© 1999 by Biometrika Trust
Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation
Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA E-mail: pourahm@math.niu.edu
We provide unconstrained parameterisation for and model a covariance using covariates. The Cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix. The entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors. An extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity, Gabriel's antedependence models, Dempster's covariance selection models and the class of graphical models. The likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed. Applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data. A graphical method, similar to that based on the correlogram in time series, is developed and used to identify parametric models for nonstationary covariances.
Key Words: Antedependence; Cholesky decomposition; Generalised linear model; Linear regression and autoregression; Link function; Multivariate normal; Nonstationary model; Stationary model
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  M. Pourahmadi Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance Correlation Parameters Biometrika, December 1, 2007; 94(4): 1006 - 1013. [Abstract] [PDF]
|
|
|
|
 |
|
 W. Zhao, H. Li, W. Hou, and R. Wu Wavelet-Based Parametric Functional Mapping of Developmental Trajectories With High-Dimensional Data Genetics, July 1, 2007; 176(3): 1879 - 1892. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
O. Rosen and D. S. Stoffer Automatic estimation of multivariate spectra via smoothing splines Biometrika, June 1, 2007; 94(2): 335 - 345. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 J. Pan and G. MacKenzie Modelling conditional covariance in the linear mixed model Statistical Modeling, April 1, 2007; 7(1): 49 - 71. [Abstract] [PDF]
|
|
|
|
 |
|
 E. Lesaffre, D. Rizopoulos, and R. Tsonaka The logistic transform for bounded outcome scores Biostat., January 1, 2007; 8(1): 72 - 85. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. Cecere, A. Jara, and E. Lesaffre Analyzing the emergence times of permanent teeth: an example of modeling the covariance matrix with interval-censored data Statistical Modeling, December 1, 2006; 6(4): 337 - 351. [Abstract] [PDF]
|
|
|
|
|
|
J. Pan and G. MacKenzie Regression models for covariance structures in longitudinal studies Statistical Modeling, April 1, 2006; 6(1): 43 - 57. [Abstract] [PDF]
|
|
|
|
|
|
R. Wu and W. Hou A Hyperspace Model to Decipher the Genetic Architecture of Developmental Processes: Allometry Meets Ontogeny Genetics, January 1, 2006; 172(1): 627 - 637. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 E. Lesaffre, A. Komarek, and D. Declerck An overview of methods for interval-censored data with an emphasis on applications in dentistry Statistical Methods in Medical Research, December 1, 2005; 14(6): 539 - 552. [Abstract] [PDF]
|
|
|
|
 |
|
 W. Zhao, Y. Q. Chen, G. Casella, J. M. Cheverud, and R. Wu A non-stationary model for functional mapping of complex traits Bioinformatics, May 15, 2005; 21(10): 2469 - 2477. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 F. Jaffrezic, E. Venot, D. Laloe, A. Vinet, and G. Renand Use of structured antedependence models for the genetic analysis of growth curves J Anim Sci, December 1, 2004; 82(12): 3465 - 3473. [Abstract] [Full Text] [PDF]
|
|