Document Type




Format of Original

9 p.

Publication Date




Source Publication

Journal of Statistical Planning and Inference

Source ISSN


Original Item ID

doi: 10.1016/j.jspi.2011.09.011


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.


Accepted version. Journal of Statistical Planning and Inference, Vol. 142, No. 3 (March 2012): 743-751. DOI. © 2012 Elsevier. Used with permission.

Mehdi Maadooliat was affiliated with Texas A&M University at the time of publication.