When a simple IRT model does not fit the data, one could consider deleting or changing bad fitting items, and/or deleting bad fitting persons. Alternatively, one could consider using more general IRT models that offer many possibilities of obtaining model fit. General frameworks for multi-level and multi-dimensional IRT models are outlined in Skrondal and Rabe-Hesketh (2004) and De Boeck and Wilson (2004). In the specific context of genetic modelling, it might also occur that a particular subset of items show relatively high genetic correlations compared to the remaining items. In that case a more appropriate model would be an independent pathway model for categorical or ordinal traits (see for instance Van den Berg et al. 2006b).
