Serial correlation or random subject effects

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Abstract
In longitudinal data analysis with random subject effects, there is often within subject serial correlation and possibly unequally spaced observations. This serial correlation can be partially confounded with the random between subject effects. In real data, it is often not clear whether there is serial correlation, random subject effects or both. Using inference based on the likelihood function, it is not always possible to identify the correct model, especially in small samples. However, it is important that some effort be made to attempt to find a good model rather than just making assumptions. This often means trying models with random coefficients, with serial correlation, and with both. Model selection criteria such as likelihood ratio tests and Akaike's Information Criterion (AIC) can be used. The problem of modelling serial correlation with unequally spaced observations is addressed. A real data example is presented where there is an apparent heterogeneity of variances, possible serial correlation and between subject random effects. In this example, it turns out that the random subject effects explains both the serial correlation and the variance heterogeneity.

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