calculateInnerWeightsPLS: Internal: Calculate the inner weights for PLS-PM

Description

PLS-PM forms "inner" composites as a weighted sum of its I related composites. These inner weights are obtained using one of the following schemes Lohmoeller1989cSEM:

centroid

According to the centroid weighting scheme each inner weight used to form composite j is either 1 if the correlation between composite j and its via the structural model related composite i = 1, ..., I is positive and -1 if it is negative.

factorial

According to the factorial weighting scheme each inner weight used to form inner composite j is equal to the correlation between composite j and its via the structural model related composite i = 1, ..., I.

path

Lets call all construct that have an arrow pointing to construct j predecessors of j and all arrows going from j to other constructs followers of j. According the path weighting scheme, inner weights are computed as follows. Take construct j:

For all predecessors of j set the inner weight of predecessor i to the correlation of i with j.
For all followers of j set the inner weight of follower i to the coefficient of a multiple regression of j on all followers i with i = 1,...,I.

Except for the path weighting scheme relatedness can come in two flavors. If .PLS_ignore_structural_model = TRUE all constructs are considered related. If .PLS_ignore_structural_model = FALSE (the default) only adjacent constructs are considered. If .PLS_ignore_structural_model = TRUE and .PLS_weight_scheme_inner = "path" a warning is issued and .PLS_ignore_structural_model is changed to FALSE.

Usage

calculateInnerWeightsPLS(
  .S                           = args_default()$.S,
  .W                           = args_default()$.W,
  .csem_model                  = args_default()$.csem_model,
  .PLS_ignore_structural_model = args_default()$.PLS_ignore_structrual_model,
  .PLS_weight_scheme_inner     = args_default()$.PLS_weight_scheme_inner
)

Value

The (J x J) matrix E of inner weights.

Arguments

.S: The (K x K) empirical indicator correlation matrix.
.W: A (J x K) matrix of weights.
.csem_model: A (possibly incomplete) cSEMModel-list.
.PLS_ignore_structural_model: Logical. Should the structural model be ignored when calculating the inner weights of the PLS-PM algorithm? Defaults to FALSE. Ignored if .approach_weights is not PLS-PM.
.PLS_weight_scheme_inner: Character string. The inner weighting scheme used by PLS-PM. One of: "centroid", "factorial", or "path". Defaults to "path". Ignored if .approach_weight is not PLS-PM.