A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

Type
Article

Authors
Huang, Jianhua Z.
Chen, Min
Maadooliat, Mehdi
Pourahmadi, Mohsen

KAUST Grant Number
KUS-CI-016-04

Date
2012-03

Abstract
Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome this and other challenges by embedding the covariance matrix of the observed data for each subject in a larger covariance matrix and employing the familiar EM algorithm to compute the maximum likelihood estimates of the parameters and their standard errors. We illustrate and assess the methodology using real data sets and simulations. © 2011 Elsevier B.V.

Citation
Huang JZ, Chen M, Maadooliat M, Pourahmadi M (2012) A cautionary note on generalized linear models for covariance of unbalanced longitudinal data. Journal of Statistical Planning and Inference 142: 743–751. Available: http://dx.doi.org/10.1016/j.jspi.2011.09.011.

Acknowledgements
Huang and Pourahmadi were partially supported by NSF of the US. Huang was also supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).

Publisher
Elsevier BV

Journal
Journal of Statistical Planning and Inference

DOI
10.1016/j.jspi.2011.09.011

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