matrixpls (version 0.4.0)

params.plsc: Parameter estimation with an adaptation of PLSc algorithm

Description

Estimates the model parameters with an adapted version of Dijkstra's (2011) PLSc. The parameters between latent variables are estimated using two-stages least squares estimation using a composite covariance matrix that has been disattenuated with estimated composite reliabilities.

Usage

params.plsc(S, model, W, fm = "dijkstra", tsls = FALSE, ...)

Arguments

S

Covariance matrix of the data.

model

There are two options for this argument: 1. lavaan script or lavaan parameter table, or 2. a list containing three matrices inner, reflective, and formative defining the free regression paths in the model.

W

Weight matrix, where the indicators are on colums and composites are on the rows.

fm

factoring method for estimating the corrected factor loadings. "dijkstra" will use the correction presented by Dijkstra (2011), where the PLS estimates of the factor loadings for a latent variable are multiplied with a scalar a,

tsls

Should estimation be done with two stage least squares instead of regression

...

All other arguments are passed through to weightFunction and parameterEstimator.

Value

• A named vector of parameter estimates.

Details

params.plsc estimates the statistical model described by model with the following steps. If model is not in the native format, it is converted to the native format containing matrices inner, reflective, and formative. The weights W and the data covariance matrix S are used to calculate the composite covariance matrix C and the indicator-composite covariance matrix IC.

C is then disattenuated. The reliability estimates used in the dissattenuation process are calculated by using Dijkstra's (2011) correction or with a separate factor analysis for each indicator block. Indicators that are used in a composite but are not specified as reflective indicators for the latent variable that the composite approximates are assumed to be perfectly reliable.

The disattenuated C is used to estimate the the inner part of the model with separate OLS regressions in the same way as in params.regression. This differs from Dijkstra's (2011) PLSc estimator that uses 2SLS. The reason for not using 2SLS is that PLS is commonly used with models that do not contain a sufficient number of exogenous variables that could be used as instruments in the 2SLS estimation.

The results from the disattenuation process are used as estimates of the reflective part of the model and the formative part of the model estimated with separate OLS regressions using the S and IC matrices.

Those elements of teh indicator-composite covariance matrix IC that correspond to factor loadings are replaced with the factor loading estimates.

The dissattenuation code for Dijkstra's method is adapted from Huang (2013), which is based on Dijkstra (2011).

References

Huang, W. (2013). PLSe: Efficient Estimators and Tests for Partial Least Squares (Doctoral dissertation). University of California, Los Angeles. Dijkstra, T. K. (2011). Consistent Partial Least Squares estimators for linear and polynomial factor models. A report of a belated, serious and not even unsuccessful attempt. Comments are invited. Retrieved from http://www.rug.nl/staff/t.k.dijkstra/consistent-pls-estimators.pdf

See Also

Other parameter estimators: params.plsregression; params.regression; params.tsls

Examples

library(plspm)

# Run the customer satisfaction examle form plspm

# 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)
inner = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)
colnames(inner) <- rownames(inner)

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

reflective<- matrix(
  c(1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1),
  27,6, dimnames = list(colnames(satisfaction)[1:27],colnames(inner)))

# empty formative model

formative <- matrix(0, 6, 27, dimnames = list(colnames(inner), colnames(satisfaction)[1:27]))

# Estimation using covariance matrix

matrixpls.out <- matrixpls(cov(satisfaction[,1:27]), model = list(inner = inner,
                                                                  reflective = reflective,
                                                                  formative = formative),
                           parameterEstimator = params.plsc)

summary(matrixpls.out)