plspm.fit {plspm}

Basic results for Partial Least Squares Path Modeling

Description

Estimate path models with latent variables by partial least squares approach without providing the full list of results as plspm(). This might be helpful when doing simulations, intensive computations, or when you don't want the whole enchilada.

Usage

  plspm.fit(Data, path_matrix, blocks, modes = NULL,
    scaling = NULL, scheme = "centroid", scaled = TRUE,
    tol = 1e-06, maxiter = 100, plscomp = NULL)

Arguments

Data

matrix or data frame containing the manifest variables.

path_matrix

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

blocks

list of vectors with column indices or column names from Data indicating the sets of manifest variables forming each block (i.e. which manifest variables correspond to each block).

scaling

optional list of string vectors indicating the type of measurement scale for each manifest variable specified in blocks. scaling must be specified when working with non-metric variables.

modes

character vector indicating the type of measurement for each block. Possible values are: "A", "B", "newA", "PLScore", "PLScow". The length of modes must be equal to the length of blocks.

scheme

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

scaled

whether manifest variables should be standardized. Only used when scaling = NULL. When (TRUE data is scaled to standardized values (mean=0 and variance=1). The variance is calculated dividing by N instead of N-1).

tol

decimal value indicating the tolerance criterion for the iterations (tol=0.000001). Can be specified between 0 and 0.001.

maxiter

integer indicating the maximum number of iterations (maxiter=100 by default). The minimum value of maxiter is 100.

plscomp

optional vector indicating the number of PLS components (for each block) to be used when handling non-metric data (only used if scaling is provided)

Details

plspm.fit performs the basic PLS algorithm and provides limited results (e.g. outer model, inner model, scores, and path coefficients).

The argument path_matrix is a matrix of zeros and ones that indicates the structural relationships between latent variables. path_matrix must be a lower triangular matrix; it contains a 1 when column j affects row i, 0 otherwise.

Value

An object of class "plspm".

outer_model

Results of the outer model. Includes: outer weights, standardized loadings, communalities, and redundancies

inner_model

Results of the inner (structural) model. Includes: path coeffs and R-squared for each endogenous latent variable

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

path_coefs

Matrix of path coefficients (this matrix has a similar form as path_matrix)

Author(s)

Gaston Sanchez, Giorgio Russolillo

References

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

Lohmoller J.-B. (1989) Latent variables path modeling 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

innerplot, plot.plspm,

Examples

## Not run: 
 ## typical example of PLS-PM in customer satisfaction analysis
 ## model with six LVs and reflective indicators

 # load dataset satisfaction
 data(satisfaction)

 # inner model matrix
 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_path = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)

 # outer model list
 sat_blocks = list(1:5, 6:10, 11:15, 16:19, 20:23, 24:27)

 # vector of reflective modes
 sat_modes = rep("A", 6)

 # apply plspm.fit
 satpls = plspm.fit(satisfaction, sat_path, sat_blocks, sat_modes,
     scaled=FALSE)

 # summary of results
 summary(satpls)

 # default plot (inner model)
 plot(satpls)
 
## End(Not run)