Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data

Normality of random effects is a routine assumption for the linear mixed model, but it may be unrealistic, obscuring important features of among-individual variation. We relax this assumption by approximating the random effects density by the seminonparameteric (SNP) representation of Gallant and Nychka (1987, Econometrics 55, 363-390), which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may be carried out using standard optimization techniques. We demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simulation and using longitudinal data from the Framingham study.

[1]  J. Raz,et al.  Semiparametric Stochastic Mixed Models for Longitudinal Data , 1998 .

[2]  G. Barrie Wetherill,et al.  Random Effects Models , 1981 .

[3]  M A Newton,et al.  An Estimation Method for the Semiparametric Mixed Effects Model , 1999, Biometrics.

[4]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[5]  T A Louis,et al.  Random effects models with non-parametric priors. , 1992, Statistics in medicine.

[6]  A. Gallant,et al.  Semi-nonparametric Maximum Likelihood Estimation , 1987 .

[7]  R. Littell.  SAS System for Mixed Models , 1996 .

[8]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[9]  S. Zeger,et al.  A Smooth Nonparametric Estimate of a Mixing Distribution Using Mixtures of Gaussians , 1996 .

[10]  M. Aitkin.  A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models , 1999, Biometrics.

[11]  M. Davidian,et al.  Estimating the parameters in the Cox model when covariate variables are measured with error. , 1998, Biometrics.

[12]  G. Verbeke,et al.  A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population , 1996 .

[13]  N. Laird.  Nonparametric Maximum Likelihood Estimation of a Mixing Distribution , 1978 .

[14]  L. Skovgaard.  NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[15]  R. Pearl.  Biometrics , 1914, The American Naturalist.

[16]  Marie Davidian,et al.  The Nonlinear Mixed Effects Model with a Smooth Random Effects Density , 1993 .

[17]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[18]  G. Verbeke,et al.  The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data , 1997 .

[19]  Stephen W. Raudenbush,et al.  Random effects models. , 1994 .