calculateWeightsGSCAm {cSEM}

Calculate weights using GSCAm

Description

Calculate composite weights using generalized structured component analysis with uniqueness terms (GSCAm) proposed by Hwang et al. (2017).

Usage

calculateWeightsGSCAm(
  .X                           = args_default()$.X,
  .csem_model                  = args_default()$.csem_model,
  .conv_criterion              = args_default()$.conv_criterion,
  .iter_max                    = args_default()$.iter_max,
  .starting_values             = args_default()$.starting_values,
  .tolerance                   = args_default()$.tolerance
   )

Arguments

.X

A matrix of processed data (scaled, cleaned and ordered).

.csem_model

A (possibly incomplete) cSEMModel-list.

.conv_criterion

Character string. The criterion to use for the convergence check. One of: "diff_absolute", "diff_squared", or "diff_relative". Defaults to "diff_absolute".

.iter_max

Integer. The maximum number of iterations allowed. If iter_max = 1 and .approach_weights = "PLS-PM" one-step weights are returned. If the algorithm exceeds the specified number, weights of iteration step .iter_max - 1 will be returned with a warning. Defaults to 100.

.starting_values

A named list of vectors where the list names are the construct names whose indicator weights the user wishes to set. The vectors must be named vectors of "indicator_name" = value pairs, where value is the (scaled or unscaled) starting weight. Defaults to NULL.

.tolerance

Double. The tolerance criterion for convergence. Defaults to 1e-05.

Details

If there are only constructs modeled as common factors calling csem() with .appraoch_weights = "GSCA" will automatically call calculateWeightsGSCAm() unless .disattenuate = FALSE. GSCAm currently only works for pure common factor models. The reason is that the implementation in cSEM is based on (the appendix) of Hwang et al. (2017). Following the appendix, GSCAm fails if there is at least one construct modeled as a composite because calculating weight estimates with GSCAm leads to a product involving the measurement matrix. This matrix does not have full rank if a construct modeled as a composite is present. The reason is that the measurement matrix has a zero row for every construct which is a pure composite (i.e. all related loadings are zero) and, therefore, leads to a non-invertible matrix when multiplying it with its transposed.

Value

A list with the elements

⁠$W⁠

A (J x K) matrix of estimated weights.

⁠$C⁠

The (J x K) matrix of estimated loadings.

⁠$B⁠

The (J x J) matrix of estimated path coefficients.

⁠$E⁠

NULL

⁠$Modes⁠

A named vector of Modes used for the outer estimation, for GSCA the mode is automatically set to 'gsca'.

⁠$Conv_status⁠

The convergence status. TRUE if the algorithm has converged and FALSE otherwise.

⁠$Iterations⁠

The number of iterations required.

References

Hwang H, Takane Y, Jung K (2017). “Generalized structured component analysis with uniqueness terms for accommodating measurement error.” Frontiers in Psychology, 8(2137), 1–12.