  The longitudinal process that leads to university student drop out in STEM
subjects 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 for
intensive 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 latent
or observed variables based on ongoing data collection has not been an
extensive research topic. From a practical perspective, there has been no
empirical study on student drop out in math that integrates ILD, dynamic
frameworks, and forecasting of critical states of the individuals allowing for
real-time interventions. In this paper, we show how Bayesian forecasting of
multivariate intra-individual variables and time-dependent class membership of
individuals (affective states) can be performed in these dynamic frameworks. To
illustrate our approach, we use an empirical example where we apply forecasting
methodology to ILD from a large university student drop out study in math with
multivariate observations collected over 50 measurement occasions from multiple
students (N = 122). More specifically, we forecast emotions and behavior
related to drop out. This allows us to model (i) just-in-time interventions,
(ii) detection of heterogeneity in trajectories, and (iii) prediction of
emerging dynamic states (e.g. critical stress levels or pre-decisional states).

Methodology;Applications