Ordinal data and residual analysis: Review and application

Experiments in which the response is ordinal polytomous are often performed in the agricultural sciences and, often, the cumulative logit models are used to analyze this variable. A particular characteristic is that the polytomous variables are objects of multivariate statistics and the ordinary residual, associated with the classical models available, is a vector for each subject. Consequently, these residuals are not easily interpreted, and their distribution is unknown. Residual analysis is an essential step in validating any statistical model, and not performing it can allow a model to incorrectly fit the data, resulting in erroneous conclusions and inferences. In this context, the work aims to review the residuals for ordinal data available in the literature, emphasizing the so-called surrogate residuals with continuous distribution. As a practicalapplication, it is present an experiment carried out with Tambaqui fish of different types of genotype. The response variable in this study is the severity of the lesions found in the livers of Tambaquis. The estimation of the parameters was performed using the maximum likelihood. The selected model by the likelihood ratio test included the proportional odds and fish genotype effect. According to this model, it was possible to verify in this study that fish with genotype 122 presented a higher probability of liver lesion classified as irreversible (71, 26%), while Tambaquis with genotype 130 had a higher probability of moderate lesion, 46, 75%. For the model diagnostics, the half-normal plot and the Kolmogorov-Smirnov test were used to examine the performance of the surrogate residual. The results obtained provided evidence of the adequacy of the selected model since the residuals did not reveal patterns or influential points in diagnostic tools.