On robust links and hypotheses testing in ordinal regression models

Anomalous data can significantly impact the reliability of likelihood-based inference in ordinal response models with negative relapses on both the level and the power of hypothesis tests. When data contamination occurs, robust testing procedures are required to ensure a reliable assessment of the relevance of the covariates. Since the various link functions differ in sensitivity to anomalous data, the paper proposes Wald and Likelihood Ratio test based on robust link functions. These tests hold robustness of validity and robustness of efficiency, and therefore retain a stable level and a good power under data contamination. The proposed tests are validated through numerical analyses and applied to occupational mobility data, highlighting their practical relevance.