Corresponding Author


Document Type

Original Article

Subject Areas

Mathematics, Statistics, Computer Science, Physics and Astronomy


Trivariate Bernoulli Distribution; Markov model; Generalized linear model; Deviance; Likelihood ratio test; Maximum likelihood estimators; Alternative quadratic exponential form


This paper provides the estimation and the test procedures for the measures of association in the correlated binary data associated with covariates. The generalized linear model (GLM) using the serial dependence and the developed alternative quadratic exponential form (AQEF) procedures are employed for the trivariate binary correlated outcome variables. The log-odds ratios, as measures of association, are estimated and the appropriate tests are suggested. For comparison between the two procedures, we used the simulation study and an application to an ecology problem which involves the estimation of the measures of association and their tests. The over-dispersion criteria is investigated for these procedures. Finally, the deviance and scaled deviance are used as tests for the goodness of fit of the model to determine the best procedure.

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