An Alternative Expression of the Covariance Structure of Multivariate Longitudinal Data

• Activity Number: 34
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Chulmin Kim*+
• Companies: Rochester Institute of Technology
• Keywords: Covariance Structure ; Longitudinal Data ; Antedependence Models

Abstract

The precision matrix specification is widely used for modeling covariance structure of longitudinal data. It specifies parsimonious models for the elements of the inverse of the covariance matrix. Antedependence (AD) models that allow the variances and same-lag correlations to vary over time can be useful for modeling covariance structure of longitudinal data when serial correlation exists among measurements within subject. When measurement times are common across the subjects, the maximum likelihood estimators of the AD model parameters can be obtained explicitly. When measurement times are not common across the subjects, extensive computations are required to obtain the maximum likelihood estimators of the parameters numerically. Zimmerman (1998) showed how this computational burden can be substantially reduced. We extend this approach to multivariate longitudinal data by developing an alternative expression of the covariance structure and its inverse of the Multivariate Antedependence (MAD) models. An example is illustrated in which the usefulness of the results.