Abstract
In this chapter we consider models for a multivariate response variable represented by serial measurements over time within subject. This setup induces correlations between measurements on the same subject that must be taken into account to have optimal model fits and honest inference. Full likelihood model-based approaches have advantages including (1) optimal handling of imbalanced data and (2) robustness to missing data (dropouts) that occur not completely at random. The three most popular model-based full likelihood approaches are mixed effects models, generalized least squares, and Bayesian hierarchical models.
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Notes
- 1.
A case study in OLS—Chapter 7 from the first edition—may be found on the text’s web site.
- 2.
We can speak interchangeably of correlations of residuals within subjects or correlations between responses measured at different times on the same subject, conditional on covariates X.
- 3.
Variograms can be unstable.
- 4.
To access regular gls functions named anova (for likelihood ratio tests, AIC, etc.) or summary use anova.gls or summary.gls .
- 5.
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Harrell, F.E. (2015). Modeling Longitudinal Responses using Generalized Least Squares. In: Regression Modeling Strategies. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-19425-7_7
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DOI: https://doi.org/10.1007/978-3-319-19425-7_7
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