Influential diagnostics with Pena’s statistic for the modified ridge regression

Kashif, Muhammad; Ullah, Muhammad Aman; Aslam, Muhammad

doi:10.1080/03610918.2019.1634204

Cited by 4 publications

(3 citation statements)

References 20 publications

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“…The detection percentage of the included influential observation is considered as the performance evaluation criteria of the proposed methods. 40,41 This assessment criteria is defined as Detection % ð Þ= Total number of detections in R replications Total number of replication × 100, where R represents the number of replications which are set to be 1000. The simulation study under various parametric conditions is completed with the help of R software.…”

Section: Monte Carlo Simulation Studymentioning

confidence: 99%

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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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Section: Monte Carlo Simulation Studymentioning

confidence: 99%

“…32,33 This issue has been well studied for the LMs. [32][33][34][35][36][37][38][39][40][41] Controlling the multicollinearity may increase the effect of influence cases. 33,38,39 Belsley et al 33 pointed out that the performance of influence diagnostics maybe change using the ridge estimation approach.…”

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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“…To evaluate the reliability and quality of regression estimates and to overcome the problems in model fitting, diagnostic techniques have been developed. Although regression diagnostics have been developed methodologically and theoretically for linear regression models together with multicollinearity (see [17][18][19][20][21][22][23][24]), some studies about the influence diagnostics in the GLM with uncorrelated explanatory variables are available in the literature. Pregibon [25] proposed the influence diagnostics for logistic regression using the one-step methods.…”

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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