Detection of aberrant response behavior in context of robust logistic regression methods

Abstract

Accurately modelling item responses is a key objective in psychometrics. Generalized linear and nonlinear models provide a useful framework for this task. However, traditional logistic regression is highly sensitive to outliers, which can strongly influence parameter estimates and compromise assessment validity. These outliers often arise due to measurement errors, misclassifications, or aberrant responses. To address this issue, we explore robust logistic regression using M-estimators within the generalized linear model framework. This approach incorporates robust weighting functions to reduce the influence of extreme values in both the response and predictor spaces. Our simulation study demonstrates that while classical logistic regression is heavily affected by misclassified outliers, robust logistic regression remains stable and provides more reliable stimates. This method presents a practical alternative to traditional item response modeling approaches, effectively mitigating the impact of anomalies without introducing additional item parameters