A novel unit exponential regression model with improved estimation method under multicollinearity

In regression analysis of bounded response variables on the interval (0,1), selecting an appropriate model is crucial for accurately identifying relationships with explanatory variables. Quantile modeling widely utilizes established models like beta and unit Lindley regression models, but they may not be appropriate for most datasets. Therefore, this paper introduces a new quantile regression model, called the unit exponential regression model (UERM), which offers greater flexibility and suitability for modeling unit data. The proposed model is derived from the family of two-parameter exponential distributions. The maximum likelihood estimation (MLE) is usually used to estimate the parameters in regression models, which is effective under standard conditions. However, when the explanatory variables are highly correlated, it can impact the MLE, resulting in unreliable parameters, inflated variance, and a higher mean squared error. To solve this issue, we suggest a better Liu estimator for the UERM, which aims to reduce multicollinearity and make the estimates more accurate by lowering variance inflation. The statistical characteristics of the proposed UERM and the Liu estimating method were examined. Extensive Monte Carlo simulations were used to assess the suitability of the proposed model and estimator. To demonstrate their scientific validity, experimental applications were conducted on real-world datasets from the fields of health and engineering. The results from both the simulations and the real-world tests show that the UERM model fits the limited data better than existing models, and the Liu estimating method is more reliable for parameters when there is multicollinearity among the explanatory variables.