Paul Buerkner writes:

A lot of concepts in psychology and the social sciences can be formulated in terms of latent variables measured indirectly by observable data. However, existing statistical approaches remain limited in how they can express latent variables and relate them to each other. The goal of this project is to build advanced statistical models that better respect the probabilistic structures of latent variables and thus allow to obtain improved insights and predictions based on such 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. Throughout the project, we will make extensive use of Stan and will later on integrate the developed methods in brms as well.

For more details about the position, please see https://www.stellenwerk.de/stuttgart/jobboerse/phd-student-position-mfd-part-time-75prozent-payment-according-to-e13-tv-l-temporary-for-the-duration-of-3-years-220304-82653/

Looks like fun!