calculateWeightsGSCA {cSEM}

Calculate composite weights using GSCA

Description

Calculate composite weights using generalized structure component analysis (GSCA). The first version of this approach was presented in Hwang and Takane (2004). Since then, several advancements have been proposed. The latest version of GSCA can been found in Hwang and Takane (2014). This is the version cSEMs implementation is based on.

Usage

calculateWeightsGSCA(
  .X                           = args_default()$.X,
  .S                           = args_default()$.S,
  .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).

.S

The (K x K) empirical indicator correlation matrix.

.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.

Value

A named list. J stands for the number of constructs and K for the number of indicators.

⁠$W⁠

A (J x K) matrix of estimated weights.

⁠$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 (2004). “Generalized Structured Component Analysis.” Psychometrika, 69(1), 81–99.

Hwang H, Takane Y (2014). Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling, Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences. Chapman and Hall/CRC.