Free Access
Genet. Sel. Evol.
Volume 37, Number 1, January-February 2005
Page(s) 31 - 56
Genet. Sel. Evol. 37 (2005) 31-56
DOI: 10.1051/gse:2004035

A general approach to mixed effects modeling of residual variances in generalized linear mixed models

Kadir Kizilkaya and Robert J. Tempelman

Department of Animal Science, Michigan State University, East Lansing, MI 48824-1225, USA

(Received 25 March 2004; accepted 24 July 2004)

Abstract - We propose a general Bayesian approach to heteroskedastic error modeling for generalized linear mixed models (GLMM) in which linked functions of conditional means and residual variances are specified as separate linear combinations of fixed and random effects. We focus on the linear mixed model (LMM) analysis of birth weight (BW) and the cumulative probit mixed model (CPMM) analysis of calving ease (CE). The deviance information criterion (DIC) was demonstrated to be useful in correctly choosing between homoskedastic and heteroskedastic error GLMM for both traits when data was generated according to a mixed model specification for both location parameters and residual variances. Heteroskedastic error LMM and CPMM were fitted, respectively, to BW and CE data on 8847 Italian Piemontese first parity dams in which residual variances were modeled as functions of fixed calf sex and random herd effects. The posterior mean residual variance for male calves was over 40% greater than that for female calves for both traits. Also, the posterior means of the standard deviation of the herd-specific variance ratios (relative to a unitary baseline) were estimated to be $0.60\pm0.09$ for BW and $0.74\pm0.14$ for CE. For both traits, the heteroskedastic error LMM and CPMM were chosen over their homoskedastic error counterparts based on DIC values.

Key words: Bayesian analysis / genetic evaluation / heterogeneous variances / threshold model

Correspondence and reprints:

© INRA, EDP Sciences 2004