Generalized linear models for ordered categorical data

Journal article, 2023

Categorical scale data are only ordinal and defined on a finite set. Continuous scale data are only ordinal and defined on a bounded interval. Due to that character, the statistical methods for scale data ought to be based on orders between outcomes only and not any metric involving distance measure. For simple two-sample scale data, variants of classical rank methods are suitable. For regression type of problems, there are known good generalized linear models for separate categories for a long time. In the present article is suggested a new generalized linear type of model based on non parametric statistics for the whole scale. Asymptotic normality for those statistics is also shown and illustrated. Both fixed and random effects are considered.