Discrete Time Markov Chains for Square Contingency Tables
Square contingency tables having the same row and column categories occur for the repeated observations on the response variable. Repeated responses may be obtained from different time points in longitudinal studies. Various models have been proposed for the dependent cross-classified data. When modeling such data, transition models like Markov type models concentrate on changes between the consecutive time points. The use of Markov models help us to summarize the data and parameter estimation in contingency table form. In this study, more parsimonious first-order and second-order models for ordinal variables are proposed and 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 many contingency tables obtained from different time points and parameter estimates can also be obtained using Markov chains. Finally, the results are compared with the standard log-linear modeling on the two classical examples.
Markov chains ; square contingency tables ; longitudinal data
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