# calculateWeightsGSCAm

##### Calculate weights using GSCAm

Calculate composite weights using generalized structured component analysis with uniqueness terms (GSCAm) proposed by Hwang2017;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 Hwang2017;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.

##### References

*Documentation reproduced from package cSEM, version 0.1.0, License: GPL-3*