A regression mixture with logistic weights for modeling heterogeneous crustacean growth data when the maturity phase is unknown

Abstract

Piecewise linear models (PLMs) have been used widely in crustacean morphometry and growth modeling when subjects belong to more than one undetermined maturity stage, for example, to model immature and adolescent male snow crab (Chionoecetes opilio) growth increment at moulting as a function of pre-moult size. PLMs assume, unrealistically, that the transition between the maturity stages occurs at a fixed size. PLMs have also often been applied without taking into account the heterogeneity of variance or without supplying parameter confidence intervals. We propose to describe the unknown maturity stage and the known growth increments as functions of the pre-moult size by regression mixture with logistic weights (RMLW), where a logistic function and two linear regressions are mixed with weights provided by the logistic function. Errors are assumed to be normally distributed with a standard deviation depending linearly on the expected growth increment. Parameters and their confidence intervals are obtained using maximum likelihood. Model diagnostic procedures and a posteriori maturity stage classification methods are presented. The methodology is applied to 1311 snow crab growth observations, and results are compared with those of other snow crab studies. The methodology has widespread applications to crustacean morphometry and can be generalized to nonlinear relationships.