Internal: Calculate the inner weights for PLS-PM
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:
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.
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.
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.
.PLS_ignore_structural_model = TRUE all constructs are considered related.
.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
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 )
The (K x K) empirical indicator correlation matrix.
A (J x K) matrix of weights.
A (possibly incomplete) cSEMModel-list.
Logical. Should the structural model be ignored when calculating the inner weights of the PLS-PM algorithm? Defaults to
FALSE. Ignored if
.approach_weightsis not PLS-PM.
Character string. The inner weighting scheme used by PLS-PM. One of: "centroid", "factorial", or "path". Defaults to "path". Ignored if
.approach_weightis not PLS-PM.
The (J x J) matrix
E of inner weights.