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The longitudinal process that leads to university student drop out in STEMsubjects can be described by referring to a) inter-individual differences(e.g., cognitive abilities) as well as b) intra-individual changes (e.g.,affective states), c) (unobserved) heterogeneity of trajectories, and d)time-dependent variables. Large dynamic latent variable model frameworks forintensive longitudinal data (ILD) have been proposed which are (partially)capable of simultaneously separating the complex data structures (e.g., DLCA;Asparouhov, Hamaker, & Muth\'en, 2017; DSEM; Asparouhov, Hamaker, & Muth\'en,2018; NDLC-SEM, Kelava & Brandt, 2019). From a methodological perspective,forecasting in dynamic frameworks allowing for real-time inferences on latentor observed variables based on ongoing data collection has not been anextensive research topic. From a practical perspective, there has been noempirical study on student drop out in math that integrates ILD, dynamicframeworks, and forecasting of critical states of the individuals allowing forreal-time interventions. In this paper, we show how Bayesian forecasting ofmultivariate intra-individual variables and time-dependent class membership ofindividuals (affective states) can be performed in these dynamic frameworks. Toillustrate our approach, we use an empirical example where we apply forecastingmethodology to ILD from a large university student drop out study in math withmultivariate observations collected over 50 measurement occasions from multiplestudents (N = 122). More specifically, we forecast emotions and behaviorrelated to drop out. This allows us to model (i) just-in-time interventions,(ii) detection of heterogeneity in trajectories, and (iii) prediction ofemerging dynamic states (e.g. critical stress levels or pre-decisional states).

psychometrika

Forecasting intra-individual changes of affective states taking into  account inter-individual differences using intensive longitudinal data from a  university student drop out study in math