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Hughes RA, Kenward MG, Sterne JAC, et al. Estimation of the linear mixed integrated Ornstein-Uhlenbeck model. J Stat Comput Simul. 2017;87(8):1541-1558doi: 10.1080/00949655.2016.1277425.
Hughes, R. A., Kenward, M. G., Sterne, J. A. C., & Tilling, K. (2017). Estimation of the linear mixed integrated Ornstein-Uhlenbeck model. Journal of statistical computation and simulation, 87(8), 1541-1558. https://doi.org/10.1080/00949655.2016.1277425
Hughes, Rachael A, et al. "Estimation of the linear mixed integrated Ornstein-Uhlenbeck model." Journal of statistical computation and simulation vol. 87,8 (2017): 1541-1558. doi: https://doi.org/10.1080/00949655.2016.1277425
Hughes RA, Kenward MG, Sterne JAC, Tilling K. Estimation of the linear mixed integrated Ornstein-Uhlenbeck model. J Stat Comput Simul. 2017 May 24;87(8):1541-1558. doi: 10.1080/00949655.2016.1277425. Epub 2017 Jan 12. PMID: 28515536; PMCID: PMC5407356.
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J Stat Comput Simul. 2017 May 24;87(8):1541-1558. doi: 10.1080/00949655.2016.1277425. Epub 2017 Jan 12.

Estimation of the linear mixed integrated Ornstein-Uhlenbeck model.

Journal of statistical computation and simulation

Rachael A Hughes, Michael G Kenward, Jonathan A C Sterne, Kate Tilling

Affiliations

  1. School of Social and Community Medicine, University of Bristol, Bristol, UK.
  2. Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK.

PMID: 28515536 PMCID: PMC5407356 DOI: 10.1080/00949655.2016.1277425

Abstract

The linear mixed model with an added integrated Ornstein-Uhlenbeck (IOU) process (linear mixed IOU model) allows for serial correlation and estimation of the degree of derivative tracking. It is rarely used, partly due to the lack of available software. We implemented the linear mixed IOU model in Stata and using simulations we assessed the feasibility of fitting the model by restricted maximum likelihood when applied to balanced and unbalanced data. We compared different (1) optimization algorithms, (2) parameterizations of the IOU process, (3) data structures and (4) random-effects structures. Fitting the model was practical and feasible when applied to large and moderately sized balanced datasets (20,000 and 500 observations), and large unbalanced datasets with (non-informative) dropout and intermittent missingness. Analysis of a real dataset showed that the linear mixed IOU model was a better fit to the data than the standard linear mixed model (i.e. independent within-subject errors with constant variance).

Keywords: 62F99; 62J99; 62M10; 62P10; Fixed effects; Integrated Ornstein–Uhlenbeck process; Newton Raphson; random effects; repeated measures

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