Here, we estimate A and E variance components using a 1PL measurement model. A main effect of sex, δ, was modelled on the latent trais. The seven original items with three response categories were transformed into 14 dichotomous dummy items for each individual as described above. A separate β-parameter was estimated for each dummy item, so that for each original item there are two β-parameters. For the variance components, locally non-informative (‘‘flat’’) inverse gamma priors were used, and for the β and δ parameters we used locally non-informative normal priors. The parameterisation modelled the variances of sum and differences scores for the latent trait (Van den Berg et al. 2006a). The appendix gives the WinBUGS script. Three independent MCMC chains were used with randomised starting values. The chains converged rapidly to the stationary distribution with relatively low autocorrelations. The first 1000 iterations were discarded as burn-in samples, and a further 1000 iterations were used for inference.
