plspm: PLS-PM: Partial Least Squares Path Modeling

Description

Estimate path models with latent variables by partial least squares approach (for both metric and non-metric data)

Usage

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

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).
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

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 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 argument for runing the non-metric approach; it is a 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. Possible values: "num" (linear transformation, suitable for numerical variables), "raw" (no transformation), "nom" (non-monotonic transformation, suitable for nominal variables), and "ord" (monotonic transformation, suitable for ordinal 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.
dataset: whether the data matrix used in the computations should be retrieved (TRUE by default).

Author

Gaston Sanchez, Giorgio Russolillo

Details

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.

plspm: Partial Least Squares Path Modeling
plspm.fit: Simple version for PLS-PM
plspm.groups: Two Groups Comparison in PLS-PM
rebus.pls: Response Based Unit Segmentation (REBUS)

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.

Russolillo, G. (2012) Non-Metric Partial Least Squares. Electronic Journal of Statistics, 6, pp. 1641-1669. https://projecteuclid.org/euclid.ejs/1348665231

Examples

Run this code

if (FALSE) {
## typical example of PLS-PM in customer satisfaction analysis
## model with six LVs and reflective indicators

# load dataset satisfaction
data(satisfaction)

# 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")
}

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