On the estimation of Bell regression model using ridge estimator
Muhammad Amin, Muhammad Nauman Akram, Abdul Majid
Abstract
The bell regression is used, when the response variable is in the form of counts with over dispersion. The bell regression coefficients are generally estimated using the maximum likelihood estimator (MLE). It is known that the performance of the traditional MLE is very sensitive to multicollinearity. Therefore, we propose a Bell ridge regression (BRR) as a solution to the multicollinearity problems. For the assessment of BRR, we conduct a Monte Carlo simulation study to monitor the performance of the proposed estimator where the mean squared error (MSE) is considered as an evaluation criterion. Also, two real examples are included to show the superiority of the BRR estimator.
Topics & Concepts
MulticollinearityStatisticsMean squared errorEstimatorMathematicsRegression analysisRegressionVariance inflation factorBias of an estimatorMonte Carlo methodMinimum-variance unbiased estimatorAdvanced Statistical Methods and ModelsAdvanced Statistical Process MonitoringAdvanced Measurement and Detection Methods