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 descriptivemeasure 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.
O problema da superdispersão em dados categorizados politômicos nominais em estudos agrários / Maria Letícia Salvador.-versão revisada de acordo com a resolução CoPGr 6018 de 2011.-Piracicaba, 2019. 48 p. Dissertação (Mestrado)-USP / Escola Superior de Agricultura "Luiz de Queiroz". 1. Seleção de modelos; 2. Máxima verossimilhança; 3. Índice de superdispersão; 4. Dirichlet-multinomial. I. Título.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.