Application of Bayesian Inference using Gibbs Sampling to Item-Response Theory Modeling of Multi-Symptom Genetic Data

Several “genetic” item-response theory (IRT) models are fitted to the responses of 1086 adolescent female twins to the 33 multi-category item Mood and Feeling Questionnaire relating to depressive symptomatology in adolescence. A Markov-chain Monte Carlo (MCMC) algorithm is used within a Bayesian framework for inference using Gibbs sampling, implemented in the program WinBUGS 1.4. The final model incorporated separate genetic and non-shared environmental traits (“A and E”) and item-specific genetic effects. Simpler models gave markedly poorer fit to the observations judged by the deviance information criterion (DIC). The common genetic factor showed major loadings on melancholic items, while the environmental factor loaded most highly on items relating to self-deprecation. The MCMC approach provides a convenient and flexible alternative to Maximum Likelihood for estimating the parameters of IRT models for relatively large numbers of items in a genetic context. Additional benefits of the IRT approach are discussed including the estimation of latent trait scores, including genetic factor scores, and their sampling errors.