matrixpls(S, model, W.model = NULL, weightFun = weightFun.pls, parameterEstim = parameterEstim.separate, weightSign = NULL, ..., validateInput = TRUE, standardize = TRUE)
formativedefining the free regression paths in the model.
S, a model specification
model, and a weight pattern
W.model. Returns a weigth matrix
W. The default is
S, model specification
model, and weight matrix
W. Returns a named vector of parameter estimates. The default is
Sand a weight matrix
W. Returns a weigth matrix
TRUE, the arguments are validated.
Sis converted to a correlation matrix before analysis.
matrixplscontaining the parameter estimates followed by weights.
matrixplsreturns the following as attributes:Additionally, all attributes returned by functions called by matrixpls are returned. This can include: This can include:
matrixplsis the main function of the matrixpls package. This function parses a model object and then uses the results to call
weightFunto to calculate indicator weight. After this the
parameterEstimfunction is applied to the indicator weights, the data covariance matrix, and the model object and the resulting parameter estimates are returned.
Model can be specified in the lavaan format or the native matrixpls format.
The native model format is a list of three binary matrices,
formative specifying the free parameters of a model:
l x l) specifies the
regressions between composites,
k x l) specifies the regressions of observed
data on composites, and
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
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 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
t(formative) must satisfy
the original restrictions of
reflective. The only restrictions that matrixpls
formative is that these must be
binary matrices and that the diagonal of
inner must be zeros.
W.model is a (
l x k) matrix that indicates
how the indicators are combined to form the composites. The original papers about
Partial Least Squares as well as all current PLS implementations define this as
t(reflective) | formative, which means that the weight patter must match the
model specified in
formative. Matrixpls does not
W.model needs to match
accepts any numeric matrix. If this argument is not specified, all elements of
correspond to non-zero elements in the
matrices receive the value 1.
Wold, H. (1982). Soft modeling - The Basic Design And Some Extensions. In K. G. Jöreskog & S. Wold (Eds.),Systems under indirect observation: causality, structure, prediction (pp. 1–54). Amsterdam: North-Holland.