Using fuzzy logistic regression for modeling vague status situations: Application to a dietary pattern study

Abstract

In some practical situations, it is not possible to categorize samples into one of two response categories because of the vague nature of the response variable. Statistical logistic regression models are, therefore, not appropriate for modeling such response variables. Moreover, the small sample size in most cases limits the use of statistical logistic regression models. Fuzzy logistic regression models, instead, can overcome these problems. In order to investigate the use of fuzzy logistic regression, the present study is designed and implemented to evaluate the relationship between dietary pattern and a set of risk factors of interest. Since it is not possible to define a healthy dietary pattern precisely, therefore, the possibility of having the healthy diet is reported for each subject as a number between zero and one. The conventional logistic model is not appropriate and fails in dealing with such imprecise data; hence, a possibilistic approach is used to model the available data and to estimate the fuzzy parameters of the model. For evaluating the model, a goodness-of-fit index and an appropriate predictive capability criterion with cross validation technique is developed. The logistic model investigated here is found to be general and inclusive enough to be recommended for modeling vague observations or ambiguous relations in any field of medical sciences.