arXiv subjects

Jakob Schwerter

Publications and source records attributed to Jakob Schwerter.

8 recordsLinked to original sources

arXiv2026

Early Prediction of Student Performance Using Bayesian Updating with Informative Priors Across Cohorts

Early identification of at risk students in higher education depends on predictive models that maintain accuracy across successive cohorts -- a requirement that single-cohort modeling approaches fail to meet. This study evaluates Bayesian updating with informative priors from a previous cohort to improve cross-cohort prediction robustness using digital trace data. We fit weekly Bayesian linear, logistic, and ordinal regression models with either uninformative default priors or informative priors derived from posterior distributions of a preceding cohort. Models were applied to six weekly self-regulated learning (SRL)-aligned engagement indicators from two consecutive cohorts of students in a blended first-year mathematics course (N1 = 307; N2 = 323). Outcomes were exam points, final grades, and a binary at risk indicator. The models were evaluated weekly based on accuracy, sensitivity, and RMSE. In the source cohort, performance was already substantial by week 6. In the target cohort, informative priors improved early classification: Logistic models with priors reduced misclassification by 22% and false negatives by 38% in week 3 relative to the uninformative default. Ordinal models with priors similarly showed the strongest improvements in early weeks, reducing misclassification by 42% in week 2 and reaching an accuracy of .77 by week 4. Linear models showed little benefit from prior information. These findings demonstrate that Bayesian updating is a viable method for improving early classification performance across cohorts, with gains concentrated in the early weeks of the semester when current-cohort data are scarce.

stat.AP↗

arXiv2026

Cross-Course Generalizability of SRL-Aligned Predictive Models Using Digital Learning Traces

STEM dropout rates remain high at universities, particularly in computer science programs with theory-intensive courses. Digital learning environments now capture rich behavioral data that could help identify struggling students early, yet the generalizability of data-driven prediction models across courses and institutions remains uncertain. Guided by self-regulated learning (SRL) theory, this study analyzed multimodal digital-trace data from three undergraduate theoretical computer science courses (N1 = 137, N2 = 104, N3 = 148) at two universities. Weekly SRL-aligned digital-trace indicators were modeled using Elastic Net, Random Forest, and XGBoost to evaluate predictive performance over time and across settings, and model calibration both within and across courses. Early prediction of at-risk students was feasible, with SRL-related behaviors such as time management, effort regulation, and sustained engagement emerging as key predictors. While Random Forest achieved the highest in-sample accuracy, Elastic Net generalized more robustly across contexts. Out-of-sample accuracy and calibration declined between institutions with different base rates, underscoring the contextual nature of predictive analytics in higher education. These findings suggest that digital learning traces enable early identification of at-risk students within courses, but generalizing predictive models beyond their original context requires caution, particularly if the at-risk rates differ between contexts.

cs.CY↗

arXiv2025

Difficulty Generating Factors for Context-free Language Construction Assignments

Computer science students often struggle with abstract theoretical concepts, particularly in introductory courses on theoretical computer science. One such challenge is understanding context-free languages and their various representations. In this study we investigate factors that influence the difficulty of constructing context-free grammars and pushdown automata for context-free languages. We propose two potential difficulty generating factors targeting how a language is presented to students: representation in natural language and as a verbose set notation. Furthermore, we propose two factors targeting the structure of the given context-free language: nesting of constructs and insertion of multiplicities. We conducted a controlled experiment using within-subject randomization in an interactive learning system, testing the proposed difficulty factors for constructing context-free grammars and pushdown automata. Our results suggest that three of the four factors significantly influence students' objective performance in solving exercises for constructing context-free grammars, while students' perceived difficulties only partly align with the objective performance measures. The findings for pushdown automata tasks differed markedly from those for context-free grammar tasks. Our variations either had negligible effects or, in some cases, even reduced difficulty. Thus, no robust statistical conclusions can be made for pushdown automata tasks. The results lay foundations for learning systems that adaptively choose appropriate exercises for individual students.

cs.CY↗

arXiv2025

Adapting tree-based multiple imputation methods for multi-level data? A simulation study

When data have a hierarchical structure, such as students nested within classrooms, ignoring dependencies between observations can compromise the validity of imputation procedures. Standard tree-based imputation methods implicitly assume independence between observations, limiting their applicability in multilevel data settings. Although Multivariate Imputation by Chained Equations (MICE) is widely used for hierarchical data, it has limitations, including sensitivity to model specification and computational complexity. Alternative tree-based approaches have shown promise for individual-level data, but remain largely unexplored for hierarchical contexts. In this simulation study, we systematically evaluate the performance of novel tree-based methods--Chained Random Forests and Extreme Gradient Boosting (mixgb)--explicitly adapted for multi-level data by incorporating dummy variables indicating cluster membership. We compare these tree-based methods and their adapted versions with traditional MICE imputation in terms of coefficient estimation bias, type I error rates and statistical power, under different cluster sizes, missingness mechanisms and missingness rates, using both random intercept and random slope data generation models. The results show that MICE provides robust and accurate inference for level 2 variables, especially at low missingness rates. However, the adapted boosting approach (mixgb with cluster dummies) consistently outperforms other methods for Level-1 variables at higher missingness rates (30%, 50%). For level 2 variables, while MICE retains better power at moderate missingness (30%), adapted boosting becomes superior at high missingness (50%), regardless of the missingness mechanism or cluster size. These findings highlight the potential of appropriately adapted tree-based imputation methods as effective alternatives to conventional MICE in multilevel data analyses.

stat.AP↗

arXiv2024

Which Imputation Fits Which Feature Selection Method? A Survey-Based Simulation Study

Tree-based learning methods such as Random Forest and XGBoost are still the gold-standard prediction methods for tabular data. Feature importance measures are usually considered for feature selection as well as to assess the effect of features on the outcome variables in the model. This also applies to survey data, which are frequently encountered in the social sciences and official statistics. These types of datasets often present the challenge of missing values. The typical solution is to impute the missing data before applying the learning method. However, given the large number of possible imputation methods available, the question arises as to which should be chosen to achieve the 'best' reflection of feature importance and feature selection in subsequent analyses. In the present paper, we investigate this question in a survey-based simulation study for eight state-of-the art imputation methods and three learners. The imputation methods comprise listwise deletion, three MICE options, four \texttt{missRanger} options as well as the recently proposed mixGBoost imputation approach. As learners, we consider the two most common tree-based methods, Random Forest and XGBoost, and an interpretable linear model with regularization.

stat.AP↗

arXiv2024

Interpretable Prediction Rule Ensembles in the Presence of Missing Data

Prediction Rule Ensembles (PREs) are robust and interpretable statistical learning techniques with potential for predictive analytics, yet their efficacy in the presence of missing data is untested. This study uses multiple imputation to fill in missing values, but uses a data stacking approach instead of a traditional model pooling approach to combine the results. We perform a simulation study to compare imputation methods under realistic conditions, focusing on sample sizes of $N=200$ and $N=400$ across 1,000 replications. Evaluated techniques include multiple imputation by chained equations with predictive mean matching (MICE PMM), MICE with Random Forest (MICE RF), Random Forest imputation with the ranger algorithm (missRanger), and imputation using extreme gradient boosting (MIXGBoost), with results compared to listwise deletion. Because stacking multiple imputed datasets can overly complicate models, we additionally explore different coarsening levels to simplify and enhance the interpretability and performance of PRE models. Our findings highlight a trade-off between predictive performance and model complexity in selecting imputation methods. While MIXGBoost and MICE PMM yield high rule recovery rates, they also increase false positives in rule selection. In contrast, MICE RF and missRanger promote rule sparsity. MIXGBoost achieved the greatest MSE reduction, followed by MICE PMM, MICE RF, and missRanger. Avoiding too-course rounding of variables helps to reduce model size with marginal loss in performance. Listwise deletion has an adverse impact on model validity. Our results emphasize the importance of choosing suitable imputation techniques based on research goals and of advancing methods for handling missing data in statistical learning.

stat.AP↗

arXiv2024

Evaluating tree-based imputation methods as an alternative to MICE PMM for drawing inference in empirical studies

Dealing with missing data is an important problem in statistical analysis that is often addressed with imputation procedures. The performance and validity of such methods are of great importance for their application in empirical studies. While the prevailing method of Multiple Imputation by Chained Equations (MICE) with Predictive Mean Matching (PMM) is considered standard in the social science literature, the increase in complex datasets may require more advanced approaches based on machine learning. In particular, tree-based imputation methods have emerged as very competitive approaches. However, the performance and validity are not completely understood, particularly compared to the standard MICE PMM. This is especially true for inference in linear models. In this study, we investigate the impact of various imputation methods on coefficient estimation, Type I error, and power, to gain insights that can help empirical researchers deal with missingness more effectively. We explore MICE PMM alongside different tree-based methods, such as MICE with Random Forest (RF), Chained Random Forests with and without PMM (missRanger), and Extreme Gradient Boosting (MIXGBoost), conducting a realistic simulation study using the German National Educational Panel Study (NEPS) as the original data source. Our results reveal that Random Forest-based imputations, especially MICE RF and missRanger with PMM, consistently perform better in most scenarios. Standard MICE PMM shows partially increased bias and overly conservative test decisions, particularly with non-true zero coefficients. Our results thus underscore the potential advantages of tree-based imputation methods, albeit with a caveat that all methods perform worse with an increased missingness, particularly missRanger.

stat.AP↗

arXiv2022

Do school reforms shape study behavior at university? Evidence from an instructional time reform

Early-life environments can have long-lasting developmental effects. Interestingly, research on how school reforms affect later-life study behavior has hardly adopted this perspective. Therefore, we investigated a staggered school reform that reduced the number of school years and increased weekly instructional time for secondary school students in most German federal states. We analyzed this quasi-experiment in a difference-in-differences framework using representative large-scale survey data on 71,426 students who attended university between 1998 and 2016. We found negative effects of reform exposure on hours spent attending classes and on self-study, and a larger time gap between school completion and higher education entry. Our results support the view that research should examine unintended long-term effects of school reforms on individual life courses.

econ.GN↗