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Keywords: multinomial regression, residuals, diagnostics, goodness of fit
Multinomial logistic and other similar regression models have been used to describe multinomial data in applications ranging from modeling the human microbiome to modeling outcomes in sports. Though much work has been done on model diagnostics for discrete, binary, and/or ordinal outcomes, model diagnostics for multinomial regression models are limited. Goodness of fit methods for multinomial regression models have mainly dealt with difficult to interpret deviance type residuals which exist on a category, and not observation, level. In this paper we develop and define residuals based on an alternative approach using squared Mahalanobis distances, extending the idea of a single randomized quantile residual for each observation in order to detect misspecification of the mean and overdispersion in multinomial regression models. We illustrate the residuals' use in both simulation and real data studies.