Main function for performing MMG-FA with multiple numbers of clusters and selection of the number of clusters. Includes factor rotation (currently, varimax and oblimin). For instructions, see 'How to use MixtureMG_FA.pdf'.
This version deals with factor loading differences (i.e., finds clusters of groups based on similarity of their factor loadings, given the user-specified number of clusters) and can be used with EFA as well as CFA.
For model selection, it is advised to use BIC_G (number of groups as sample size) in combination with CHull (see paper, https://www.rdocumentation.org/packages/multichull/versions/1.0.0)
Note that this code already supports covariance matrix input (i.e., inputting a list (or vertical concatenation) of the group-specific covariance matrices; means are not necessary as they don't affect the clustering in this case). This is not yet the case for the other codes and the main 'MixtureMG_FA' code.
MixtureMG_FA_intercepts: For finding clusters of groups with scalar invariance (while assuming metric invariance)
Please cite https://www.tandfonline.com/doi/full/10.1080/10705511.2020.1866577
This version deals with intercept differences (i.e., finds clusters of groups based on similarity of their intercepts, given the user-specified number of clusters) and can be used with EFA as well as CFA. It builds on invariance of the loadings. Deal with loading non-invariances as described in the Discussion of the paper on the metric invariance variant.
For model selection, it is advised to use BIC_G (number of groups as sample size) in combination with CHull (see paper, https://www.rdocumentation.org/packages/multichull/versions/1.0.0)
MixtureMG_FA_loadingsandintercepts: For finding clusters of groups with scalar invariance (while not assuming metric invariance)
Please cite both abovementioned papers on mixture multigroup factor analysis.
This version deals with loading and intercept differences (i.e., finds clusters of groups based on similarity of their loadings and intercepts, given the user-specified number of clusters) and can be used with EFA as well as CFA. In case of CFA, it builds on configural invariance (invariant zero-loading pattern). In case of EFA, only the same number of factors is assumed across all groups/clusters.
For model selection, it is advised to use BIC_G (number of groups as sample size) in combination with CHull (see paper, https://www.rdocumentation.org/packages/multichull/versions/1.0.0) Since, for this particular version of mixture multigroup factor analysis, model selection and cluster/parameter recovery has not yet been evaluated in a simulation study, I advise to compare results with the results for the stepwise approach (first find clusters of groups with metric invariance with the 'loadings' and then, per cluster, use the 'intercepts' code to look for clusters with scalar invariance, see Discussion of both papers).