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Box–Cox transformations in Bayesian analysis of compositional data
Author(s) -
Iyengar Malini,
Dey Dipak K.
Publication year - 1998
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/(sici)1099-095x(199811/12)9:6<657::aid-env329>3.0.co;2-1
Subject(s) - compositional data , covariate , bayesian probability , multivariate statistics , data set , statistics , raw data , measure (data warehouse) , computer science , econometrics , data mining , mathematics
Compositional data often result when raw data are normalized or when data is obtained as proportions of a certain heterogeneous quantity. These conditions are fairly common in geology, economics and biology. The result is, therefore, a vector of such observations per specimen. The usual multivariate procedures are seldom adequate for the analysis of compositional data and there is a relative dearth of alternative techniques suitable for the same. The presence of covariates further adds to complexity of the situation. In this manuscript, a complete Bayesian methodology to model such data is developed and is illustrated on a real data set comprising sand, silt and clay compositions taken at various water depths in an Arctic lake. Alternative methods such as maximum likelihood estimates are compared with the proposed Bayesian estimates. Simulation based approach is adopted to ascertain adequacy of the fit. Several models are finally compared via a posterior predictive loss measure. Copyright © 1998 John Wiley & Sons, Ltd.