paramsEstimator functions estimates the statistical model described by model
parameterEstim.separate(
S,
model,
W,
...,
parametersInner = estimator.ols,
parametersReflective = estimator.ols,
parametersFormative = estimator.ols,
disattenuate = FALSE,
reliabilities = reliabilityEstim.weightLoadingProduct
)Covariance matrix of the data.
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.
Weight matrix, where the indicators are on colums and composites are on the rows.
All other arguments are passed through to parametersInner,
parametersReflective, andparametersFormative
A function used to estimate the inner model matrix. The default is
estimator.ols
A function used to estimate the reflective model matrix. The
default is estimator.ols
A function used to estimate the formative model matrix. The
default is estimator.ols
If TRUE, C is
disattenuated before applying parametersInner.
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
A named vector of parameter estimates.
parameterEstim.separate returns the following as attributes:
the composite correlation matrix (after disattenuation, if requested).
the indicator-composite covariance matrix (after disattenuation, if requested).
the inner model matrix with estimated parameters.
the reflective model matrix with estimated parameters.
the formative model matrix with estimated parameters.
the reliability estimates used in disattenuation.
Additionally, all attributes returned by functions called by parameterEstim.separate are returned. This can include:
the PLSc loading estimate correction factors.
parameterEstim.separate: Estimates the model parameters in inner, reflective, and
formative separately.
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.
Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1<U+2013>36. Retrieved from http://www.jstatsoft.org/v48/i02