The present paper deals with the robustness of estimators and tests for ordinal response models. In this context, gross-errors in the response variable, specific deviations due to some respondents’ behavior, and outlying covariates can strongly affect the reliability of the maximum likelihood estimators and that of the related test procedures.
The paper highlights that the choice of the link function can affect the robustness of inferential methods, and presents a comparison among the most frequently used links. Subsequently robust $M$-estimators are proposed as an alternative to maximum likelihood estimators. Their asymptotic properties are derived analytically, while their performance in finite samples is investigated through extensive numerical experiments either at the model or when data contaminations occur. Wald and $t$-tests for comparing nested models, derived from $M$-estimators, are also proposed. $M$ based inference is shown to outperform maximum likelihood inference, producing more reliable results when robustness is a concern.
"Robust inference for ordinal response models." Electron. J. Statist. 11 (2) 3407 - 3445, 2017. https://doi.org/10.1214/17-EJS1314