# calculateInnerWeightsPLS

0th

Percentile

##### 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:

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.

Keywords
internal
##### 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
)
##### 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.

##### Value

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

##### Aliases
• calculateInnerWeightsPLS
Documentation reproduced from package cSEM, version 0.1.0, License: GPL-3

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