| Abstract | In longitudinal data analysis, there are many practical situations where we need
to deal with transitions to a number of states and which are repeated over time generating
a large number of trajectories from beginning to end of the study. This problem becomes
increasingly difficult to model if the number of follow-ups is increased for a set of longitudinal data. A covariate-dependent Markov transition model is proposed using the logistic
link function for polytomous outcome data. A generalized and more flexible approach of
constructing the likelihood function for the first or higher order is demonstrated in this paper to deal with the branching of a number of transition types starting from no depression
at the beginning of the study. The proposed method can be employed to resolve a longstanding problem in dealing with modeling for transitions, reverse transitions and repeated
transitions by reducing the number of trajectories to a large extent resulting in estimating
relatively few parameters. The problem of depression in elderly, in terms of short and longterm health and economic consequence, needs to be assessed more critically. This study
uses the longitudinal data from the six waves of the Health and Retirement Survey to examine the transition to depression, reverse transition from depression to no depression and also
repeated transition from no depression to depression after experiencing a reverse transition
during a study period. The results indicate that age is negatively associated with reverse and
repeated transitions, gender is negatively associated with transition and reverse transition
indicating that females are more likely to experience both. The proposed method clearly
provides a wider range of useful information in revealing the dynamics of the depression
pattern among elderly.
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