Affiliations: [a] Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran | [b] Department of Health and Community Medicine, School of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran | [c] Department of Community Oral Health, Dental School, Shahid Beheshti University of Medical Sciences, Tehran, Iran | [d] Department of Biostatistics, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran | [e] Department of Community Nutrition, School of Nutrition and Food Science, Isfahan University of Medical Sciences, Isfahan, Iran | [f] Department of Statistics and Epidemiology, School of Public Health, Tabriz University of Medical Sciences, Tabriz, Iran
Correspondence:
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Corresponding author: Mahshid Namdari, Department of Community Oral Health, Dental School, Shahid Beheshti University of Medical Sciences, Tehran, Iran. Tel.: +98 21 22439936; E-mail:[email protected]
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.
