Existing methods can perform likelihood-based clustering on a multivariate data matrix of ordinal data, using finite mixtures to cluster the rows (observations) of the matrix. These models can incorporate the main effects of individual rows and columns, as well as cluster effects, to model the matrix of responses. However, many real-world applications also include available covariates, which provide insights into the main characteristics of the clusters and determine clustering structures based on both the individuals’ similar patterns of responses and the effects of the covariates on the individuals' responses. In our research we have extended the mixture-based models to include covariates and test what effect this has on the resulting clustering structures. We focus on clustering the rows of the data matrix, using the proportional odds cumulative logit model for ordinal data. We fit the models using the Expectation-Maximization algorithm and assess performance using a simulation study. We also illustrate an application of the models to the well-known arthritis clinical trial data set.

A reliable interval estimation of the latent mean incidence rate is important but challenging in infectious disease surveillance because count data are often zero-inflated and overdispersed. This study compared frequentist (normal approximation (NA), bootstrap percentile (BP), and bootstrap-t (BT)) and Bayesian (equal-tailed interval (ETI) and highest density interval (HDI)) intervals under the zero-inflated negative binomial (ZINB) model. A Monte Carlo simulation study varied levels of zero inflation, dispersion, and the observation period, evaluating conditional and unconditional coverage and average interval length. NA and BP showed undercoverage throughout the evaluated scenarios. BT improved conditional coverage over BP in 47 of 54 scenarios but generally produced wider intervals. Bayesian intervals often had higher coverage, although overcoverage and diagnostic failures prevented a uniform advantage. HDI was shorter than ETI in every scenario. An empirical application to dengue surveillance data from Phayao Province, Thailand, illustrated the five interval procedures under a fitted ZINB model; however, the NB model had lower AIC/BIC values. Temporal diagnostics and block bootstrap results indicated sensitivity to dependence assumptions. Overall, interval performance depended on the scenario, prior specification, and successful interval construction; no method uniformly achieved nominal coverage.