ON BIASED INFERENCES ABOUT VARIANCE-COMPONENTS IN THE BINARY THRESHOLD-MODEL

A simulation study was conducted to study frequentist properties of th ree estimators of the variance component in a mixed effect binary thre shold model. The three estimators were: the mode of a normal approxima tion to the marginal posterior distribution of the component, which is denoted in the literature as marginal maximum likelihood (MML); the m ean of the marginal posterior distribution of the component, using the Gibbs sampler to perform the marginalisations (GSR); and third, the m ode of the joint posterior distributions of location and the variance parameter, used in conjunction with the iterative bootstrap bias corre ction (MJP-IBC). The latter was recently proposed in the literature as a method to obtain nearly unbiased estimators. The results of this st udy confirm that MML can yield biased inferences about the variance co mponent, and that the sign of the bias depends on the amount of inform ation associated with either fixed effects or with random effects. GSR can produce positively biased inferences when the amount of data per fixed effect is small. When lived effects are poorly estimated, the bi as persists, despite the fact that posterior distributions are guarant eed to be proper, and that the amount of information about the varianc e component is large. In this case, the marginal posterior distributio n of the variance component is highly peaked and symmetric, but it sho ws a shift towards the right with respect to the true (simulated) valu e. This bias can be reduced by assigning a Gaussian probability densit y function to the prior distribution of the fixed effects, but this st rategy does not work with very sparse data structures. The method base d on MJP-IBC yielded unbiased inferences about the variance component in all the cases studied. This estimator is computationally simple, bu t contrary to GSR with normal priors for the fixed effects, can lead t o estimates that fall outside the parameter space.