A transition model for fuzzy correlated longitudinal responses

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Longitudinal study is type of studies that researchers visit subject in several time. Therefore, there are observations of the same subjects that are correlated. These types of studies are widely used in medical science. On the other hand, in medical studies, we frequently face situations that response mastered by linguistic terms. A new transition model which will be able to handle correlation between fuzzy responses is introduced. In this paper we model the transition possibility by fuzzy logistic regressions, and representing how the covariates relate to changes in response. With p covariates, there are ( p + 1) parameters including intercepts, which we estimate by extended least squares method. These possibilities depend on the covariates. By using a real data set, an applied example is provided to explain the applicability of the proposed model in clinical studies. In the clinical studies, the effect of hydro-alcoholic extract of Urtica Dioica on menorrhagia (for which the status is basically expressed by linguistic/fuzzy terms) is investigated also the effect of mental intervention in recovery of patients with Lichen Planus disease.

Fuzzy data
longitudinal study
transition model
fuzzy logistic regression
possibilistic odds
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