Comparing multiple factor analysis and related metric scaling

Abstract

Some statistical models, quite different in the symbolic mathematical sense, may provide similar results. After commenting two probability examples, we comment and compare multiple factor analysis (MFA) with related metric scaling (RMDS), two multivariate procedures dealing with mixed data. Each data set can be quantitative, binary, qualitative or nominal, and has been observed on the same individuals but coming from several sources. Then MFA and RMDS are two approaches for representing the individuals. We study the analogies and differences between both methodologies to guide users interested in performing multidimensional representations of mixed-type data. Though in general MFA and RMDS provide similar results, we prove that RMDS takes into account the association between the different sets of variables, providing, in some cases, better and more coherent representations. We also propose a parametric RMDS which includes MFA as a particular case. Article in memory of John C. Gower (1930-2019).

Keywords:

• Mixed data
• Multi-dimensional scaling
• Multiple factor analysis
• Related metric scaling
• Statistical distances

Acknowledgments

The authors are indebted to an associate editor and one anonymous referee for useful suggestions and comments.

Additional information

Funding

Work supported in part by grants RTI2018-095518-B-C22 (MCIU/AEI/FEDER) and FONDECYT 1160429.