Multivariate t semiparametric mixed-effects model for longitudinal data with multiple characteristics

Abstract

Semiparametric mixed-effects models (SMM) have received increasing attention in recent years because of the greater flexibility in analysing longitudinal trajectories. However, the normality assumption of SMM may be unrealistic when outliers occur in the data. This paper presents a semiparametric extension of the multivariate t linear mixed-effects model (MtLMM), called the multivariate t semiparametric mixed model (MtSMM). To be specific, the MtSMM incorporates a parametric linear function related to the fixed covariate effects and random effects which have a joint multivariate t distribution together with an arbitrary nonparametric smooth function to capture the unexpected patterns. A computationally analytical EM-based algorithm is developed for carrying out maximum likelihood estimation of the MtSMM. Simulation studies and a real example concerning the analysis of PBCseq data are used to investigate the empirical behaviour of the proposed methodology.

Keywords:

• Multiple characteristics
• multivariate t distribution
• outliers
• semiparametric modelling
• smoothing spline

Acknowledgments

The authors would like to thank the AE and two anonymous referees for their insightful comments which substantially improve the paper. W.L. Wang and T.I. Lin would like to acknowledge the support of the Ministry of Science and Technology of Taiwan under grant numbers MOST 107-2628-M-035-001-MY3 and MOST 107-2118-M-005-002-MY2, respectively.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

W. L. Wang and T. I. Lin would like to acknowledge the support of the Ministry of Science and Technology of Taiwan under [grant numbers MOST 107-2628-M-035-001-MY3 and MOST107-2118-M-005-002-MY2].