Bayesian Distributional Latent Variable Models

• Applicant: Dr. Paul-Christian Bürkner
• Subject Area: Personality Psychology, Clinical and Medical Psychology, Methodology
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 497785967

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 the 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 more applied psychological fields. In order 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. The primary goal of the proposed research is to develop a framework for Bayesian distributional latent variable models (BD-LVMs) that combines the principles of IRT and SEM with the flexibility of distributional regression powered by modern Bayesian estimation methods. The primary goal can be subdivided into three objectives: O1: Distributional structural models. Develop and evaluate distributional structural models where latent variables estimated by standard measurement models are used within distributional regression as endogenous and/or exogenous variables. O2: Distributional measurement models. Develop and evaluate distributional measurement models to flexibly define latent variables via distributional properties of indicator variables, thus generalizing standard definitions of latent variables. O3: Provisioning as open-source code. Implement the developed methods in Bayesian statistical software. We will focus on the implementation in the probabilistic programming language Stan and the brms R package as a higher-level interface to Stan.

• DFG Programme: Research Grants