Fitting Higher Order Markov Chains

When the interest is in making statements about change based on repeated measurements of discrete data, e.g., brand-switching data, one way to do so is by using Markov chain models. This article presents a hierarchy of such models that is very flexible in overcoming drawbacks of the simple Markov chain model by simultaneously including and allowing to test separately for stationarity, order of the process, heterogeneity and unreliability. A reanalysis of the Snow Crop brand-switching data reveals heterogeneity and unreliability to be relevant, ruling out nonstationarity and higher order dependence though models of the latter type fare well in terms of goodnessof-fit. The higher order issue is addressed in detail by reporting results from recovery studies ending up with a caveat about using higher order models.

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