Dynamic latent variable models: Finite sample properties and regularized estimation
Final Report Abstract
The project focused on methodical developments of dynamic latent variable models, particularly the NDLC-SEM (Nonlinear Dynamic Latent Class Structural Equation Model) approach. The primary scientific questions focused on the performance of these models in situations with small sample sizes (number of persons N vs. number of time points T ), the integration of regularization methods in the presence of a large number of covariates, and the empirical validation of these models through their application to a dataset on dropout in mathematics (Tübingen SAM dataset). One of the key outcomes of the project was the successful reanalysis of the SAM dataset. It was demonstrated that the NDLC-SEM framework is capable of accurately predicting affective states and potential dropout risks as latent states. In particular, temporally varying predictors, such as changes in affective experiences, were identified, allowing for the prediction of dropouts approximately eight weeks in advance. These results underscore the value of dynamic models, as they can simultaneously account for both inter-individual differences and intra-individual changes in the prediction process. Another significant advancement was the development of a Forward Filtering Backward Sampling (FFBS) forecasting procedure, specifically designed for prediction in regimeswitching time series models. This procedure enables the prediction of not only quantitative but also discrete latent states by integrating continuous latent state variables. This represents a major methodological innovation that previous models were unable to achieve. In addition to these methodological advancements, the project also laid the theoretical foundations for the application of regularization methods in dynamic latent models. This was particularly relevant for handling the numerous covariates often collected in psychological and educational studies. It was shown that the use of regularization methods, such as ridge-like approaches, can make the estimation of such models more robust, which is especially advantageous in settings with small sample sizes. Concrete recommendations were also developed on how to design studies concerning the number of persons (N ) and time points (T ) in combination with the choice of prior distributions. The project led to several significant publications that not only contribute to the theoretical advancement of dynamic latent variable models but also demonstrate their practical utility in empirical research, particularly in areas where the prediction of behavioral and state changes is of central importance.
Publications
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Forecasting Intra-individual Changes of Affective States Taking into Account Inter-individual Differences Using Intensive Longitudinal Data from a University Student Dropout Study in Math. Psychometrika, 87(2), 533-558.
Kelava, Augustin; Kilian, Pascal; Glaesser, Judith; Merk, Samuel & Brandt, Holger
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On the Requirements of Non-linear Dynamic Latent Class SEM: A Simulation Study with Varying Numbers of Subjects and Time Points. Structural Equation Modeling: A Multidisciplinary Journal, 30(5), 789-806.
Andriamiarana, Vivato; Kilian, Pascal; Kelava, Augustin & Brandt, Holger
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An Alternative Prior for Estimation in High-Dimensional Settings. Structural Equation Modeling: A Multidisciplinary Journal, 31(6), 939-951.
Nagel, Michael; Fischer, Lukas; Pawlowski, Tim & Kelava, Augustin
