Developing a ridge estimator for the gamma regression model

Algamal, Zakariya Yahya

doi:10.1002/cem.3054

Cited by 44 publications

(23 citation statements)

References 27 publications

(47 reference statements)

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“…The chemical dataset adopted in this study was employed in the study of Algamal [ 3 , 19 ]. He employed the quantitative structure-activity relationship (QSAR) model to study the relationship between the biological activities IC 50 of 65 imidazo [4, 5-b] pyridine derivatives – an anticancer compound – and 15 molecular descriptors.…”

Section: Real-life Data: Algamal Datamentioning

confidence: 99%

“…Batah et al [ 14 ] proposed a modified Jackknife ridge estimator by combining the ideas of the generalized ridge estimator and Jackknifed ridge estimator. Also, Algamal [ 3 ] developed the modified Jackknifed ridge gamma regression estimator. Recently, the modified version of the ridge regression estimator with two biasing parameters was proposed for both the LRM and GRM [ 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

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A New Ridge-Type Estimator for the Gamma Regression Model

et al. 2021

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The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

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Section: Real-life Data: Algamal Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Ridge-Type Estimator for the Gamma Regression Model

et al. 2021

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“…Regression models have several applications in chemometrics and other disciplines. [1][2][3][4][5] Influence diagnostics are vital to any regression modeling for testing the model reliability as it determines the strange effect of influential observations on regression model fitting. There are several methods to diagnose the influential observations in the linear regression model.…”

Section: Introductionmentioning

confidence: 99%

Influence diagnostics in the inverse Gaussian ridge regression model: Applications in chemometrics

Amin

Faisal

Akram

2021

Journal of Chemometrics

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The influential observation affects the regression model inferences. Literature has shown that the problems of multicollinearity and influential observations can jointly exist in a model. The ridge regression estimator has been developed to handle the challenge of multicollinearity. The detection of influential observations with multicollinearity and its impact on the ridge estimates is necessary for better decision making. In this article, we proposed some influence diagnostics for the inverse Gaussian ridge regression model (IGRRM). The proposed diagnostics are evaluated with the help of a simulation study and two chemometric-related data sets. We found that the covariance ratio (CVR) method is better than other methods for the detection of influential observations under smaller dispersion. While for larger dispersion, all the IGRRM diagnostics perform equally well for the identification of influential observations.

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“…Furthermore, Månsson (2012) suggested ridge estimators for the negative binomial regression model. Recently, Amin et al (2020a) and Algamal (2018a) proposed some ridge estimators and recommended best ridge estimator for the gamma RR. Algamal (2018b) presented an efficient estimation algorithm of biasing parameter of the ridge estimator.…”

Section: Introductionmentioning

confidence: 99%

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

Amin

Qasim

Afzal

et al. 2020

Communications in Statistics - Simulation and Computation

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In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods.

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Developing a ridge estimator for the gamma regression model

Cited by 44 publications

References 27 publications

A New Ridge-Type Estimator for the Gamma Regression Model

A New Ridge-Type Estimator for the Gamma Regression Model

Influence diagnostics in the inverse Gaussian ridge regression model: Applications in chemometrics

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

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