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http://dx.doi.org/10.5351/CSAM.2014.21.2.169

Autoregressive Cholesky Factor Modeling for Marginalized Random Effects Models  

Lee, Keunbaik (Department of Statistics, Sungkyunkwan University)
Sung, Sunah (GS HomeShopping Inc.)
Publication Information
Communications for Statistical Applications and Methods / v.21, no.2, 2014 , pp. 169-181 More about this Journal
Abstract
Marginalized random effects models (MREM) are commonly used to analyze longitudinal categorical data when the population-averaged effects is of interest. In these models, random effects are used to explain both subject and time variations. The estimation of the random effects covariance matrix is not simple in MREM because of the high dimension and the positive definiteness. A relatively simple structure for the correlation is assumed such as a homogeneous AR(1) structure; however, it is too strong of an assumption. In consequence, the estimates of the fixed effects can be biased. To avoid this problem, we introduce one approach to explain a heterogenous random effects covariance matrix using a modified Cholesky decomposition. The approach results in parameters that can be easily modeled without concern that the resulting estimator will not be positive definite. The interpretation of the parameters is sensible. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using this method.
Keywords
Population-averaged effect; heterogeneity; Quasi-Monte Carlo; autoregressive model; positive definite;
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1 Lee, K. and Daniels, M. J. (2008). Marginalized models for longitudinal ordinal data with application to quality of life studies, Statistics in Medicine, 27, 4359-4380.   DOI
2 Lee, K., Joo, Y., Yoo, J. K. and Lee, J. (2009). Marginalized random effects models for multivariate longitudinal binary data, Statistics in Medicine, 28, 1284-1300.   DOI
3 Lee, K. and Mercante, D. (2010). Longitudinal nominal data analysis using marginalized models, Computational Statistics and Data Analysis, 54, 208-218.   DOI
4 Lee, K., Kang, S., Liu, X. and Seo, D. (2011). Likelihood-based approach for analysis of longitudinal nominal data using marginalized random effects models, Journal of Applied Statistics, 38, 1577-1590.   DOI
5 Lee, K., Lee, J., Hagan, J. and Yoo, J. K. (2012). Modeling the random effects covariance matrix for generalized linear mixed models, Computational Statistics and Data Analysis, 56, 1545-1551.   DOI
6 Pan, J. and MacKenzie, G. (2003). On modelling mean-covariance structures in longitudinal studies, Biometrika, 90, 239-244.   DOI
7 Pan, J. and MacKenzie, G. (2006). Regression models for covariance structures in longitudinal studies, Statistical Modelling, 6, 43-57.   DOI
8 Pinheiro, J. D. and Bates, D. M. (1996). Unconstrained parameterizations for variance-covariance matrices, Statistics and Computing, 6, 289-296.   DOI
9 Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation, Biometrika, 86, 677-690.   DOI   ScienceOn
10 Pourahmadi, M. (2000). Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix, Biometrika, 87, 425-435   DOI
11 Pourahmadi, M. and Daniels, M. J. (2002). Dynamic conditionally linear mixed models for longitu-dinal fata, Biometrics, 58, 225-231.   DOI
12 Wang, Y. and Daniels, M. J. (2013). Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances, Journal of Multivariate Analysis, 116, 130-140.   DOI
13 Fitzmaurice, G. M. and Laird, N. M. (1993). A likelihood-based method for analysing longitudinal binary responses, Biometrika, 80, 141-151.   DOI   ScienceOn
14 Heagerty, P. J. (1999). Marginally specified logistic-normal models for longitudinal binary data, Biometrics, 55, 688-698.   DOI
15 Daniels, M. J. and Pourahmadi, M. (2009). Modeling repeated count data subject to informative dropout, Journal of Multivariate Analysis, 100, 2352-2363.   DOI
16 Daniels, M. J. and Zhao, Y. D. (2003). Modelling the random effects covariance matrix in longitudinal data, Statistics in Medicine, 22, 1631-1647.   DOI
17 Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 125-134.
18 Lee, K. and Daniels, M. J. (2007). A Class of Markov models for longitudinal ordinal data, Biometrics, 63, 1060-1067.   DOI
19 Daniels, M. J. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data, Biometrika, 89, 553-566.   DOI
20 Heagerty, P. J. and Kurland, B. F. (2001). Misspecified maximum likelihood estimates and generalized linear mixed models, Biometrika, 88, 973-985.   DOI
21 Kim, J., Kim, E., Yi, H., Joo, S., Shin, K., Kim, J., Kimm, K., and Shin, C. (2006). Short-term incidence rate of hypertension in Korea middle-aged adults. Journal of Hypertension, 24, 2177-2182.   DOI   ScienceOn
22 Heagerty, P. J. (2002). Marginalized transition models and likelihood inference for longitudinal categorical data, Biometrics, 58, 342-351.   DOI
23 Lee, K., Daniels, M. J. and Joo, Y. (2013). Flexible marginalized models for bivariate longitudinal ordinal data, Biostatistics, 14, 462-476.   DOI