Modelling structural zeros in compositional data via a zero-censored multivariate normal model

Abstract

Compositional data are multivariate data constrained to lie within the simplex. When zero values are present, most methods fail to apply unless a zero value replacement is performed prior to the analysis. In this paper we present a new model for analyzing compositional data with zero values present. Unlike the model of \cite{butler2008} that projects every zero value towards a vertex, we project them onto their corresponding edge and assume that zero values are censored values from a multivariate normal distribution. We utilize the EM algorithm to estimate the model parameters, in a computationally efficient manner. Simulated and real data illustrate the performance of the proposed model.