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1. The Context of Urgency in STEM Dropout

The research targets the critical issue of university student dropout from Science, Technology, Engineering, and Mathematics (STEM) fields, which represents an important issue for both modern economies and individuals. The study focuses specifically on mathematics students at a German university. This focus is motivated by the severe attrition rates in the subject — approximately 40% of students drop out in the early phase of math studies in Germany, a rate considerably higher than the 33% average across all subjects. Since the majority of students drop out during their first semester, large introductory courses, such as calculus and algebra, were considered suitable contexts for this examination. The cohort attending the calculus lecture during the 2017/2018 winter semester was deemed prototypical for the general phenomenon.

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2. Theoretical Foundation: The Procedural Nature of Dropout

The research design builds on the consensus that the university dropout decision has a procedural nature, requiring longitudinal study designs to model it appropriately. To capture this complex process, the study simultaneously analyzed two fundamental types of individual factors, recognizing that stable characteristics alone often fail to capture the critical psychological processes leading to dropout.

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2.1 Inter-Individual Differences (Stable Trait Level)

This level comprises relatively stable personal characteristics or traits that remain consistent over time and across situations.
These factors describe differences between individuals. Examples of Inter-Individual Measures:
  • Gender
  • Cognitive ability (IQ)
  • Pre-university academic performance (GPA)

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2.2 Intra-Individual Changes (Volatile State Level)

This level consists of changeable psychological states that vary within an individual over time in response to external experiences and stimuli.
Investigating these intra-individual changes is central to forecasting because they capture the dynamic longitudinal process leading to dropout. Given their volatility, these states require a high-frequency longitudinal design. Examples of Intra-Individual Measures:
  • Motivational states
  • Affective states
  • Goal orientation
  • Current intention to quit the course
The overall model specification integrates these two levels, alongside latent heterogeneity (latent classes) and time-dependent variables, to represent the dropout process in full dynamic complexity.

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3. Study Setting, Sample, and Participation

The empirical basis for this project is the SAM (University Dropout in Mathematics) study. Setting:
Data were collected from a first-semester cohort attending a calculus lecture and tutorial sessions at a German university during the 2017/2018 winter semester. Sample:
  • N=122N = 122 students participated in online surveys.
  • Participation rate: 67.03% of the eligible population.
Sample Characteristics:
  • Average age: 19.60 years
  • Gender: 55 female (45.08%), 66 male (54.09%)
  • Programs: Mathematics B.Sc., Mathematics B.Ed. (teacher candidates), and Physics B.Sc.
  • Academic background: Mean GPA (Abitur) = 1.86

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4. Intensive Longitudinal Data (ILD) Collection Methodology

To effectively capture the volatile state-level changes, the SAM study implemented a rigorous ILD framework, integrating data from three distinct sources across the semester.

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4.1 Source 1: Initial Assessment (Stable Trait Measures)

Conducted during week 2 of the first semester, the initial assessment collected inter-individual characteristics. Measures Included:
  • Cognitive Abilities (IQ): German adaptation of the Culture Fair Intelligence Test Scale 3 (CFT-3)
  • Academic Performance:
    • German GPA (Abitur)
    • Final math grade from school
    • Performance on TIMSS items
  • Psychosocial Measures:
    • Personality via BFI-2-XS (Big Five Inventory short form)
    • Locus of Control via IE-4 scale
    • Professional interests via Holland’s RIASEC model (AIST-R)
  • Affective Baseline:
    • Positive and Negative Affect measured using PANAS (PAP/PAN scales)

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4.2 Source 2: High-Frequency Online Surveys (Changeable State Measures)

Beginning one week after the initial assessment, the core longitudinal data collection was conducted via frequent online surveys. Frequency and Duration:
  • Nt=50N_t = 50 measurement occasions
  • Spanning 131 days (~3 surveys per week)
  • Each survey lasted approximately 5 minutes
  • Average participation per student: 20.22 surveys
Survey Content:
  • Re-assessed motivational and affective states
  • Captured dropout-related factors:
    • Current intention to quit
    • Fear of failure
    • Feelings of being overwhelmed or stressed
    • Self-assessed understanding of course content

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4.3 Source 3: Outcome and Performance Data

This dataset informed the criterion variable (dropout) and supported latent state estimation. Key Details:
  • Weekly collection: Tutorial performance and attendance
  • Dropout identification: Enabled early detection of dropout events during the semester
This design allowed the latent discrete state variable (SitS_{it}), representing the “intention to quit”, to be treated as partially observed whenever manifest dropout occurred (i.e., if a student quit at time tt, then Sit=s=2S_{it} = s=2 was observed).
Summary:
The SAM Study’s design exemplifies a methodological innovation in educational psychology — leveraging Intensive Longitudinal Data to model dynamic intra-individual change and predict critical dropout-related psychological states in real time.