A Markov chain model of extrabinomial variation

This paper studies the properties of a {0, 1}-state Markov chain model of extrabinomial variation. If n is even, the Markov chain binomial model is always overdispersed relative to the binomial model with parameters n and p, while if n is odd, it may be over- or underdispersed relative to the binomial model. Expressions for the likelihood and variance functions are obtained, and for n=3, the Markov chain binomial model is compared with the additive and multiplicative binomial models of Altham (1978), as well as to the beta-binomial model.