In IRT models, the latent scores θj are typically assumed to be random draws from a normal distribution. When we are interested in the extent to which individual differences on the latent trait are heritable, we only need to decompose the variance of the θjs using, for example, the classical twin design. There are two approaches. The first approach is to first estimate the parameters of the IRT model using standard IRT software (such as, Bilog, Multilog, Parscale, Testfact, ConQuest, OPLM), and then to have the same software estimate each individual score on the latent trait. Next, one uses these estimates of the θjs as observed values in a standard variance decomposition analysis. This we call the two-step approach.
