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ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors


  • Wang, Wan-Lun
  • Fan, Tsai-Hung


For the analysis of longitudinal data with multiple characteristics, we are devoted to providing additional tools for multivariate linear mixed models in which the errors are assumed to be serially correlated according to an autoregressive process. We present a computationally flexible ECM procedure for obtaining the maximum likelihood estimates of model parameters. A score test statistic for testing the existence of autocorrelation among within-subject errors of each characteristic is derived. The techniques for the estimation of random effects and the prediction of further responses given past repeated measures are also investigated. The methodology is illustrated through an application to a set of AIDS data and two small simulation studies.

Suggested Citation

  • Wang, Wan-Lun & Fan, Tsai-Hung, 2010. "ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1328-1341, May.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1328-1341

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    References listed on IDEAS

    1. Chi, Eric M. & Reinsel, Gregory C., 1991. "Asymptotic properties of the score test for autocorrelation in a random effects with AR(1) errors model," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 453-457, May.
    2. Lin, Tsung I. & Ho, Hsiu J., 2008. "A simplified approach to inverting the autocovariance matrix of a general ARMA(p,q) process," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 36-41, January.
    3. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    4. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
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    Cited by:

    1. Hsiao, Cheng & Zhou, Qiankun, 2015. "Statistical inference for panel dynamic simultaneous equations models," Journal of Econometrics, Elsevier, vol. 189(2), pages 383-396.
    2. D. Concordet & R. Servien, 2014. "Individual prediction regions for multivariate longitudinal data with small samples," Biometrics, The International Biometric Society, vol. 70(3), pages 629-638, September.
    3. Wang, Wan-Lun & Fan, Tsai-Hung, 2012. "Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 300-310.
    4. Paolo Vidoni, 2017. "Improved multivariate prediction regions for Markov process models," Statistical Methods & Applications, Springer;SocietĂ  Italiana di Statistica, vol. 26(1), pages 1-18, March.

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