Diagnostics for categorical response models based on quantile residuals and distance measures

Area of Science:

• Statistics
• Statistical Modeling

Background:

• Polytomous categorical data are common in research and often analyzed using generalized logit models.
• Model diagnostics for these data are challenging due to the multivariate nature of standard residuals, complicating interpretation and visualization.

Purpose of the Study:

• To propose and evaluate new residual types and diagnostic techniques for polytomous categorical data.
• To address the limitations of existing methods, particularly for nominal data structures.

Main Methods:

• The study proposes randomized quantile residuals for both individual and grouped data structures.
• Euclidean and Mahalanobis distance measures are introduced to reduce residual dimensionality.
• Simulation studies were conducted to assess the performance of the proposed methods.
• Half-normal plots with simulation envelopes were employed for model performance evaluation.

Main Results:

• The proposed randomized quantile residuals demonstrated good performance in diagnostic assessments.
• The distance measurements facilitated improved interpretation of graphical diagnostic techniques.
• The methods were effective for both individual and grouped data structures.

Conclusions:

• Randomized quantile residuals offer a viable alternative for diagnosing generalized logit models with polytomous data.
• Distance measures enhance the interpretability of residual-based diagnostic plots.
• The proposed techniques provide valuable tools for analyzing complex categorical data structures.