The Effects of Covariance Structures on Modelling of Longitudinal Data


Extending the general linear model to the linear mixed model takes into account the within-subject correlation between observations with introduction of random effects. Fixed covariance structures of random error and random effect are assumed in linear mixed models. However, a potential risk of model selection still exists. That is, if the specified structure is not appropriate to real data, we cannot make correct statistical inferences. Joint modelling method removes all specifications about covariance structures and comes over the above risk. It simply models covariance structures just like modelling the mean structures in the general linear model. Our conclusions include: a) The estimators of fixed effects parameters are similar, that is, the expected mean values of response variables are similar. b) The standard deviations from different models are obviously different, which indicates that the width of confidence interval is evidently different. c) Through comparing the AIC or BIC value, we conclude that the data-driven mean-covariance regression model can fit data much better and result in more precise and reliable statistical inferences.

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Chen, Y. , Fei, Y. and Pan, J. (2015) The Effects of Covariance Structures on Modelling of Longitudinal Data. Open Access Library Journal, 2, 1-10. doi: 10.4236/oalib.1102086.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Wang, Y.G. and Carey, V. (2003) Working Correlation Structure Misspecification, Estimation and Covariate Design: Implications for Generalised Estimating Equations Performance. Biometrika, 90, 29-41.
[2] Pourahmadi, M. (1999) Joint Mean-Covariance Models with Applications to Longitudinal Data: Unconstrained Parameterization. Biometrika, 86, 677-690.
[3] Pourahmadi, M. (2000) Maximum Likelihood Estimation of Generalised Linear Models for Multivariate Normal Covariance Matrix. Biometrika, 87, 425-435.
[4] Kenward, M.G. (1987) A Method for Comparing Profiles of Repeated Measurements. Applied Statistics, 36, 296-308.
[5] Laird, N.M. and Ware, J.J. (1982) Random-Effects Models for Longitudinal Data. Biometrics, 38, 963-974.
[6] Patterson, H.D. and Thompson, R. (1971) Recovery of Interblock Information When Block Sizes Are Unequal. Biometrika, 58, 545-554.
[7] Harville, D. (1974) Bayesian Inference for Variance Components Using Only Error Constrasts. Biometrika, 61, 383-385.
[8] Diggle, P.J. and Kenward, M.G. (1994) Informative Drop-Out in Longitudinal Data Analysis. Applied Statistics, 43, 49-93.

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