A logistic normal mixture model for compositional data allowing essential zeros

John Bear, Dean Billheimer

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The usual candidate distributions for modeling compositions, the Dirichlet and the logistic normal distribution, do not include zero components in their support. Methods have been developed and rened for dealing with zeros that are rounded, or due to a value being below a detection level. Methods have also been developed for zeros in compositions arising from count data. However, essential zeros, cases where a component is truly absent, in continuous compositions are still a problem. The most promising approach is based on extending the logistic normal distribution to model essential zeros using a mixture of additive logistic normal distributions of different dimension, related by common parameters. We continue this approach, and by imposing an additional constraint, develop a likelihood, and show ways of estimating parameters for location and dispersion. The proposed likelihood, conditional on parameters for the probability of zeros, is a mixture of additive logistic normal distributions of different dimensions whose location and dispersion parameters are projections of a common location or dispersion parameter. For some simple special cases, we contrast the relative efficiency of different location estimators.

Original languageEnglish (US)
Pages (from-to)3-23
Number of pages21
JournalAustrian Journal of Statistics
Volume45
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Composition
  • Essential zero
  • Logistic normal
  • Projection
  • Subcomposition

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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