Testing the Transition Probabilities in Square Contingency Tables

Repeated responses may be obtained from different time points in longitudinal studies. When modelling such data, transition models like Markov type models concentrate on changes between the consecutive time points. Markov model consists of all possible states of a randomly changing system where it is assumed that next states depend only on the current state. For categorical data, Markov models help us to summarize the data and parameter estimation in contingency table form. Square contingency tables having the same row and column categories occur for the repeated observations on the response variable. In this paper, a computer program written in C# is developed to test whether the stationary probabilities are constant for several square contingency tables. It is also shown that if the transition probabilities are the same for each time interval, a single transition matrix may be estimated from the aggregrated tables. Limiting behavior of Markov chains as n→∞ is also calculated.