A New Conway Maxwell–Poisson Liu Regression Estimator—Method and Application

• Published in: Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
• Main Authors: Akram, Muhammad Nauman, Amin, Muhammad, Sami, Faiza, Mastor, Adam Braima, Egeh, Omer Mohamed, Muse, Abdisalam Hassan
• Format: Article
• Language: English
• Subjects: Approximation; Bias; Generalized linear models; Mathematics; Maximum likelihood estimators; Monte Carlo simulation; Parameter estimation; Poisson density functions; Random variables; Regression models; Simulation; Standard error
• ISSN: 2314-4629; 2314-4785
• DOI: 10.1155/2022/3323955

Poisson regression is a popular tool for modeling count data and is applied in medical sciences, engineering and others. Real data, however, are often over or underdispersed, and we cannot apply the Poisson regression. To overcome this issue, we consider a regression model based on the Conway–Maxwell Poisson (COMP) distribution. Generally, the maximum likelihood estimator is used for the estimation of unknown parameters of the COMP regression model. However, in the existence of multicollinearity, the estimates become unstable due to its high variance and standard error. To solve the issue, a new COMP Liu estimator is proposed for the COMP regression model with over-, equi-, and underdispersion. To assess the performance, we conduct a Monte Carlo simulation where mean squared error is considered as an evaluation criterion. Findings of simulation study show that the performance of our new estimator is considerably better as compared to others. Finally, an application is consider to assess the superiority of the proposed COMP Liu estimator. The simulation and application findings clearly demonstrated that the proposed estimator is superior to the maximum likelihood estimator.