Clustering Nominal Data With Equivalent Categories A Simulation Study Comparing Retricted GROUPALS And Restricted Latent Class Analyses

Two techniques were compared on their cluster recovery in the analysis of simulated data sets with
known cluster structure, by means of the adjusted Rand index.

The first technique was GROUP ALS, an algorithm for the simultaneous scaling (by homogeneity analysis) and clustering of categorical variables. To account for equivalent categories, equality constraints of the category quantifications for the same categories of the different variables were incorporated in the GROUP ALS algorithm, resulting in a new technique. The second technique was latent class analysis, with the extra restriction to account for parallel indicators that the conditional probabilities were equal across the variables.

Restricted LCA obtained higher cluster recovery than restricted GROUP ALS. For both techniques, increasing the number of variables and the number of categories per variable positively affected cluster recovery, while the presence of more classes negatively affected cluster recovery. These effects were more pronounced for restricted GROUPALS. Relative class size was predominantly a factor of importance for restricted GROUP ALS, where unbalanced classes negatively affected cluster recovery, but it did not affect cluster recovery for restricted LCA much. Finally, increasing the number of variables seemed to alleviate the negative effect of
more underlying classes for both techniques and the negative effect of unbalanced class size in restricted GROUPALS.