The ridge prediction error sum of squares statistic in linear mixed models

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dc.contributor.authorKuran, Özge
dc.contributor.authorÖzkale, M. Revan
dc.date.accessioned2024-04-24T15:59:47Z
dc.date.available2024-04-24T15:59:47Z
dc.date.issued2023
dc.departmentDicle Üniversitesien_US
dc.description.abstractIn case of multicollinearity, PRESS statistics has been proposed to be used in the selection of the ridge biasing parameter of the ridge estimator which is introduced as an alternative to BLUE. This newly proposed PRESS statistic for the ridge estimator, CPRESSk, depends on the conditional ridge residual and can be computed once at a time by fitting the linear mixed model with all the observations. We also define R-RidPred(2) statistic to evaluate the predictive ability of the ridge fit. Since the PRESS statistic for the BLUE is a special CPRESSk statistic, we indirectly also give closed form solution of the PRESS statistic for the BLUE. Then, we compared the predictive performance of the linear mixed model via the statistics CPRESSk, GCV(k) and C-p by considering a real data analysis and a simulation study where the optimal ridge biaisng parameter is obtained by minimizing each statistic. The study shows that the ridge predictors improve the predictive performance of a linear mixed model over BLUE in the presence of multicollinearity and each statistic gives a different optimum ridge biasing value and they show the best predictive performance at their optimum ridge biasing values. In addition, the simulation study has shown that the intensity of variance and multicollinearity is effective in determining the optimum ridge biasing value and this optimum ridge biasing value is effective on the superiority of the predictive performance of ridge estimator over BLUE.en_US
dc.identifier.citationKuran, Ö. ve Özkale, M. R.(2023). The ridge prediction error sum of squares statistic in linear mixed models. Metrika, 1-17.
dc.identifier.doi10.1007/s00184-023-00927-z
dc.identifier.issn0026-1335
dc.identifier.issn1435-926X
dc.identifier.scopus2-s2.0-85173731546
dc.identifier.scopusqualityQ3
dc.identifier.urihttps://doi.org/10.1007/s00184-023-00927-z
dc.identifier.urihttps://hdl.handle.net/11468/14258
dc.identifier.wosWOS:001079882600001
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoenen_US
dc.publisherSpringer Heidelbergen_US
dc.relation.ispartofMetrika
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCross-validationen_US
dc.subjectLinear mixed modelen_US
dc.subjectMulticollinearityen_US
dc.subjectPrediction error sum of squaresen_US
dc.subjectRidge estimationen_US
dc.subjectConditional ridge residualen_US
dc.titleThe ridge prediction error sum of squares statistic in linear mixed modelsen_US
dc.titleThe ridge prediction error sum of squares statistic in linear mixed models
dc.typeArticleen_US

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