Dynamic Latent Variable Models and Network Models

The collection and processing of so-called itensive longitudinal data (ILD) has increased substantially in psychology (and other social and behavioral sciences) in recent years (Trull & Ebner-Priemer, 2014). Dynamic latent variable models have been applied to ILD (e.g., dynamic structural equation models, DSEM, Asparouhov, Hamaker, & Muthén, 2018), which combine autoregressive time series models with confirmatory latent measurement models and multilevel modeling (for the purpose of accounting for inter-individual differences in trajectories). Although dynamic latent variable models are a rather general class of procedures, they have certain limitations with respect to the Bayesian estimation procedures applied and their confirmatory nature of the measurement models. A more explorative alternative to the analysis of multivariate relationships of observed variables is offered by so-called network models (e.g., Borsboom, 2008, 2022). These methods allow an unstructured examination of the relationship of variables for the purpose of detecting significant activation patterns. They have recently been further developed for ILD and inter-individual differences (cf. Epskamp, 2020), but have few discussed similarities and differences to dynamic latent variable models mentioned above in the literature. E.g., in the group of network models, the representation of heterogeneity (e.g., via latent classes) is not as flexible as in dynamic latent variable models. In this research project, four goals shall be addressed: 1. comparable submodels from both classes of methods shall be described and a systematic, taxonomic discussion of the models shall take place. This will be done against the background of the identification of relevant model gaps and the transferability of estimation procedures. 2) Reanalyzes of multilevel ILDs from a study on dropout in mathematics will be conducted using network models that have already been investigated with dynamic latent variable models in order to identify new patterns of correlation in the high-dimensional data. 3) Taking into account the taxonomic discussion, we aim to transfer and develop frequentist estimators for the submodels of dynamic latent variable models (e.g., FIML and multi-step approaches), for which Bayesian estimation has dominated so far. 4. building on the publication of a general Forward Filtering Backward Sampling (FFBS) algorithm for dynamic latent variable models (Kelava, Kilian, Glaesser, Merk, & Brandt, 2022), a forecasting algorithm for network models will be developed so that patterns of variables can be predicted (e.g., cognitions associated with dropout or clinical symptoms).

Project Team

Augustin Kelava

Vivato Andriamiarana

Kevin Kistermann

Grant

Funded by the Deutsche Forschungsgemeinschaft (DFG): Link

Status: started (10/2024 - )

On a generalization of the local independence assumption in item response theory

Local independence (LI) is a fundamental assumption of Item Response Theory (IRT) and captures the idea that, conditional on the value of some latent variable (e.g., ability), there is no association between a series of manifest variables (e.g., answers to items in psychological or educational tests). In practice, however, several effects (e.g., fatigue, changes in format, dependence between items) can substantially violate LI. This threatens model validity, invalidates the likelihood, and results in problematic estimates of the parameters and false substantial inferences. Research on the topic has been extensive, yet violations of LI remain an open problem with blurred boundaries. In an attempt to disentangle the concepts involved, a generalization of LI based on Knowledge Space Theory (KST) was recently suggested by Noventa, Spoto, Heller, & Kelava (2019). This integrated KST-IRT approach accounts indeed for `invasive' relations between items while retaining the usual characterization of LI. The combinatorial and set-theoretic approach of KST is used to identify the partial order representing the relation between the items and to obtain a generalized class of likelihoods that accounts for both response and trait dependence. Furthermore, the KST-IRT approach allows generalizing and transferring of techniques from polytomous items to collections of dichotomous ones, thus providing a further approach to the modeling of local dependence and an alternative item-based approach to testlets. The present project aims at investigating whether the KST-IRT approach can be used to formally systematize and investigate the different forms of local dependence and the different - and often unlinked - approaches that can be found in literature. Additionally, a new perspective is investigated on the modelling and testing of local dependence, polytomous items, and testlets based on bringing together different definitions and approaches that originated in the fields of Psychometrics and Mathematical Psychology. From an applied perspective, the project aims at implementing estimation procedures for the KST-IRT models in the open source R framework.

Project Team

Stefano Noventa

Andrea Spoto

Jürgen Heller

Florian Wickelmaier

Augustin Kelava

Grant

Funded by the Deutsche Forschungsgemeinschaft (DFG)

Status: finished (06/2021-06/2024)

Publications

Anselmi, P., Noventa, S., & Heller, J. (2024). Knowledge Structures and Related Theories. In J. Heller & L. Stefanutti (Eds.). Advanced Series on Mathematical Psychology: Volume 7. Knowledge Structures. Recent Developments in Theory and Application. World Scientific Publishing. https://doi.org/10.1142/9789811280481\_0003

Noventa, S., Faleh, R., & Kelava, A. (2024). On an EM-based closed-form solution for 2 parameter IRT models. arXiv preprint, arXiv:2411.18351. https://doi.org/10.48550/arXiv.2411.18351

Noventa, S. & Heller, J. (2024). Probabilistic Knowledge structures. In J. Heller & L. Stefanutti (Eds.). Advanced Series on Mathematical Psychology: Volume 7. Knowledge Structures. Recent Developments in Theory and Application. World Scientific Publishing. DOI: https://doi.org/10.1142/9789811280481\_0002 

Noventa, S., Ye, S., Kelava, A. & Spoto, A. (2024). On the Identifiability of 3- and 4-Parameter Item Response Theory Models From the Perspective of Knowledge Space Theory. Psychometrika, 89, 486-516. DOI: https://doi.org/10.1007/s11336-024-09950-z 

Noventa, S., Heller, J., & Kelava, A. (2024). Toward a unified perspective on assessment models, part I: Foundations of a framework. Journal of Mathematical Psychology, 122, 102872. DOI: https://doi.org/10.1016/j.jmp.2024.102872

Noventa, S., Heller, J., Ye, S., & Kelava, A. (2025). Toward a unified perspective on assessment models, part II: Dichotomous latent variables. Journal of Mathematical Psychology, 125, 10292. https://doi.org/10.1016/j.jmp.2025.102926

Ye, S., Kelava, A. & Noventa, S. (2023). Parameter Estimation of KST-IRT Model under Local Dependence. Psych, 5(3), 908-927. DOI: https://doi.org/10.3390/psych5030060 

Dynamic latent variable models: Finite sample properties and sparse estimation

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 a existing intensive longitudinal data sets analyses will be carried out using the latest technical approaches. 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.

Project team
Augustin Kelava
Holger Brandt
Vivato Andriamiarana

Grant

Funded by The Deutsche Forschungsgemeinschaft (DFG)

Status: finished (08/2020-07/2023)

Publications

Andriamiarana, V., Kilian, P., Brandt, H., & Kelava, A. (2025). Are Bayesian regularization methods a must for multilevel dynamic latent variables models? Behavior Research Methods, 57(2), 71. Link

Andriamiarana, V., Kilian, P., Kelava, A., & Brandt, H. (2023). On the requirements of non-linear dynamic latent class SEM: A simulation study with varying numbers of subjects and time points. Structural Equation Modeling, 30(5), 789-806. Link

Kelava, A., Kilian, P., Glaesser, J., Merk, S., & Brandt, H. (2022). Forecasting intraindividual changes of affective states taking into account interindividual differences using intensive longitudinal data from a university student drop out study in math. Psychometrika, 87(2), 533-558. Link

Nagel, M., Fischer, L., Pawlowski, T., & Kelava, A. (2024). An alternative prior for estimation in high-dimensional settings. Structural Equation Modeling: A Multidisciplinary Journal, 31(6), 939–951. Link

Due to a ruling of the Federal Constitutional Court, the previous regulation on the allocation of study places, by which a place was allocated after deduction of an advance quota according to the best Abitur grades (20%), after waiting time (20%) and a selection by the universities (60%), will have to be changed. In addition to the Abitur grade, further aptitude-based criteria are to be incorporated into the selection procedure of the universities. At present, corresponding selection criteria, including professional aptitude and voluntary services as well as competitions, are being agreed upon. The question of professional suitability thus represents a further aspect for student selection and the endeavour to select the prospective students with respect to their professional suitability has also existed for years due to the high number of applicants. So far, however, it is still unclear to what extent a selection based on previous practical professional experience actually represents a relevant additional qualification for later students. So far, a practical/professional pre-qualification bonus has been postulated as a success factor for vocational aptitude. The background of this is often the idea that applicants could have better access to the contents of their studies and also to later concrete professional practice on the basis of their previous experience, since they have already come into contact with the field in advance. It is therefore expected that applicants with vocational qualifications will be able to perform better in their studies, profit from their professional experience positively during their studies and later careers. Additionally it is to be expected that they will be better informed than applicants without a practical/professional pre-qualification about what to expect in their everyday medical careers.

This is the starting point for the proposed study with the following two core questions and subquestions: 

1. Are there any indications that students with previous practical experience in a profession perform better in their studies due to their previous experience than students without this previous experience?

a. Do students with previous work experience perform better in general, cognitive, psychosocial or practical activities than students without previous work experience? Is the bonus for the cognitive part in student selection justified? Or are they merely effects of self-enhancement from the individual's point of view

b. Do the advantages of the previous work experience remain constant, do they only occur at the beginning (more cognitive challenges) or only towards the end (more practical challenges)?

2. Are there any indications that a certain previous work experience shows lasting effects and that these significantly influence the medical specialisation after their studies (e.g. surgeon, general practitioner) (e.g. Azizzadeh, McCollum, Miller, Holliday, Shilstone, & Lucci Jr, 2003)?

This project is done in cooperation with the University of Heidelberg and the University of Freiburg under the lead of Prof. Dr. Zipfel of the medical faculty at the University of Tübingen and Prof. Dr. Kelava of the Methods Center at the University of Tübingen.

Grant

This project is funded by the  Ministry for Science, Research and Art of the county Baden-Württemberg.

Status

The project started on Jan 1, 2019

Ziel des Projektes war die Entwicklung eines serious game, in dem Fertigkeiten für die Durchführung narrativer Interviews geschult werden. Die Studierenden des Seminars entwickelten in Arbeitsgruppen einzelne Module des Spiels und erhielten dafür Unterstützung durch die Projektleitung, einen professionellen Spieleentwickler und eine Illustratorin. 

Projekt-Team: Leitung: Ursula Offenberger und Kevin Körner, Mitarbeitende: Studierende des Masterseminars “Einführung in die qualitative Interviewforschung” 

Laufzeit: 10/2021-4/2022

Förderung: Eberle-Stiftung zur Förderung von Digital Humanities

Das Projekt hatte zum Ziel, Angebote des Methodenzentrums für Bachelorstudierende der WISO-Fakultät zu etablieren und Blended-Learning-Konzepte weiterzuentwickeln. Insbesondere wurden Analysewerkstätten für qualitativ-interpretative Sozialforschung durchgeführt, Schulungen für computerunterstützte qualitative Datenanalyse (insbesondere ATLAS.ti und MAXQDA) angeboten, Online-Materialien zur Qualitativen Forschung bereitgestellt und Podcast-Sendungen mit Tübinger qualitativ forschenden ProfessorInnen veröffentlicht. 

Projekt-Team: Ursula Offenberger (Leitung), Maja Urbanczyk

Veröffentlichungen: E-Learning Modul zur Einführung in die Qualitative Forschung

Podcast “Nähkästchen Qualitative Forschung”

Laufzeit: 4/2019-12/2020

Förderung: Ministerium für Wissenschaft und Kunst des Landes Baden-Württemberg