An efficient computing strategy for prediction in mixed linear models

After estimation of effects from a linear mixed model, it is often useful to form predicted values for certain factor/variate combinations. This process has been well-defined for linear models, but the introduction of random effects means that a decision has to be made about the inclusion or exclusion of random model terms from the predictions, including the residual error. For spatially correlated data, kriging then becomes prediction from the fitted model. In many cases, the size of the matrices required to calculate predictions and their covariance matrix directly can be prohibitive. An efficient computational strategy for calculating predictions and their standard errors is given, which includes the ability to detect the invariance of predictions to the parameterisation used in the model.