Smooth Random Effects Distribution in a Linear Mixed Model

Authors: Ghidey, Wendimagegn¹; Lesaffre, Emmanuel¹; Eilers, Paul²

Source: Biometrics, Volume 60, Number 4, 1 December 2004 , pp. 945-953(9)

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Abstract:

Summary A linear mixed model with a smooth random effects density is proposed. A similar approach to P-spline smoothing of <link href="#b2">Eilers and Marx (1996, Statistical Science11, 89-121) is applied to yield a more flexible estimate of the random effects density. Our approach differs from theirs in that the B-spline basis functions are replaced by approximating Gaussian densities. Fitting the model involves maximizing a penalized marginal likelihood. The best penalty parameters minimize Akaike's Information Criterion employing <link href="#b3">Gray's (1992, Journal of the American Statistical Association87, 942-951) results. Although our method is applicable to any dimensions of the random effects structure, in this article the two-dimensional case is explored. Our methodology is conceptually simple, and it is relatively easy to fit in practice and is applied to the cholesterol data first analyzed by <link href="#b16">Zhang and Davidian (2001, Biometrics57, 795-802). A simulation study shows that our approach yields almost unbiased estimates of the regression and the smoothing parameters in small sample settings. Consistency of the estimates is shown in a particular case.

Document Type: Research article

DOI: http://dx.doi.org/10.1111/j.0006-341X.2004.00250.x

Affiliations: 1: Biostatistical Centre, Catholic University of Leuven, Kapucynenvoer 35, B-3000 Leuven, Belgium 2: Medical Statistics, University of Leiden, 2300 RC Leiden, The Netherlands

Publication date: 2004-12-01