Broken Biological Size Relationships: A Truncated Semiparametric Regression Approach with Measurement Error
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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 in which a plant's biomass is apportioned to reproductive and other life activities. Working with a theory proposed by Weiner (1988) based an analogy between a biological plant and an industrial plant leads to a truncated regression model formulation. We consider a dataset involving 542 goldenrod plants that has been analyzed in a limited fashion by others. Important extensions that we provide include nonparametric modeling of the size relationship, introduction of covariate information, incorporation of heterogeneity across plant families, and inclusion of measurement error models for both response and explanatory variables. Our approach is through hierarchical models taking advantage of available prior information on the magnitudes of the size variables. Models are fitted using simulation methods enabling a full range of inference. An attractive model choice criterion demonstrates the need to accommodate all of the aforementioned aspects for the given dataset. Our flexible modeling approach can be adapted to investigate other biological size relationships. 1997 Taylor & Francis Group, LLC.
