Title: Joint sparse principal component analysis
Authors: Katrijn Van Deun - Tilburg University (Netherlands) [presenting]
Abstract: Comparing multivariate relations between different groups forms the core of many studies in the empirical sciences. Latent variable approaches (e.g., principal component and factor analysis) are most useful to explore such multivariate relations. The loadings are key to the interpretation of these latent variable models as they express the strength of association of the observed variables with the latent variables. Preferably variables load on one or a few components only and have zero loadings elsewhere as this eases interpretation. In addition, when comparing multiple groups, also a clear distinction between those variables that function in the same way over groups and those that do not is needed: Loadings should be exactly equal between those groups where the variables function in the same way and unequal elsewhere. We propose a multigroup latent variable model, joint sparse principal component analysis, that has these properties. Sparsity is imposed using cardinality constraints while equal loadings are obtained as the result of a fusion penalty. We efficiently solve the estimation problem by using an alternating optimization procedure that includes the alternating direction method of multipliers as one of the steps and tunes the cardinality and fusion penalty with a BIC-like statistic.