calculateWeightsGSCAm: Calculate weights using GSCAm
In cSEM: Composite-Based Structural Equation Modeling

calculateWeightsGSCAm

R Documentation

Calculate weights using GSCAm

Description

Calculate composite weights using generalized structured component analysis with uniqueness terms (GSCAm) proposed by \insertCiteHwang2017;textualcSEM.

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 \insertCiteHwang2017;textualcSEM. 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.