TY - JOUR

T1 - On generalized degrees of freedom with application in linear mixed models selection

AU - You, Chong

AU - Müller, Samuel

AU - Ormerod, John T.

PY - 2016/1

Y1 - 2016/1

N2 - The concept of degrees of freedom plays an important role in statistical modeling and is commonly used for measuring model complexity. The number of unknown parameters, which is typically used as the degrees of freedom in linear regression models, may fail to work in some modeling procedures, in particular for linear mixed effects models. In this article, we propose a new definition of generalized degrees of freedom in linear mixed effects models. It is derived from using the sum of the sensitivity of the expected fitted values with respect to their underlying true means. We explore and compare data perturbation and the residual bootstrap to empirically estimate model complexity. We also show that this empirical generalized degrees of freedom measure satisfies some desirable properties and is useful for the selection of linear mixed effects models.

AB - The concept of degrees of freedom plays an important role in statistical modeling and is commonly used for measuring model complexity. The number of unknown parameters, which is typically used as the degrees of freedom in linear regression models, may fail to work in some modeling procedures, in particular for linear mixed effects models. In this article, we propose a new definition of generalized degrees of freedom in linear mixed effects models. It is derived from using the sum of the sensitivity of the expected fitted values with respect to their underlying true means. We explore and compare data perturbation and the residual bootstrap to empirically estimate model complexity. We also show that this empirical generalized degrees of freedom measure satisfies some desirable properties and is useful for the selection of linear mixed effects models.

KW - Deviance

KW - Information criterion

KW - Resampling

KW - Bootstrap

UR - http://www.scopus.com/inward/record.url?scp=84953345940&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP110101998

UR - http://purl.org/au-research/grants/arc/DE130101670

U2 - 10.1007/s11222-014-9488-7

DO - 10.1007/s11222-014-9488-7

M3 - Article

AN - SCOPUS:84953345940

VL - 26

SP - 199

EP - 210

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 1-2

ER -