Diferentes estratégias para modelagem de respostas politômicas ordinais em estudos longitudinais

Abstract

The modeling of polytomous responses, especially ordinal, has been the subject of increasing interest in recent years, and has been gaining ground in research on quality of life, health status indicators, assessment of student proficiency, among others. Its use goes from cross-sectional studies, which assume independence among the observations, to longitudinal studies, where more than one response from the same individual is observed over time. There are several methods proposed in the literature for modeling polytomous responses in transversal studies, being the most commonly used the cumulative logits model, also known as proportional odds model due to the assumption of proportionality in odds, i.e., the model assumes that there is an approximately linear increase in odds ratios for the regression coefficients. In many practical situations this assumption is violated. There is, however, another model that generalizes the proportional odds, known as partial proportional odds, which allows no odds proportionality to a subset of covariates that violated that assumption. In longitudinal studies, the conventional models - marginal models, generalized linear mixed models and transition models - for analysis of correlated data can also be used to model polytomous responses. In this work modeling of ordinal polytomous responses in longitudinal studies is discussed from the perspective of marginal, generalized linear mixed models and transition models. The specification and interpretation of the models is illustrated and discussed by analyzing two real data sets.