Prediction in linear mixed models
Article first published online: 10 SEP 2004
Australian & New Zealand Journal of Statistics
Volume 46, Issue 3, pages 325–347, September 2004
How to Cite
Welham, S., Cullis, B., Gogel, B., Gilmour, A. and Thompson, R. (2004), Prediction in linear mixed models. Australian & New Zealand Journal of Statistics, 46: 325–347. doi: 10.1111/j.1467-842X.2004.00334.x
- Issue published online: 10 SEP 2004
- Article first published online: 10 SEP 2004
- Received June 2002; revised March 2003; accepted June 2003.
- Cited By
- best linear unbiased prediction;
- linear mixed models;
- residual maximum likelihood
Following estimation of effects from a linear mixed model, it is often useful to form predicted values for certain factor/variate combinations. The process has been well defined for linear models, but the introduction of random effects into the model means that a decision has to be made about the inclusion or exclusion of random model terms from the predictions. This paper discusses the interpretation of predictions formed including or excluding random terms. Four datasets are used to illustrate circumstances where different prediction strategies may be appropriate: in an orthogonal design, an unbalanced nested structure, a model with cubic smoothing spline terms and for kriging after spatial analysis. The examples also show the need for different weighting schemes that recognize nesting and aliasing during prediction, and the necessity of being able to detect inestimable predictions.