Dynamic latent variable models: Finite sample properties and regularized estimation

• Applicant: Professor Dr. Augustin Kelava
• Subject Area: Personality Psychology, Clinical and Medical Psychology, Methodology
• Term: from 2020 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 438291703

In recent years, technical developments have led to a substantial increase in the availability of so-called intensive longitudinal data (Trull & Ebner-Priemer, 2013). At the same time, elaborate theories (e.g., college student drop-out theories) call for the empirical integration of different data levels. These are intra-individual differences (e.g. affective changes), inter-individual differences (e.g. vulnerabilities) and time-specific influences (e.g. interventions). Often only unspecific functional forms of relationships are assumed and latent unobserved heterogeneities of trajectories can be found empirically. In order to model (intensive) longitudinal data and the theoretically expected processes, so-called dynamic latent variable models have been developed (e.g., Asparouhov, Hamaker, & Muthén, 2017, 2018). They do not fully meet the theoretically required complexity (e.g., in the case of college student drop-out theories). Thus, Kelava and Brandt (2019) proposed a comprehensive (so-called NDLC-SEM) framework. However, it can be stated that a) dynamic latent variable models were rarely used empirically, also because of their limitations, b) their finite sample properties are unclear with respect to the balance between sample size, number of measurement occasions, and the choice of prior distributions, and c) modern regularization techniques for the sparse estimation of these highly parameterized models (e.g., for the purpose of covariate selection) have not been sufficiently investigated. This project has three goals: 1.) Using an existing intensive longitudinal data set on college student drop-out in mathematics, reanalyses will be carried out using the latest technical approaches and, in particular, the temporal process of the discontinuation of studies will be examined. Furthermore, these results are compared with the results of traditional methodological approaches (e.g., multilevel analyses). 2.) As a second goal, extensive simulation studies will be conducted to investigate under which circumstances reliable parameter estimates can be expected for selected dynamic (NDLC-SEM) models. This concerns in particular the question of the balance of the following determinants: i) number of cases, ii) number of measurement occasions, iii) model complexity, and iv) specification of the prior distributions. 3.) As a third goal, regularization techniques (e.g., Bayesian adaptive Lasso and horseshoe+ Priors) will be investigated in detail in the context of dynamic latent variable models with regard to their ability to reduce parameters and select variables.

• DFG Programme: Research Grants