This reference might be of use in this discussion.

Aust. N. Z. J. Stat. 46(3), 2004, 325–347
PREDICTION IN LINEAR MIXED MODELS
Sue Welham1∗, Brian Cullis2, Beverley Gogel3,
Arthur Gilmour4 and Robin Thompson1
Rothamsted Research, Wagga Agricultural Institute,
Queensland DPI and Orange Agricultural Institute
Summary
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.
Key words: best linear unbiased prediction; BLUP; linear mixed models; prediction; REML; residual
maximum likelihood.
1. Introduction

Dr Steven G. Candy
Senior Applied Statistician
Wildlife Conservation and Fisheries
Australian Antarctic Division
203 Channel Hwy, Kingston, Tasmania, 7050, Australia
ph: (+61) 3 62 323135


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