An analysis of clustered categorical data--application in dental health

Quite often in medical studies multiple discrete indicators are used to measure some characters that are defined only conceptually and are difficult to measure directly. Studies of this type exhibit categorical responses of dependent nature. Analysis of such categorical data appears to be extremely difficult (intractable) particularly in the presence of risk (causal) factors. In the present article, our purpose is to develop a latent mixture regression model for analysing such multivariate categorical data. Such a mixture model accommodates correlated and overdispersed data through the incorporation of random effects. Unfortunately, a full likelihood analysis is often hampered by the need for numerical integration. Two different procedures have been considered here. Both involve intensive computations. Numerical investigation has been carried out on the basis of a survey data covering 220 individuals from medical colleges in and around Calcutta (India). The purpose of the study is to compare tooth cleaning efficiency of brushes manufactured by different companies.