A probit model for multivariate random length ordinal data

Multivariate random length ordinal data are data such that the ordinal response variable is observed a random number of times for each experimen¬tal unit. For example, depression may occur a random number of times and the severity of each depression episode is measured by an ordinal scale (e.g., l=mildly depressed, 2=moderately depressed, 3=very depressed). There is a need to evaluate how treatment or disease status impacts both the sever¬ity of the ordinal responses and the number of occurrences. In this paper, we propose a probit model which can realistically describe the relationships between the number of events and the ordinal responses of these events. This model also takes into account the correlation among multiple ordinal measurements. We describe estimation issues and the asymptotic efficiency of the maximum likelihood estimators. A simulation study is performed to examine the asymptotic behavior of the maximum likelihood estimators. An example using data from a pediatric longitudinal study is presented for illustration of the proposed methodology.