Research at the Institute
Quantitative
GLI Project
On a generalization of the local independence assumption in item response theory
Student Selection in Medicine
DLV Project
Dynamic latent variable models: Finite sample properties and sparse estimation
Summary
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 (Mercator Fellow)
Grant
Funded by The Deutsche Forschungsgemeinschaft (DFG)
Status: Not started
NON-NORM Project
In the past years, there was a growing insight that using linear latent variable models did not suffice neither to answer detailed research questions nor to account for the challenges of complex empirical data. Typical challenges are multilevel data structures, non-normal data and nonlinear relationships between variables. The modeling of such data specifities has two advantages: First, if these data specificites were neglected, the results and conclusion drawn by the researchers might be spurious. And, second, a more detailed modeling allows for a more in-depth analysis of research questions, for example, by identifying unobserved subgroups or the differentiation of nonlinear relationships on individual and cluster level.
The NON-NORM research project addresses the following extensions of (nonlinear) latent variable models: A general nonlinear multilevel structural equation mixture model (GNM-SEMM) will be extended to allow for an analysis of longitudinal heteroskedastic data. An R-package will be provided for substantial researchers. Semiparametric structural equation models will be generalized to non-Bayesian, nonparametric, distribution-free structural equation models. The finite sample properties of the developed semi- and nonparametric models will be examined in simulation studies. Finally, multidimensional item response models will be extended to allow for nonlinear semiparametric effects.
Project team: Augustin Kelava (PI), Holger Brandt (PI), Stefano Noventa, Tim Schaffland, & Nora Umbach
Grant:
Funded by The Deutsche Forschungsgemeinschaft (DFG): KE 1664/1-1, KE 1664/1-2, BR 5175-1-2
Status: April 1, 2013 - July 31, 2018 (completed)
Software:
nlsem: Fitting Structural Equation Mixture Models – Estimation of structural equation models with nonlinear effects and underlying nonnormal distributions.
r-package: https://cran.r-project.org/web/packages/nlsem/index.html
Matlab: An implementation of the non-parametric structural equation modeling approach (Kelava, Kohler, Krzyzak, & Schaffland, 2017) can be found here: https://github.com/tifasch/nonparametric
SAM – College drop-out in Mathematics (German: “Studienabbruch in der Mathematik”)
The high drop-out rate in mathematics and natural sciences during the university B.Sc. phase is a well-known phenomenon (Heublein, 2014). The research project “University drop-out in Mathematics” addresses the following questions: a) what is the relative importance of individual predictors of drop-out in the interaction of multiple causes? b) How can drop-out be modelled as a process (taking into account the interdependencies of the predictors)? c) How can the probability of dropping out of university be reduced in term time (given very limited resources)?
The modelling of university drop-out will provide detailed insights into the temporal antecedents of drop-out. In the first step, a preliminary forecast model is developed (based on the reanalysis of extensive data sets). In Tübingen, this result is to be used initially to identify the multiple risk factors in existing cohorts and to make predictions on the probability of dropping out. The risk assessment makes it possible to advise students at risk. In the course of the project, further longitudinal data will be collected, and analytical techniques and the identification of risk constellations will be improved, so that a more targeted approach to those at risk can be implemented.
The sub-project “Determinants and Intervention” at the University of Stuttgart can in turn be divided into two sub-projects. Competence measurement instruments will be developed or existing instruments will be adapted in order to construct time-sensitive prediction models of drop-out (sub-project 1). This will enable us to track the subject-specific achievements of students in the first year of their studies, which is a particularly sensitive period for drop-out. In addition to this, an intervention involving an experimental and control group design is being developed and carried out in order to reduce the performance and motivation-related drop-outs or change of course of study in mathematics (sub-project 2). This intervention follows the Cognitive Apprenticeship Approach (e.g. Collins, Brown & Newman, 1989) Several studies in the vocational school sector have already shown this approach to be effective in improving competence and motivation.
Grant:
This research is funded by a grant of the Federal Ministry of Education and Research (Bundesministerium für Bildung und Forschung; BMBF).
Status: running (since April 1, 2017)