Model selection via conditional conceptual predictive statistic under ridge regression in linear mixed models

ABSTRACT

In this paper, we focus on the progress of variant of conceptual predictive ($C_p$) statistic and we propose the model selection criterion that depend on $C_p$ statistic under ridge regression for linear mixed model selection. The proposed criterion is conditional ridge $C_p$ ($CR{C}_p$) statistic based on the expected conditional Gauss discrepancy. Two versions of $CR{C}_p$ statistic under the assumptions that the variance components are known and unknown are derived. To examine the performance of the proposed criterion, a real data analysis and a Monte Carlo simulation study are given.

KEYWORDS:

• Conditional Gauss discrepancy
• conditional ridge $C_p$
• linear mixed model selection
• multicollinearity
• ridge regression

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Özge Kuran  http://orcid.org/0000-0001-5632-001X

M. Revan Özkale  http://orcid.org/0000-0001-7085-7403

Notes

1 Any two values of k will not be enough to see whether it increases or decreases. Therefore, it should be at least three k values.