Weekly Bulletin

mpirical research in the social, health, and economic sciences is often based on categorical variables, such as questionnaire responses, self-reported health, or counting processes. Yet, just like in continuous variables, contamination might be present in such data, for instance (but not limited to) careless responses, which can cause severe biases in the commonly employed maximum likelihood estimation. However, robustifying estimation against contamination is challenging because categorical variables, by their very nature, cannot take arbitrarily large values and may not even admit a numerical interpretation in the first place. Consequently, the extensive literature on outlier-robust M-estimation may not be applicable. As a remedy, we propose a general framework for robust estimation and inference of models for categorical data, called C-estimation ("C" for categorical; Welz, 2024). In addition to offering enhanced robustness, we show that C-estimators are asymptotically consistent, normally distributed, and fully efficient. The latter property starkly contrasts M-estimation, which is characterized by a fundamental tradeoff between robustness and efficiency. C-estimators avoid this tradeoff by exploiting the categorical nature of the data. Furthermore, C-estimators do not incur any additional computational cost and are therefore also attractive from a practical perspective. This talk aims to strike a balance between theoretical aspects of C-estimators and an application thereof to psychometric structural equation models (SEMs) with ordinal measurements. We show that using a robustly estimated polychoric correlation Matrix (Welz, Mair & Alfons, 2025+) for SEM estimation can substantially improve SEM fit, enhance the accuracy of parameter estimates, and help identify low-quality responses (such as careless responses). Furthermore, the proposed approach is very general because it does not necessitate any adjustments to the SEM itself and it can be used in conjunction with any method for SEM fitting, such as maximum likelihood, least-squares-based approaches like Diagonally Weighted Least Squares (DWLS), or Bayesian techniques. Our proposed procedure is implemented in the free open-source R package "robcat" (https://CRAN.R-project.org/package=robcat), whose source is written in fast and efficient C++ code. REFERENCES: - Welz, M. (2024). Robust estimation and inference for categorical data [arXiv:2403.11954]. https://doi.org/10.48550/arXiv.2403.11954 - Welz, M., Mair, P., & Alfons, A. (2025+). Robust estimation of polychoric correlation. Psychometrika, https://doi.org/10.1017/psy.2025.10066