Models for Longitudinal Data with Random Effects and AR(1) Errors

For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the "conditional independence" random effect...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1989-06, Vol.84 (406), p.452-459
Main Authors: Chi, Eric M., Reinsel, Gregory C.
Format: Article
Language:English
Subjects:
Autocorrelation
Autoregressive model
Bayes estimators
Covariance matrices
Empirical Bayes estimate
Exact sciences and technology
Inference from stochastic processes
time series analysis
Longitudinal data
Mathematics
Matrices
Maximum likelihood estimation
Modeling
Multilevel models
Prediction
Probability and statistics
Sciences and techniques of general use
Score test
Statistics
Theory and Methods
Time series models
White noise
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Summary:For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the "conditional independence" random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregressive) AR(1) errors is then derived. Empirical Bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with AR(1) errors model are also considered. A numerical example is presented to illustrate these methods.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1989.10478790