))) { a<-table.element(a,colnames(dum)[i],header=TRUE) } a<-table.row.end(a) for (i in 1:length(rownames(dum))) { a<-table.row.start(a) a<-table.element(a,rownames(dum)[i],header=T) for (j in 1:length(colnames(dum))) { a<-table.element(a,dum[i,j]) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file="mytable15.tab")

Cite this software as:

Wessa P. (2016), Partial Least Squares - Path Modeling (v1.0.10) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_partial_least_squares.wasp/

The R code is based on :

Tenenhaus, M., Esposito Vinzi, V., Chatelin Y.M., and Lauro, C. (2005) PLS path modeling. Computational Statistics & Data Analysis, 48, pp. 159-205.

Tenenhaus, M., and Pages, J. (2001) Multiple factor analysis combined with PLS path modelling. Application to the analysis of relationships between physicochemical variables, sensory profiles and hedonic judgements. Chemometrics and Intelligent Laboratory Systems, 58, pp. 261-273.

Tenenhaus, M., and Hanafi, M. A bridge between PLS path modeling and multi-block data analysis. Handbook on Partial Least Squares (PLS): Concepts, methods, and applications. Springer: In press.

Lohmoller, J.-B. (1989) Latent variables path modelin with partial least squares. Heidelberg: Physica-Verlag.

Wold, H. (1985) Partial Least Squares. In: Kotz, S., Johnson, N.L. (Eds.), Encyclopedia of Statistical Sciences, Vol. 6. Wiley, New York, pp. 581-591.

Wold, H. (1982) Soft modeling: the basic design and some extensions. In: K.G. Joreskog & H. Wold (Eds.), _Systems under indirect observations: Causality, structure, prediction, Part 2, pp. 1-54. Amsterdam: Holland.

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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