Authors : Farzaneh Moradi, Alireza Arabpour and Ali Shadrokh
Abstract: Statistical logistic regression is used for modeling a binary response variable based on a set of explanatory variables. In practice, the state of the response variable may be described in linguistic terms rather than in exact ones. So, it is not possible to categorize the samples in one of two response categories and no usual probability distribution can be considered for such binary response variables. Therefore, statistical logistic regression is not appropriate for modeling. In this study, researchers propose an adaptive fuzzy least squares model based on possibility of success that is defined by some linguistic terms. Also for each α-cut, using bootstrap technique, researchers discuss the problem of statistical inference. To evaluate the goodness of fit, a criterion named the capability index is calculated. At the end, because of widespread applications of logistic regression in clinical studies and also, the abundance of vague observations in clinical diagnosis, the suspected cases to Systematic Lupus Erythematosus (SLE) disease is modeled via an explanatory variable to detect the application of the model. The results showed that the proposed model could be a rational substituted model of an ordinary one in modeling the clinical vague status.
Farzaneh Moradi, Alireza Arabpour and Ali Shadrokh, 2016. A Bootstrap-Based Method of Statistical Inference in Fuzzy Logistic Regression. Journal of Engineering and Applied Sciences, 11: 2105-2112.