Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 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

Rachael A Hughes  1 , Michael G Kenward  2 , Jonathan A C Sterne  1 , Kate Tilling  1
Affiliations

Estimation of the linear mixed integrated Ornstein-Uhlenbeck model

Rachael A Hughes et al. J Stat Comput Simul. .

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.

PubMed Disclaimer

Figures

Figure 1.
Figure 1.
Line plots of height measurements from 10 students who attended Christ's Hospital School between 1936 and 1969.
See this image and copyright information in PMC

References

    1. Laird N, Ware J. Random-effects models for longitudinal data. Biometrics. 1982;38:963–974. doi: 10.2307/2529876 - DOI - PubMed
    1. Boscardin W, Taylor J, Law N. Longitudinal models for AIDS marker data. Stat Methods Med Res. 1998;7(1):13–27. doi: 10.1191/096228098674392113 - DOI - PubMed
    1. Sowers MF, Crutchfield M, Randolph JF, et al. Urinary ovarian and gonadotrophin hormone levels in premenopausal women with low bone mass. J Bone Miner Res. 1998;13(7):1191–1202. doi: 10.1359/jbmr.1998.13.7.1191 - DOI - PubMed
    1. Diggle P. An approach to the analysis of repeated measurements. Biometrics. 1988;44(4):959–971. doi: 10.2307/2531727 - DOI - PubMed
    1. Taylor J, Cumberland W, Sy J. A stochastic model for analysis of longitudinal AIDS data. J Am Stat Assoc. 1994;89(427):727–736. doi: 10.1080/01621459.1994.10476806 - DOI

LinkOut - more resources