plspm: PLS-PM: Partial Least Squares Path Modeling
In gastonstat/plspm2: Tools for Partial Least Squares Path Modeling

Description Usage Arguments Details Value Author(s) References See Also Examples

Estimate path models with latent variables by partial least squares approach

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

`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 between 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)
`boot.val`	whether bootstrap validation should be performed. (`FALSE` by default).
`br`	number bootstrap resamples. Used only when `boot.val=TRUE`. When `boot.val=TRUE`, the default number of re-samples is 100, but it can be specified in a range from 100 to 1000.
`dataset`	whether the data matrix used in the computations should be retrieved (`TRUE` by default).

The function plspm estimates a path model by partial least squares approach providing the full set of results.

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.

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`)
`crossloadings`	Correlations between the latent variables and the manifest variables (also called crossloadings)
`inner_summary`	Summarized results 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`	Goodness-of-Fit index
`data`	Data matrix containing the manifest variables used in the model. Only available when `dataset=TRUE`
`boot`	List of bootstrapping results; only available when argument `boot.val=TRUE`

Gaston Sanchez, Giorgio Russolillo

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.

innerplot, plot.plspm,

## typical example of PLS-PM in customer satisfaction analysis
## model with six LVs and reflective indicators

# load dataset satisfaction
data(satisfaction, package="plspm2")

# path 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)

# plot diagram of path matrix
innerplot(sat_path)

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

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

# apply plspm
satpls = plspm(satisfaction, sat_path, sat_blocks, modes = sat_mod, 
    scaled = FALSE)

# plot diagram of the inner model
innerplot(satpls)

# plot loadings
outerplot(satpls, what="loadings")

# plot outer weights
outerplot(satpls, what="weights")