Author(s):
1. Roman Zainab:
Bahauddin Zakariya University,Multan-,Pakistan
2. Ume Roman:
University of Sargodha,Sargodha-,Pakistan
3. Muhammad Amin:
University of Sargodha,Sargodha-,Pakistan
Abstract:
For modeling count data, the Poisson regression model (PRM) is widely usedwhen the response variable takes non-negative integer values and follows thePoisson distribution. However, strong correlations between explanatoryvariables lead to multicollinearity, which inflates the variance of the maximumlikelihood estimator (MLE) and results in unstable parameter estimates.Multicollinearity can be mitigated by using biased estimators, such as the ridgeestimator, to reduce the variance of regression coefficients. Another approach isto impose exact linear restrictions on the parameters in the regression model,which leads to the restricted maximum likelihood estimator (RMLE). Therestricted Poisson ridge regression estimator (RPRRE), an existing method forhandling multicollinearity in the PRM with exact linear restrictions, also dealswith the issue of multicollinearity. We proposed another new biased estimator,the restricted modified ridge-type estimator for the PRM (RPMRTE), to furtherenhance performance the PRM’s estimates under these conditions. Theperformance of the RPMRTE is compared with that of the RMLE and theRPRRE using the mean squared error (MSE) criterion. Both simulation studiesand a real data application are presented to illustrate the theoretical results. Thefindings demonstrate that the proposed estimator outperforms the RMLE andRPRRE. Therefore, the RPMRTE is recommended for the PRM in the presence ofmulticollinearity and exact linear restrictions.
Page(s):
183-183
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025
Keywords:
multicollinearity
,
Poisson regression
,
Restricted Maximum Likelihood Estimator
,
Restricted Modified Ridge Type Estimator
,
Restricted Ridge Regression Estimator
References:
References are not available for this document.
Citations
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