Statistical analysis of ordered categorical data via a structural heteroskedastic threshold model

In the standard threshold model, differences among statistical subpopulations in the distribution of ordered polychotomous responses are modeled via differences in location parameters of an underlying normal scale. A new model is proposed whereby subpopulations can also differ in dispersion (scaling) parameters. Heterogeneity in such parameters is described using a structural linear model and a loglink function involving continuous or discrete covariates. Inference (estimation, testing procedures, goodness of fit) about parameters in fixed-effects models is based on likelihood procedures. Bayesian techniques are also described to deal with mixed-effects model structures. An application to calving ease scores in the US Simmental breed is presented; the heteroskedastic threshold model had a better goodness of fit than the standard one.