arXiv subjects

Max Welz

Publications and source records attributed to Max Welz.

4 recordsLinked to original sources

arXiv2025

Robust estimation of polyserial correlation coefficients: A density power divergence approach

The association between a continuous and an ordinal variable is commonly modeled through the polyserial correlation model. However, this model, which is based on a partially-latent normality assumption, may be misspecified in practice, due to, for example (but not limited to), outliers or careless responses. The typically used maximum likelihood (ML) estimator is highly susceptible to such misspecification: One single observation not generated by partially-latent normality can suffice to produce arbitrarily poor estimates. As a remedy, we propose a novel estimator of the polyserial correlation model designed to be robust against the adverse effects of observations discrepant to that model. The estimator leverages density power divergence estimation to achieve robustness by implicitly downweighting such observations; the ensuing weights constitute a useful tool for pinpointing potential sources of model misspecification. The proposed estimator generalizes ML and is consistent as well as asymptotically Gaussian. As price for robustness, some efficiency must be sacrificed, but substantial robustness can be gained while maintaining more than 98% of ML efficiency. We demonstrate our estimator's robustness and practical usefulness in simulation experiments and an empirical application in personality psychology where our estimator helps identify outliers. Finally, the proposed methodology is implemented in free open-source software.

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arXiv2024

Robust Estimation of Polychoric Correlation

Polychoric correlation is often an important building block in the analysis of rating data, particularly for structural equation models. However, the commonly employed maximum likelihood (ML) estimator is highly susceptible to misspecification of the polychoric correlation model, for instance through violations of latent normality assumptions. We propose a novel estimator that is designed to be robust against partial misspecification of the polychoric model, that is, when the model is misspecified for an unknown fraction of observations, such as careless respondents. To this end, the estimator minimizes a robust loss function based on the divergence between observed frequencies and theoretical frequencies implied by the polychoric model. In contrast to existing literature, our estimator makes no assumption on the type or degree of model misspecification. It furthermore generalizes ML estimation, is consistent as well as asymptotically normally distributed, and comes at no additional computational cost. We demonstrate the robustness and practical usefulness of our estimator in simulation studies and an empirical application on a Big Five administration. In the latter, the polychoric correlation estimates of our estimator and ML differ substantially, which, after further inspection, is likely due to the presence of careless respondents that the estimator helps identify.

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arXiv2024

Robust Estimation and Inference for Categorical Data

While there is a rich literature on robust methodologies for contamination in continuously distributed data, contamination in categorical data is largely overlooked. This is regrettable because many datasets are categorical and oftentimes suffer from contamination. Examples include inattentive responding and bot responses in questionnaires or zero-inflated count data. We propose a novel class of contamination-robust estimators of models for categorical data, coined $C$-estimators (``$C$'' for categorical). We show that the countable and possibly finite sample space of categorical data results in non-standard theoretical properties. Notably, in contrast to classic robustness theory, $C$-estimators can be simultaneously robust \textit{and} fully efficient at the postulated model. In addition, a certain particularly robust specification fails to be asymptotically Gaussian at the postulated model, but is asymptotically Gaussian in the presence of contamination. We furthermore propose a diagnostic test to identify categorical outliers and demonstrate the enhanced robustness of $C$-estimators in a simulation study.

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arXiv2023

When Respondents Don't Care Anymore: Identifying the Onset of Careless Responding

Questionnaires in the behavioral sciences tend to be lengthy. However, literature suggests that survey length is a contributing factor to careless responding, with longer questionnaires yielding higher probability that participants start responding carelessly. Consequently, in long surveys a large number of participants may engage in careless responding, posing a major threat to internal validity. We propose a novel method for identifying the onset of careless responding (or an absence thereof) that searches for a changepoint in combined measurements of multiple dimensions in which carelessness may manifest, such as inconsistency and invariability. It is highly flexible, based on machine learning, and provides statistical guarantees for controlling the false positive rate. In simulation experiments, the proposed method achieves high accuracy in identifying carelessness onset and discriminates well between attentive and various types of careless responding, even when a large number of careless respondents are present. An empirical application highlights how identifying partial carelessness uncovers novel insights on careless responding behavior. Furthermore, we provide the freely available open source software package "carelessonset" to facilitate adoption by empirical researchers.

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