DUGi

Bayesian-multiplicative treatment of count zeros in compositional data sets

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Compositional count data are discrete vectors representing the numbers of outcomes falling into any of several mutually exclusive categories. Compositional techniques based on the log-ratio methodology are appropriate in those cases where the total sum of the vector elements is not of interest. Such compositional count data sets can contain zero values which are often the result of insufficiently large samples. That is, they refer to unobserved positive values that may have been observed with a larger number of trials or with a different sampling design. Because the log-ratio transformations require data with positive values, any statistical analysis of count compositions must be preceded by a proper replacement of the zeros. A Bayesian-multiplicative treatment has been proposed for addressing this count zero problem in several case studies. This treatment involves the Dirichlet prior distribution as the conjugate distribution of the multinomial distribution and a multiplicative modification of the non-zero values. Different parameterizations of the prior distribution provide different zero replacement results, whose coherence with the vector space structure of the simplex is stated. Their performance is evaluated from both the theoretical and the computational point of view

This research was supported by the Ministerio de Economia y Competividad under the project ’METRICS’ Ref. MTM2012-33236, by the Agencia de Gestio d’Ajuts Universitaris i de Recerca of the Generalitat de Catalunya under the project Ref: 2009SGR424, and by the Scottish Government’s Rural and Environment Science and Analytical Services Division (RESAS). The authors also gratefully acknowledge the support by the Operational Program Education for Competitiveness-European Social Fund (project CZ.1.07/2.3.00/20.0170 of the Ministry of Education, Youth and Sports of the Czech Republic)

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