When Relative and absolute information matter: compositional predictor with a total in generalized linear models

Abstract

The analysis of Compositional Data (CoDa) consists in the study of the relative importance of parts of a whole rather than the size of the whole, because absolute information is either unavailable or not of interest. On the other hand, when absolute and relative information are both relevant, research hypotheses concern both. This article introduces a model including both the logratios used in CoDa and a total variable carrying absolute information, as predictors in an otherwise standard statistical model. It shows how logratios can be tailored to the researchers' hypotheses and alternative ways of computing the total. The interpretational advantages with respect to traditional approaches are presented and the equivalence and invariance properties are proven. A sequence of nested models is presented to test the relevance of relative and absolute information. The approach can be applied to dependent metric, binary, ordinal or count variables. Two illustrations are provided, the first on tourist expenditure and satisfaction and the second on solid waste management and floating population