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ThiÃ³ i FernÃ¡ndez de Henestrosa, Santiago
MartÃn FernÃ¡ndez, Josep Antoni 

Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Aitchison, John
Kay, Jim W. 

2003 October 15  
One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By an
essential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur in
many compositional situations, such as household budget patterns, time budgets,
palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful in
such situations. From consideration of such examples it seems sensible to build up a
model in two stages, the first determining where the zeros will occur and the second
how the unit available is distributed among the nonzero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zerocompositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data Geologische Vereinigung; Universitat de Barcelona, Equip de Recerca ArqueomÃ¨trica; Institut dâ€™EstadÃstica de Catalunya; International Association for Mathematical Geology; Patronat de lâ€™Escola PolitÃ¨cnica Superior de la Universitat de Girona; FundaciÃ³ privada: Girona, Universitat i Futur. 

application/pdf  
Aitchison, J.; Kay, J.W. â€™Possible solution of some essential zero problems in compositional data analysisâ€™ a CODAWORKâ€™03. Girona: La Universitat, 2003 [consulta: 2 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/652  
848458111X  
http://hdl.handle.net/10256/652  
eng  
Universitat de Girona. Departament dâ€™InformÃ tica i MatemÃ tica Aplicada  
Tots els drets reservats  
EstadÃstica matemÃ tica  
Possible solution of some essential zero problems in compositional data analysis  
info:eurepo/semantics/conferenceObject  
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