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

Sami, Faiza; Amin, Muhammad; Butt, Muhammad Moeen

doi:10.1002/cpe.6477

Cited by 25 publications

(10 citation statements)

References 30 publications

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“…A special case of the Generalized Linear Models (GLM) is the Poisson Regression Model (PRM) which is generally applied for count or frequency data modelling. Other count data models include: Bell regression model, Negative binomial regression model, zero inflated bell regression model, zero inflated regression model Sami et al, 2021;Rashad and Algamal, 2019;Majid et al, 2021). The PRM is employed to model the relationship between a response variable and one or more explanatory variable where the response variable denotes a rare event or count data.…”

Section: Introductionmentioning

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 was 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: Introductionmentioning

confidence: 99%

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

et al. 2021

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“…In other related studies [48][49][50], Poisson regression models were fitted for RTF data with the basic assumption that the data produced same mean and variance. However, Shaik and Hossain [51] faulted the use of the Poisson regression model, as the underlying assumptions are difficult to satisfy.…”

Section: Literature Reviewmentioning

confidence: 99%

Predictive Probability Models of Road Traffic Human Deaths with Demographic Factors in Ghana

2022

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Road traffic carnages are global concerns and seemingly on the rise in Ghana. Several risk factors have been studied as associated with road traffic fatalities. However, inadequate road traffic fatality (RTF) data and inconsistent probability outcomes for RTF remain major challenges. The objective of this study was to illustrate and estimate probability models that can predict road traffic fatalities. We relied on 66,159 recorded casualties who were involved in road traffic accidents (RTAs) in Ghana from 2015 to 2019. Three generalized linear models, namely, logistic regression, probit regression, and linear probability model, were used for the analysis. We found that gender and age groups have significant effects in predicting the probability of road traffic fatality for all three models. Through a likelihood ratio test, however, it was determined that the logit regression model produced consistent probabilities of traffic fatalities which are very close to the actual probability values across the age groups and gender, compared to the other two models. Thus, we recommend intensified campaign for the use of seat belts in vehicles, targeted at the aged and male users of road transport, to reduce the possibility of death in any RTA.

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“…The concept of the ridge estimator is to add a small definite amount (k) to the diagonal entries of the covariance matrix to increase the conditioning of this matrix, reduce the mean squared error (MSE), and achieve consistent coefficients. For a review of the ridge estimator in both linear and GLMs, e.g., as shown in References Rady et al [3], Abonazel and Taha [4], Qasim et al [5], Alobaidi et al [6], and Sami et al [7].…”

Section: Introductionmentioning

confidence: 99%

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

Abonazel

Algamal

Awwad

et al. 2022

Front. Appl. Math. Stat.

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The beta regression is a widely known statistical model when the response (or the dependent) variable has the form of fractions or percentages. In most of the situations in beta regression, the explanatory variables are related to each other which is commonly known as the multicollinearity problem. It is well-known that the multicollinearity problem affects severely the variance of maximum likelihood (ML) estimates. In this article, we developed a new biased estimator (called a two-parameter estimator) for the beta regression model to handle this problem and decrease the variance of the estimation. The properties of the proposed estimator are derived. Furthermore, the performance of the proposed estimator is compared with the ML estimator and other common biased (ridge, Liu, and Liu-type) estimators depending on the mean squared error criterion by making a Monte Carlo simulation study and through two real data applications. The results of the simulation and applications indicated that the proposed estimator outperformed ML, ridge, Liu, and Liu-type estimators.

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

Cited by 25 publications

References 30 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

Predictive Probability Models of Road Traffic Human Deaths with Demographic Factors in Ghana

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

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