Broken Biological Size Relationships: A Censored Semiparametric Regression Approach with Measurement Error

Biological size relationships, i.e., regression of one size variable on another are typically monotone but often break down at extreme values of the variables. Here we study the way a plant's biomass is apportioned to reproductive and other life activities. Working with a theory proposed by Weiner (1988) which is based upon an analogy between a biological plant and an industrial plant leads to a censored regression model formulation. We consider a data set involving 542 goldenrod plants which has been analyzed in a limited fashion in Schmid and Weiner (1993) and in Schmid, Polasek, Weiner, Krause and Stoll (1994). Important extensions we provide include nonparametric modeling of the size relationship, the introduction of covariate information, incorporation of heterogeneity across plant families and inclusion of measurement error models for both response and covariate variables. Our general approach is through hierarchical models taking advantage of available prior information on the magnitudes of the size variables. Models are t using simulation methods enabling a full range of inference. An attractive model choice criterion demonstrates the need to accommodate all of the above aspects for the given data set. Our exible modeling approach can be adapted to investigate other biological size relationships.