parameterEstim: Parameter estimation of full model

In matrixpls: Matrix-Based Partial Least Squares Estimation

Description

paramsEstimator functions estimates the statistical model described by model

Usage

parameterEstim.separate(
  S,
  model,
  W,
  ...,
  parametersInner = estimator.ols,
  parametersReflective = estimator.ols,
  parametersFormative = estimator.ols,
  disattenuate = FALSE,
  reliabilities = reliabilityEstim.weightLoadingProduct
)

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.
...	All other arguments are passed through to parametersInner, parametersReflective, andparametersFormative
parametersInner	A function used to estimate the inner model matrix. The default is estimator.ols
parametersReflective	A function used to estimate the reflective model matrix. The default is estimator.ols
parametersFormative	A function used to estimate the formative model matrix. The default is estimator.ols
disattenuate	If TRUE, C is disattenuated before applying parametersInner.
reliabilities	A function for calculating reliability estimates based on the data covariance matrix S, factor loading matrix loadings, and a weight matrix W. Returns a vector of reliability estimates. The default is reliabilityEstim.weightLoadingProduct

Details

Model can be specified in the lavaan format or the native matrixpls format. The native model format is a list of three binary matrices, inner, reflective, and formative specifying the free parameters of a model: inner (l x l) specifies the regressions between composites, reflective (k x l) specifies the regressions of observed data on composites, and formative (l x k) specifies the regressions of composites on the observed data. Here k is the number of observed variables and l is the number of composites.

If the model is specified in lavaan format, the native format model is derived from this model by assigning all regressions between latent variables to inner, all factor loadings to reflective, and all regressions of latent variables on observed variables to formative. Regressions between observed variables and all free covariances are ignored. All parameters that are specified in the model will be treated as free parameters.

The original papers about Partial Least Squares, as well as many of the current PLS implementations, impose restrictions on the matrices inner, reflective, and formative: inner must be a lower triangular matrix, reflective must have exactly one non-zero value on each row and must have at least one non-zero value on each column, and formative must only contain zeros. Some PLS implementations allow formative to contain non-zero values, but impose a restriction that the sum of reflective and t(formative) must satisfy the original restrictions of reflective. The only restrictions that matrixpls imposes on inner, reflective, and formative is that these must be binary matrices and that the diagonal of inner must be zeros.

Model estimation proceeds as follows. 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. These are matrices are used to separately estimate each of the three model matrices inner, reflective, and formative. This approach of estimating the parameter matrices separately is the standard way of estimation in the PLS literature.

The default estimation approach is to estimate all parameters with a series of OLS regressions using estimator.ols.

Value

A named vector of parameter estimates.

parameterEstim.separate returns the following as attributes:

C	the composite correlation matrix (after disattenuation, if requested).
IC	the indicator-composite covariance matrix (after disattenuation, if requested).
inner	the inner model matrix with estimated parameters.
reflective	the reflective model matrix with estimated parameters.
formative	the formative model matrix with estimated parameters.
Q	the reliability estimates used in disattenuation.

Additionally, all attributes returned by functions called by parameterEstim.separate are returned. This can include:

c	the PLSc loading estimate correction factors.

Functions

• parameterEstim.separate: Estimates the model parameters in inner, reflective, and formative separately.

References

Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36. Retrieved from http://www.jstatsoft.org/v48/i02

matrixpls documentation built on April 28, 2021, 5:07 p.m.