plspm (version 0.2-2)

plspm: PLS-PM: Partial Least Squares Path Modeling

Description

Estimate path models with latent variables by partial least squares approach

Usage

plspm(x, inner, outer, modes = NULL, scheme = "centroid", scaled = TRUE, boot.val = FALSE,
        br = NULL, plsr = FALSE, tol = 0.00001, iter = 100, dataset = TRUE)

  plspm.fit(x, inner, outer, modes = NULL, scheme = "centroid", scaled = TRUE, tol = 0.00001, iter = 100)

Arguments

x

A numeric matrix or data frame containing the manifest variables.

inner

A square (lower triangular) boolean matrix representing the inner model (i.e. the path relationships betwenn latent variables).

outer

List of vectors with column indices from x representing the outer model (i.e. which manifest variables correspond to the latent variables).

modes

A character vector indicating the type of measurement for each latent variable. "A" for reflective measurement or "B" for formative measurement (NULL by default).

scheme

A string of characters indicating the type of inner weighting scheme. Possible values are "centroid", "factor", or "path".

scaled

A logical value indicating whether scaling data is performed (TRUE by default).

boot.val

A logical value indicating whether bootstrap validation is performed (FALSE by default).

br

An integer indicating the number bootstrap resamples. Used only when boot.val=TRUE.

plsr

A logical value indicating whether pls regression is applied (FALSE by default).

tol

Decimal value indicating the tolerance crietrion for the iterations (tol=0.00001 by default).

iter

An integer indicating the maximum number of iterations (iter=100 by default).

dataset

A logical value indicating whether the data matrix should be retrieved (TRUE by default).

Value

• An object of class "plspm". When the function plspm.fit is called, it returns a list with basic results:
• outer.mod
  Results of the outer (measurement) model. Includes: outer weights, standardized loadings, communalities, and redundancies.
• inner.mod
  Results of the inner (structural) model. Includes: path coefficients and R-squared for each endogenous latent variable.
• latents
  Matrix of standardized latent variables (variance=1 calculated divided by N) obtained from centered data (mean=0).
• scores
  Matrix of latent variables used to estimate the inner model. If scaled=FALSE then scores are latent variables calculated with the original data (non-stardardized). If scaled=TRUE then scores and latents have the same values.
• out.weights
  Vector of outer weights.
• loadings
  Vector of standardized loadings (i.e. correlations with LVs.)
• path.coefs
  Matrix of path coefficients (this matrix has a similar form as inner.mat).
• r.sqr
  Vector of R-squared coefficients.
• If the function plspm is called, the previous list of results also contains the following elements:
• outer.cor
  Correlations between the latent variables and the manifest variables (also called crossloadings).
• inner.sum
  Summarized results by latent variable of the inner model. Includes: type of LV, type of measurement, number of indicators, R-squared, average communality, average redundancy, and average variance extracted
• effects
  Path effects of the structural relationships. Includes: direct, indirect, and total effects.
• unidim
  Results for checking the unidimensionality of blocks (These results are only meaningful for reflective blocks).
• gof
  Table with indexes of Goodness-of-Fit. Includes: absolute GoF, relative GoF, outer model GoF, and inner model GoF.
• data
  Data matrix containing the manifest variables used in the model. Only when dataset=TRUE.
• boot
  List of bootstrapping results; only available when argument boot.val=TRUE.

Details

The function plspm estimates a path model by partial least squares approach while providing all results. The function plspm.fit performs the basic PLS algorithm and provides simple results (e.g. outer weights, LVs scores, path coefficients, R2, and loadings). The argument inner.mat is a matrix of zeros and ones that indicates the structural relationships between latent variables. This must be a lower triangular matrix. inner.mat will contain a 1 when column j affects row i, 0 otherwise. The argument sets is a list of vectors of indices indicating the sets of manifest variables associated to the latent variables. The length of sets must be equal to the number of rows of inner.mat. The argument modes is a character vector indicating the type of measurement for each latent variable. A value of "A" is used when a latent variable has reflective manifest variables, and a value of "B" is used when the latent variable has formative manifest variables. The length of modes must be equal to the number of rows of inner.mat (i.e. equal to the length of sets). The argument scaled is TRUE by default. This means that data in x is scaled to standardized values (i.e. mean=0 and variance=1, calculating the variance dividing by N instead of N-1). Unless the data has the same scale for all variables, it is strongly recommended to keep this argument unchanged. When bootstrap validation is performed, the default number of re-samples is 100. However, br can be specified in a range from 100 to 1000. The argument plsr gives the option to calculate the path coefficients by means of pls regression. The argument tol can be specified in a range from 0 to 0.001. The minimum value of iter is 100.

References

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.

See Also

print.plspm, summary.plspm, plot.plspm.

Examples

## example of PLS-PM in ecological analysis
  ## model with three LVs and formative indicators
  data(arizona)
  ari.inner <- matrix(c(0,0,0,0,0,0,1,1,0),3,3,byrow=TRUE)
  dimnames(ari.inner) <- list(c("ENV","SOIL","DIV"),c("ENV","SOIL","DIV"))
  ari.outer <- list(c(1,2),c(3,4,5),c(6,7,8)) 
  ari.mod <- c("B","B","B")  ## formative indicators
  res1 <- plspm(arizona, inner=ari.inner, outer=ari.outer, modes=ari.mod,
  scheme="factor", scaled=TRUE, plsr=TRUE)
  res1
  summary(res1)
  
  ## typical example of PLS-PM in customer satisfaction analysis
  ## model with six LVs and reflective indicators
  data(satisfaction)
  IMAG <- c(0,0,0,0,0,0)
  EXPE <- c(1,0,0,0,0,0)
  QUAL <- c(0,1,0,0,0,0)
  VAL  <- c(0,1,1,0,0,0)
  SAT  <- c(1,1,1,1,0,0) 
  LOY  <- c(1,0,0,0,1,0)
  sat.inner <- rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)
  sat.outer <- list(1:5,6:10,11:15,16:19,20:23,24:27)
  sat.mod <- rep("A",6)   ## reflective indicators
  res2 <- plspm(satisfaction, sat.inner, sat.outer, sat.mod, scaled=FALSE, boot.val=TRUE)
  summary(res2)
  plot(res2)
  
  ## example of PLS-PM in sensory analysis
  ## estimate a path model for the orange juice data
  data(orange)
  senso.inner <- matrix(c(0,0,0,1,0,0,1,1,0),3,3,byrow=TRUE)
  dimnames(senso.inner) <- list(c("PHYCHEM","SENSORY","HEDONIC"),
                              c("PHYCHEM","SENSORY","HEDONIC"))
  senso.outer <- list(1:9,10:16,17:112)
  senso.mod <- rep("A",3)
  res3 <- plspm.fit(orange, senso.inner, senso.outer, senso.mod, 
                scheme="centroid", scaled=TRUE)
  summary(res3)

  ## example of PLS-PM in multi-block data analysis
  ## estimate a path model for the wine data set 
  ## requires package FactoMineR 
  library(FactoMineR)
  data(wine)
  SMELL <- c(0,0,0,0)
  VIEW <- c(1,0,0,0)
  SHAKE <- c(1,1,0,0)
  TASTE <- c(1,1,1,0)
  wine.inner <- rbind(SMELL,VIEW,SHAKE,TASTE)
  wine.outer <- list(3:7,8:10,11:20,21:29)
  wine.mods <- rep("A",4)
  # using function plspm.fit (basic pls algorithm)
  res4 <- plspm.fit(wine, wine.inner, wine.outer, wine.mods, scheme="centroid")                
  plot(res4, what="all", arr.pos=.4, box.prop=.4, cex.txt=.8)