The grouped continuous model for multivariate ordered categorical variables and covariate adjustment

The grouped continuous model for multivariate ordered categorical data is described. This is based on partitioning an underlying multivariate normal distribution. Straightforward maximum likelihood estimation is really feasible only for one- and two-way tables. We introduce an estimation system based on maximum likelihood estimation in the one- and two-way marginal tables of higher-order tables. This is computationally feasible and an example involving aspects of bird colouring is given. The approach is extended to provide a regression model for multivariate ordered categorical data, with an estimation scheme again based on the one- and two-way marginal tables. The above example is developed to investigate the covariate effect of time. The asymptotic efficiency of these sampling schemes is discussed; it appears that they have high efficiency.