Inference for threshold models with variance components from the generalized linear mixed model perspective

Abstract

The analysis of threshold models with fixed and random effects and associated variance components is discussed from the perspective of generalized linear mixed models (GLMMs). Parameters are estimated by an interative procedure, referred to as iterated re-weighted REML (IRREML). This procedure is an extension of the iterative re-weighted least squares algorithm for generalized linear models. An advantage of this approach is that it immediately suggests how to extend ordinary mixed-model methodology to GLMMs. This is illustrated for lambing difficulty data. IRREML can be implemented with standard software available for ordinary normal data mixed models. The connection with other estimation procedures, eg, the maximum a posteriori (MAP) approach, is discussed. A comparison by simulation with a related approach shows a distinct pattern of the bias of MAP and IRREML for heritability. When the number of fixed effects is reduced, while the total number of observations is kept about the same, bias decreases from a large positive to a large negative value, seemingly independently of the sizes of the fixed effects. © 1995 Elsevier/INRA.