Bias reduction of approximate maximum likelihood estimates for heritability in threshold models

Approximate maximum likelihood estimates, such as penalized quasi-likelihood and iterated reweighted REML estimates, for heritability or intraclass correlation in threshold models for binary data can be seriously biased. Two approaches to correct for this bias are studied, with emphasis on animal breeding models for binary data. Scope for reduction of bias of heritability estimates is found to be slim because of the commonly large number of fixed effects in animal breeding models. Minimal dimensions for the data are identified such that bias and root-mean-squared error are of modest size and useful inference on heritability (or intraclass correlation) is feasible.