Robust Liu-Type Estimation for Multicollinearity in Fuzzy Logistic Regression

TL;DR

This paper proposes robust Liu-type estimators to address multicollinearity in fuzzy logistic regression, demonstrating improved accuracy and stability through simulations and real data application.

Contribution

It introduces and compares new fuzzy Liu-type estimators specifically designed to handle multicollinearity in fuzzy logistic regression models.

Findings

FLLTPE and FLLTE outperform other estimators in simulations.

Proposed estimators improve stability and accuracy in fuzzy logistic regression.

Real data application confirms the effectiveness of the new estimators.

Abstract

This article addresses the fuzzy logistic regression model under conditions of multicollinearity, which causes instability and inflated variance in parameter estimation. In this model, both the response variable and parameters are represented as fuzzy triangular numbers. To overcome the multicollinearity problem, various Liu-type estimators were employed: Fuzzy Maximum Likelihood Estimators (FMLE), Fuzzy Logistic Ridge Estimators (FLRE), Fuzzy Logistic Liu Estimators (FLLE), Fuzzy Logistic Liu-type Estimators (FLLTE), and Fuzzy Logistic Liu-type Parameter Estimators (FLLTPE). Through simulations with various sample sizes and application to real fuzzy data on kidney failure, model performance was evaluated using mean square error (MSE) and goodness of fit criteria. Results demonstrated superior performance of FLLTPE and FLLTE compared to other estimators.