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University student dropout, particularly in Science, Technology, Engineering, and Mathematics (STEM) subjects, represents a significant challenge for both modern economies and the affected individuals. In the German context, for example, approximately 40 percent of students drop out in the early phase of math studies, a rate considerably higher than the average across all subjects. Traditional models of student attrition often rely on factors that are static or measured only periodically, failing to capture the dynamic, time-sensitive psychological processes that immediately precede a student’s decision to quit.

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The Project Solution: A Dynamic, Real-Time Forecasting Approach

Our project introduces a new methodological approach designed to forecast critical states related to university student dropout, allowing for real-time inferences and the possibility of intervention based on ongoing data collection. This approach utilizes Intensive Longitudinal Data (ILD) and dynamic latent variable model frameworks, such as the Nonlinear Dynamic Latent Class Structural Equation Model (NDLC-SEM). The project focuses on studying individual factors associated with dropout by separating and analyzing two fundamental levels of individual characteristics:

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1. Inter-Individual Differences

These are relatively stable personal characteristics or traits that generally remain consistent across time and situations.
  • Examples: Cognitive abilities (IQ), gender, and pre-university academic performance.
  • Role in the Model: These factors describe differences between individuals (e.g., why one student is generally more academically prepared than another).

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2. Intra-Individual Changes (Affective and Cognitive States)

These refer to changeable psychological states that vary within an individual over time in response to external experiences and stimuli. Investigating these changes is crucial because they capture the individual psychological processes directly linked to outcomes like dropout.
  • Examples: Motivational and affective states, goal orientation, fear of failure, subjective feelings of being overwhelmed/stressed, positive and negative affective states (PAN/PAP), and the current intention to quit.
  • Role in the Model: These factors describe the longitudinal process that leads to dropout and are best studied using high-frequency longitudinal designs (ILD) due to their volatile nature. The model specifically forecasts multivariate intra-individual changes of affective states and time-dependent class membership (unobserved heterogeneity, or “intention to quit”).

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Key Impact and Value Proposition

By applying the proposed forecasting method (using a Forward Filtering Backward Sampling (FFBS) method) to ILD gathered from university math students, the project achieved significant predictive results:
  • Prediction of Critical States: Demonstrated the capability to predict emerging critical dynamic states (such as high stress levels or pre-decisional states) related to dropout.
  • The Intervention Window: For students who eventually dropped out, the model detected the switch to the latent state of “intention to quit” on average at time point t = 22.2 (approximately the 8th week of the study program). This critical period is 8 weeks before the actual dropout behavior was observed (on average at t = 45.0).
  • Actionable Insights: Indicates that early monitoring and timely interventions are essential and more likely to be successful. The methodology provides a data-driven basis to identify individuals at risk well in advance of their decision, offering a clear opportunity to intervene and potentially prevent attrition.
  • Model Performance: The simulation study showed that the method’s sensitivity (correctly detecting persons who switched states) was very good (above 0.91) even with smaller sample sizes, supporting the validity of forecasting individual trajectories and changes over time.