A new estimator for the multicollinear Poisson regression model: simulation and application

Lukman, Adewale F.; Adewuyi, Emmanuel T.; Månsson, Kristofer; Kibria, B. M. Golam

doi:10.1038/s41598-021-82582-w

Cited by 35 publications

(54 citation statements)

References 27 publications

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“…where ρ is the level of multicollinearity between the independent variables (Kibria et al 2015;Kibria and Banik, 2016;Lukman et al, 2019b, Lukman et al 2020b. z ij are pseudo-random numbers generated using the standard normal distribution such that i ranges from 1 to n and j from 1 to p. As a common restriction used in simulation studies, it is assumed that P p j¼1 β 2 j ¼ 1 and…”

Section: Simulation Design and Real-life Application Simulation Study And Resultsmentioning

confidence: 99%

Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

et al. 2021

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Background: Multicollinearity greatly affects the Maximum Likelihood Estimator (MLE) efficiency in both the linear regression model and the generalized linear model. Alternative estimators to the MLE include the ridge estimator, the Liu estimator and the Kibria-Lukman (KL) estimator, though literature shows that the KL estimator is preferred. Therefore, this study sought to modify the KL estimator to mitigate the Poisson Regression Model with multicollinearity. Methods: A simulation study and a real-life study were carried out and the performance of the new estimator was compared with some of the existing estimators. Results: The simulation result showed the new estimator performed more efficiently than the MLE, Poisson Ridge Regression Estimator (PRE), Poisson Liu Estimator (PLE) and the Poisson KL (PKL) estimators. The real-life application also agreed with the simulation result. Conclusions: In general, the new estimator performed more efficiently than the MLE, PRE, PLE and the PKL when multicollinearity was present.

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Section: Simulation Design and Real-life Application Simulation Study And Resultsmentioning

confidence: 99%

Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

et al. 2021

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“…where Q is the orthogonal matrix whose columns are the eigenvectors of S. Hence, the scalar MSE of the COMPRR model is generally obtained by applying the tr (.) operator on Equation (22), which can be defined as…”

Section: L(ymentioning

confidence: 99%

“…This approach is also extended for the count data models to overcome the effect of multicollinearity on the regression estimates. [14][15][16][17][18][19][20][21][22] In the ridge regression approach, the ridge parameter (k) contributing a vital role to estimate the model coefficients. For count data modeling with multicollinearity, some researchers have also proposed the ridge regression approach and suggested some ridge parameters.…”

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confidence: 99%

“…Algamal and Alanaz 21 and Rashad and Algamal 14 also proposed some ridge parameters for the Poisson regression model. Lukman et al 22 proposed the new biased estimator for Poisson regression model to overcome the issue of multicollinearity. Amin et al 11 proposed a new James-Stein estimator for the Poisson regression model to circumvent the issue of multicollinearity among the regressors.…”

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confidence: 99%

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On the ridge estimation of the Conway‐Maxwell Poisson regression model with multicollinearity: Methods and applications

Sami

Amin

Butt

2021

Concurrency and Computation

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In data analysis, count data modeling contributing a significant role. The Conway-Maxwell Poisson (COMP) is one of the flexible count data models to deal over and under dispersion. In the COMP regression model, when the explanatory variables are correlated, then the maximum likelihood estimator does not give efficient results due to the large standard error (SE) of the estimates. To overcome the effect of multicollinearity, we have proposed some ridge regression estimators in the COMP regression model by introducing dispersion parameter in the context of overdispersion, equidispersion, and underdispersion. The Iterative reweighted least method is used for the estimation of ridge regression coefficients in the COMP regression model. To evaluate the performance of the proposed estimators, we use mean squared error (MSE) as the performance evaluation criteria. Theoretical comparison of the proposed estimators with the competitor estimators is made and conditions of efficiency have been derived. The proposed estimator is evaluated with the help of a simulation study and two real applications. The results of the simulation study and real applications show the superiority of the proposed estimator because the proposed estimator produces smaller MSE and SEs of the COMP regression estimates with multicollinearity.

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“…e Liu estimator is an ace in this regard as it avoids the disadvantages of the ridge estimator [10], where the main advantage of the ridge is easy to use, and it can be written in the explicate and the objective formulas. In the literature, various studies are available for the PRM to overcome the presence of collinearity [7,[11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Influence Diagnostic Methods in the Poisson Regression Model with the Liu Estimator

Khan

Amanullah

Amin

et al. 2021

Computational Intelligence and Neuroscience

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There is a long history of interest in modeling Poisson regression in different fields of study. The focus of this work is on handling the issues that occur after modeling the count data. For the prediction and analysis of count data, it is valuable to study the factors that influence the performance of the model and the decision based on the analysis of that model. In regression analysis, multicollinearity and influential observations separately and jointly affect the model estimation and inferences. In this article, we focused on multicollinearity and influential observations simultaneously. To evaluate the reliability and quality of regression estimates and to overcome the problems in model fitting, we proposed new diagnostic methods based on Sherman–Morrison Woodbury (SMW) theorem to detect the influential observations using approximate deletion formulas for the Poisson regression model with the Liu estimator. A Monte Carlo method is done for the assessment of the proposed diagnostic methods. Real data are also considered for the evaluation of the proposed methods. Results show the superiority of the proposed diagnostic methods in detecting unusual observations in the presence of multicollinearity compared to the traditional maximum likelihood estimation method.

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A new estimator for the multicollinear Poisson regression model: simulation and application

Cited by 35 publications

References 27 publications

Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

On the ridge estimation of the Conway‐Maxwell Poisson regression model with multicollinearity: Methods and applications

Influence Diagnostic Methods in the Poisson Regression Model with the Liu Estimator

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