A LATENT CLASS PROCEDURE FOR THE STRUCTURAL-ANALYSIS OF 2-WAY COMPOSITIONAL DATA

This paper develops a new procedure for simultaneously performing mult idimensional scaling and cluster analysis on two-way compositional dat a of proportions. The objective of the proposed procedure is to deline ate patterns of variability in compositions across subjects by simulta neously clustering subjects into latent classes or groups and estimati ng a joint space of stimulus coordinates and class-specific vectors in a multidimensional space. We use a conditional mixture, maximum likel ihood framework with an E-M algorithm for parameter estimation. The pr oposed procedure is illustrated using a compositional data set reflect ing proportions of viewing time across television networks for an area sample of households.