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

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  • Wang, Wan-Lun
  • Fan, Tsai-Hung

Abstract

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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    1. 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.
    2. 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.
    3. Xiao Song & Marie Davidian & Anastasios A. Tsiatis, 2002. "A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 58(4), pages 742-753, December.
    4. 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.
    5. 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. M. Taavoni & M. Arashi, 2021. "Kernel estimation in semiparametric mixed effect longitudinal modeling," Statistical Papers, Springer, vol. 62(3), pages 1095-1116, June.
    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. Hong-Yan Jiang & Rong-Xian Yue, 2019. "Pseudo-Bayesian D-optimal designs for longitudinal Poisson mixed models with correlated errors," Computational Statistics, Springer, vol. 34(1), pages 71-87, March.
    5. Rhee, Anbin & Kwak, Min-Sun & Lee, Keunbaik, 2022. "Robust modeling of multivariate longitudinal data using modified Cholesky and hypersphere decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    6. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    7. 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.
    8. Vana-Gür, Laura, 2024. "Multivariate ordinal regression for multiple repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).
    9. Paolo Vidoni, 2017. "Improved multivariate prediction regions for Markov process models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 1-18, March.

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