ANALYSIS OF MULTINOMIAL DATA WITH OVERDISPERSION DIAGNOSTICS AND APPLICATION
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Abstract
In agronomic experiments, the presence of polytomous variables is common, and the generalized logit model can be used to analyze these data. One of the characteristics of the generalized logit model is the assumption that the variance is a known function of the mean, and the observed variance is expected to be close to that assumed by the model. However, it is not uncommon for extra-multinomial variation to occur, due to the systematic observation of data that are more heterogeneous than the variance specified by the model, a phenomenon known as overdispersion. In this context, the present work discusses a diagnostic of overdispersion in multinomial data, with the proposal of a descriptive measure for this problem, as well as presenting a methodological alternative through the Dirichlet- multinomial model. The descriptive
measure is evaluated through simulation, based on two particular scenarios. As a motivational study, we report an experiment applied to fruit growing, whose objective was to compare the flowering of adult plants of an orange tree, grafted on “Rangpur”
lime or “Swingle” citrumelo, with as response variable the classification of branches into three categories: lateral flower, no flower or aborted flower, terminal flower. Through the proposed descriptive measure, evidence of overdispersion was verified, indicating that the generalized logit model may not be the most appropriate. Thus, as a methodological alternative, the Dirichlet-multinomial model was used. Compared to the generalized logit model, the Dirichlet-multinomial proved to be more suitable to fit the data with overdispersion, by allowing the inclusion of an additional parameter to accommodate the excessive extra-multinomial dispersion.
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