Modelling the random effects covariance matrix in longitudinal data
A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to mo...
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| Published in | Statistics in medicine Vol. 22; no. 10; pp. 1631 - 1647 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
30.05.2003
Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 |
| DOI | 10.1002/sim.1470 |
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| Abstract | A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject‐specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects. Copyright © 2003 John Wiley & Sons, Ltd. |
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| AbstractList | A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects. A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject‐specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects. Copyright © 2003 John Wiley & Sons, Ltd. A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects.A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects. |
| Author | Zhao, Yan D. Daniels, Michael J. |
| AuthorAffiliation | 2 Eli Lilly & Company, Lilly Corporate Center, Faris II, Indianapolis, IN 46285, U.S.A 1 Department of Statistics, University of Florida, Gainesville, FL 32611, U.S.A |
| AuthorAffiliation_xml | – name: 2 Eli Lilly & Company, Lilly Corporate Center, Faris II, Indianapolis, IN 46285, U.S.A – name: 1 Department of Statistics, University of Florida, Gainesville, FL 32611, U.S.A |
| Author_xml | – sequence: 1 givenname: Michael J. surname: Daniels fullname: Daniels, Michael J. email: mdaniels@stat.ufl.edu organization: Department of Statistics, University of Florida, Gainesville, FL 32611, U.S.A – sequence: 2 givenname: Yan D. surname: Zhao fullname: Zhao, Yan D. organization: Eli Lilly & Company, Lilly Corporate Center, Faris II, Indianapolis, IN 46285, U.S.A |
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Statistical Analysis With Missing Data. Wiley: New York, 1987. – reference: Pourahmadi M, Daniels MJ. Dynamic conditional linear mixed models for longitudinal data. Biometrics 2002; 58:225-231. – reference: Bock RD. Multivariate Statistical Methods in Behavioral Research. McGraw Hill: New York, 1975; 54. – reference: Heagerty PJ, Kurland BF. Misspecified maximum likelihood estimate and generalised linear mixed models. Biometrika 2001; 88:973-986. – reference: Leonard T, Hsu JSJ. Bayesian inference for a covariance matrix. Annals of Statistics 1992; 20:1669-1696. – reference: Davidian M, Giltinan DM. Nonlinear Models for Repeated Measurement Data. Chapman and Hall: 1995. – reference: Lin X, Raz J, Harlow SD. Linear mixed models with heterogeneous within-cluster variances. Biometrics 1997; 53:910-923. – reference: Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit (with discussion). 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| Snippet | A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed... |
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| SubjectTerms | Antidepressive Agents - therapeutic use Biological and medical sciences Cholesky decomposition Depression - therapy heterogeneity Humans Longitudinal Studies Medical sciences mixed models Models, Statistical Psychotherapy |
| Title | Modelling the random effects covariance matrix in longitudinal data |
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