A quasi-score approach to the analysis of ordered categorical data via a mixed heteroskedastic threshold model

This article presents an extension of the methodology developed by Gilmour et al. [19], for ordered categorical data, taking into account the heteroge neity of residual variances of latent variables. Heterogeneity of residual variances is described via a structural linear model on log-variances. This method involves two main steps: i) a 'marginalization' with respect to the random effects leading to quasi-score estimators; ii) an approximation of the variance-covariance matrix of the observations which leads to an analog ue of the Henderson mixed model equations for continuous Gaussian data. Thi s methodology is illustrated by a numerical example of footshape in sheep. (C) Inra/Elsevier, Paris.