Modeling the interaction between persons and items for binary response data, item response theory (IRT) has been found useful in a wide variety of applications. Over the past decades, studies have been conducted on the development and application of unidimensional as well as multidimensional IRT models. However, little literature exists on IRT-based models that incorporate one general trait and several specific trait dimensions. This book, therefore, proposes such models in the Bayesian hierarchical framework, assesses their performances in various testing situations and further compares them with the conventional IRT models using Bayesian model choice techniques. Results from the analysis suggest that the proposed models offer a better way to represent the test situations not realized in existing models. The methodology and analysis should shed some light on the development of complex IRT models and the statistical procedures for parameter estimation, and should be especially useful to professionals in educational and psychological measurement, or anyone who may be considering utilizing IRT models for assessing persons' continuous latent traits.