The existence of heterogeneous genetic and residual variances across environments has been established for a number of production traits (e.g. San Cristobal et al., 1993; Meuwissen et al., 1996). The ignorance of such heteroskedascity can lead to biased predictions of breeding values, potentially favoring a disproportionate numbers of animals selected from high variance environments (Hill, 1984).  Recently, residual heteroskedasticity extensions have been 
 proposed for threshold model analysis of ordinal categorical data (Foulley and Gianola, 1996; Jaffrézic et al., 1999). However, many of the proposed models invoke analytical approximations which appear tenuous, particularly for the analysis of categorical data. 
 Furthermore, we perceive the lack of a unifying framework for structural modeling of heterogeneous variances in generalized linear mixed model (GLMM) analysis of either continuous production or categorical fitness traits. The objective of our study is to propose a Bayesian structural multiplicative model on residual variances for observed or augmented variables in heteroskedastic GLMM, concentrating on a cumulative probit threshold model analysis of ordinal data based on use of Markov Chain Monte Carlo (MCMC) methods.  

K. Kizilkaya, Robert J Tempelman

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume 2002. Session 16, , 16.15, 2002
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