Bayesian Distributional Latent Variable Models

In psychology and related sciences, a lot of research is concerned with studying latent variables, that is, constructs which are not directly observable.  Statistical methods for modeling latent variables based on manifest (observable) indicators are thus crucial to scientific progress in those fields. Two major interconnected statistical areas dealing with latent variables exist, namely, Item Response Theory (IRT) and Structural Equation Modeling (SEM). Although the two fields are closely connected, the frontiers of IRT and SEM have developed in different directions. IRT has focused on building increasingly complex measurement models of psychological data. They are often represented as distributional models, where not only the location but also other response distribution parameters such as scale or shape are related to item or person characteristics. Such distributional models have gained considerable momentum in various fields, such as cognitive psychology, where individuals' responses are determined by multiple underlying processes. In comparison, SEM research has focused more strongly on extending the structural model part which enables increasingly complex regression models involving latent endogenous and/or exogenous variables. A combination of these two major frontiers would enable researchers to tackle a lot of advanced psychological research questions at the intersection of psychometrics, personnel psychology, cognitive psychology, and applied psychology. For us to gain better insights into behavioral and cognitive processes, their mathematical approximations should match the processes' complexity in both overall distributional form and its components that are expressed as complex functions of predicting variables.