Goodness of fit test for higher order binary Markov chain models

When the interest is in making statements about change based on repeated measurements of discrete data, one way to do so is using Markov chain models. Goodness of fit test to find a good model is very important in analyzing the underlying patterns and relationships in the repeated measures data. To test for the various associations in the models, the likelihood ratio and Wald tests are used. However, it has been observed that the efficient score tests can provide equally good tests and can provide an easier alternative. In this paper, we provide an extension of Tsiatis method for goodness of fit test on higher order Markov chains. In our method, we follow the approach of Tsiatis goodness of fit test in logistic regression models. New method provided in this paper is applied to real-life data to examine the suitability of the techniques.