Lukman Adewale F, Dawoud Issam, Kibria B M Golam, Algamal Zakariya Y, Aladeitan Benedicta
Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria.
Department of Biostatistics and Epidemiology, University of Medical Sciences, Ondo, Nigeria.
Scientifica (Cairo). 2021 Jun 18;2021:5545356. doi: 10.1155/2021/5545356. eCollection 2021.
The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.
已知的线性回归模型（LRM）主要用于对响应变量（生物活性）与一个或多个物理化学或结构性质之间的定量构效关系（QSAR）进行建模，这些性质作为解释变量，主要适用于响应变量分布呈正态时。伽马回归模型常用于处理偏态因变量。两个模型中的参数均使用最大似然估计器（MLE）进行估计。然而，在存在多重共线性的情况下，两个模型的MLE都会变得不稳定。在本研究中，我们提出了一种新的估计器，并建议了一些偏差参数，用于在存在多重共线性时估计伽马回归模型的回归参数。通过均方误差准则进行了模拟研究和实际应用，以评估估计器的性能。模拟和实际应用的结果表明，所提出的伽马估计器产生的均方误差值低于其他考虑的估计器。
