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Modelling covariance structure in bivariate marginal models for longitudinal data

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posted on 2022-11-11, 20:27 authored by Jing Xu, Gilbert MackenzieGilbert Mackenzie
It can be more challenging and demanding to efficiently model the covariance matrices for multivariate longitudinal data than for univariate case because of the correlations between responses arising from multiple variables and repeated measurements over time. In addition to the more complicated covariance structures, the positive-definiteness constraint is still the major obstacle in modelling covariance matrices as in univariate case. In this paper, we develop a data-based method to model the covariance structures. Using this method, the constrained and hard-to-model parameters of ∑i are traded in for uncon- strained and interpretable parameters. Estimates of these parameters, together with the parameters in the mean, are obtained by maximum likelihood approach, and the large- sample asymptotic properties are derived when the observations are normally distributed. A simulation is carried out to illustrate the asymptotics. Application to a set of bivariate visual data shows that our method performs very well even when modelling bivariate nonstationary dependence structures.

History

Publication

Biometrika;99(3), pp. 649-662

Publisher

Oxford University Press

Note

peer-reviewed

Other Funding information

SFI

Rights

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version Modelling covariance structure in bivariate marginal models for longitudinal data, 2012,99(3), pp. 649-662 is available online at:http://dx.doi.org/10.1093/biomet/ass031

Language

English

Also affiliated with

  • BIO-SI - Bio-Statistics & Informatics Project

Department or School

  • Mathematics & Statistics

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