Open Access Open Access  Restricted Access Subscription Access

Discrete Time Markov Chains for Square Contingency Tables

Serpil Aktaş , Ceyhan İnal


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

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.