Azzalini (1994) proposed a first order Markov chain for binary data. Azzalini’s model is extended for ordinal data and introduces a second order model. Further, the test statistics are developed and the power of the test is determined. An application using real data is also presented.
Biswas, Soma Chowdhury; Islam, M. Ataharul; and Islam, Jamal Nazrul
"Higher Order Markov Structure-Based Logistic Model and Likelihood Inference for Ordinal Data,"
Journal of Modern Applied Statistical Methods:
2, Article 12.
Available at: http://digitalcommons.wayne.edu/jmasm/vol10/iss2/12