Abstract
An estimation procedure will be presented for a class of threshold models for ordinal data. These models may include both fixed and random effects with associated components of variance on an underlying scale. The residual error distribution on the underlying scale may be rendered greater flexibility by introducing additional shape parameters, e.g. a kurtosis parameter or parameters to model heterogeneous residual variances as a function of factors and covariates. The estimation procedure is an extension of an iterative re‐weighted restricted maximum likelihood procedure, originally developed for generalized linear mixed models. This procedure will be illustrated with a practical problem involving damage to potato tubers and with data from animal breeding and medical research from the literature.
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