Ordered Multi-Category Logits Model Under Dirichlet Distribution

When the outcomes of multi-category are longitudinally observed or clustered within a subject they are correlated each other. The DMN (Dirichlet multinomial) distribution is more suitable to model these kinds of dataset rather than the multinomial distribution in overcoming the overdispersion. But until now we cannot find any available package that fits ordered DMN logits regression for ordinal outcomes. In this paper, we suggest an algorithm that can do the role of fitting ordered logits regression model for DMN ordinal outcomes. We implement the algorithm mainly focusing on the adjacent-category logits and also provide validation results through two practical data sets. The well-known vglm in R package VGAM plays a benchmark in comparing results. A small scale simulation design has been performed to show the goodness-of-fit of DMN logits model under partial parallel constraints on regression coefficients. The proposed ordered DMN logits model appears to have a good performance.