Binary variable binomial distribution. Logistische Regression – Wikipedia

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The authors declare that they have no competing interests. The two last authors contributed to the statistical methodology and finalization of the writing.

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All authors read and approved the final manuscript. Abstract Background In medical and biomedical areas, binary and binomial outcomes are very common. Such data are often collected longitudinally from a given subject repeatedly overtime, which result in clustering of the observations within subjects, leading to correlation, on the one hand.

The repeated binary outcomes from a given subject, on the other hand, constitute a binomial outcome, binary variable binomial distribution the prescribed mean-variance relationship is often violated, leading to the so-called overdispersion.


A new model which combines both overdispersion, and correlation simultaneously, also known as the combined model is applied. In addition, the commonly used methods for binary and binomial data, such as the simple logistic, which accounts neither for the overdispersion nor the correlation, the beta-binomial model, and the logistic-normal model, which accommodate only for the overdispersion, and correlation, respectively, are also considered for comparison purpose.

As an alternative estimation technique, a Bayesian implementation of the combined model is also presented. Results The combined model results in model improvement in fit, and hence the preferred one, based on likelihood comparison, and DIC criterion. Further, the two estimation approaches result in fairly similar parameter estimates and inferences in both of our case studies.

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Conclusion We applied a flexible modeling framework to analyze binary and binomial longitudinal data. Instead of accounting for overdispersion, and correlation separately, both can be accommodated simultaneously, by allowing two separate sets of the beta, and the normal random effects at once.

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