A Latent Class Procedure for the Structural Analysis of Two-Way Compositional Data

Abstract

This paper develops a new procedure for simultaneously performing multidimensional scaling and cluster analysis on two-way compositional data of proportions. The objective of the proposed procedure is to delineate patterns of variability in compositions across subjects by simultaneously clustering subjects into latent classes or groups and estimating a joint space of stimulus coordinates and class-specific vectors in a multidimensional space. We use a conditional mixture, maximum likelihood framework with an E-M algorithm for parameter estimation. The proposed procedure is illustrated using a compositional data set reflecting proportions of viewing time across television networks for an area sample of households.

Keywords: Compositional data, Finite mixture distributions, Cluster analysis, Multidimensional scaling, E-M algorithm, Latent class analysis