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Estimation of the linear mixed integrated Ornstein-Uhlenbeck model
Rachael A Hughes1, Michael G Kenward2, Jonathan A C Sterne1
1School of Social and Community Medicine, University of Bristol, Bristol, UK.
Journal of Statistical Computation and Simulation
|May 19, 2017
Summary
The linear mixed Ornstein-Uhlenbeck (IOU) model, now available in Stata, effectively handles serial correlation in data. Simulations confirm its feasibility for fitting complex datasets, outperforming standard models.
Area of Science:
- Statistics
- Biostatistics
- Econometrics
Background:
- The linear mixed model is a standard tool for analyzing correlated data.
- Incorporating an integrated Ornstein-Uhlenbeck (IOU) process enhances models by capturing serial correlation and estimating derivative tracking.
- Limited software availability has hindered the adoption of the linear mixed IOU model.
Purpose of the Study:
- To implement the linear mixed IOU model in Stata.
- To assess the feasibility of fitting this model using restricted maximum likelihood.
- To compare performance across various optimization algorithms, parameterizations, data structures, and random-effects structures.
Main Methods:
- Implementation of the linear mixed IOU model in Stata.
- Monte Carlo simulations using balanced and unbalanced datasets.
- Comparison of different optimization algorithms, IOU process parameterizations, data structures, and random-effects structures.
- Restricted maximum likelihood (REML) fitting approach.
Main Results:
- The linear mixed IOU model is practical and feasible to fit, particularly for large and moderately sized balanced datasets.
- Feasible fitting was also demonstrated for large unbalanced datasets with dropout and intermittent missingness.
- The linear mixed IOU model provided a superior fit compared to the standard linear mixed model in a real-data analysis.
Conclusions:
- The Stata implementation makes the linear mixed IOU model accessible for researchers.
- The model is a viable and often superior alternative to standard linear mixed models for data with serial correlation.
- This advancement facilitates more accurate modeling of complex longitudinal and time-series data.
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