Contrastive Multiple Correspondence Analysis (cMCA): Using Contrastive Learning to Identify Latent Subgroups in Political Parties.

Scaling methods have long been utilized to simplify and cluster high-dimensional data. However, the latent spaces derived from these methods are sometimes uninformative or unable to identify significant differences in the data. To tackle this common issue, we adopt an emerging analysis approach called contrastive learning. We contribute to this emerging field by extending its ideas to multiple correspondence analysis (MCA) in order to enable an analysis of data often encountered by social scientists -- namely binary, ordinal, and nominal variables. We demonstrate the utility of contrastive MCA (cMCA) by analyzing three different surveys of voters in Europe, Japan, and the United States. Our results suggest that, first, cMCA can identify substantively important dimensions and divisions among (sub)groups that are overlooked by traditional methods; second, for certain cases, cMCA can still derive latent traits that generalize across and apply to multiple groups in the dataset; finally, when data is high-dimensional and unstructured, cMCA provides objective heuristics, above and beyond the standard results, enabling more complex subgroup analysis.