A Logistic Normal Mixture Model Allowing Essential Zeros

• Autores: John Bear, Dean Billheimer
• Localización: Proceedings of the 6th International Workshop on Compositional Data Analysis: Girona, 1-7 de juny de 2015 / coord. por Santiago Thió Fernández de Henestrosa, Josep Antoni Martín Fernández, 2015, ISBN 978-84-8458-451-3
• Idioma: inglés
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• Resumen

  • 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 refined for dealing with zeros that are rounded, or due to a value being below a detection level, Palarea-Albaladejo et al. (2014); Pawlowsky-Glahn and Buccianti (2011); Martin-Fernandez et al. (2011); Palarea-Albaladejo and MartinFernandez (2008); Fry et al. (2000). Methods have also been developed for zeros in compositions arising from count data, Billheimer et al. (2001); Bacon-Shone (2008); Daunis-i-Estadella et al. (2008). However, essential zeros, cases where a component is truly absent, in continuous compositions are still a problem. Aitchison and Kay (2003) proposed an approach for extending the logistic normal distribution to model essential zeros. They posited a mixture of additive logistic normal distributions of different dimension, related by common parameters. They discussed possible ways of estimating parameters but did not derive estimators for location or dispersion parameters. We continue their 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.