Exploring and Developing the Item Response Model with Hierarchical Latent Traits

Many latent traits in human sciences have a hierarchical structure. This study aims to construct an item response model to account for such a hierarchical structure in latent traits, which is called item response model with hierarchical latent traits (MHLT). Through a series of simulations, the Markov chain Monte Carlo (MCMC) estimation was used to estimate model parameters and the Bayesian model checking techniques including the posterior predictive model checking (PPMC) and model comparison methods were implemented to detect the misfit of the MHLT to the data. Five test statistics for the PPMC were included: the Bayesian chi-square test, standard deviation of the biserial correlations, and reproduced correlation matrix, raw score covariance between tests, and test of identical latent trait. For model comparison, the author computed the pseudo-Bayes factor (PsBF) and Bayesian DIC index. The model parameter recovery was assessed by the bias and root mean square error (RMSE). The results are predicted that the Bayesian model fit checking techniques can detect the misfit to the inappropriate data sets and the model parameter can be well recovered with the computer program WinBUGS.