Prediction in linear mixed models

Abstract

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.

Parent-of-origin effects cause genetic variation in pig performance traits

“…where the prediction error variances and covariances of both genetic effects for each animal were retrieved from the inverted left-hand side of the mixed model equations as described for ASReml in Gilmour et al (2004) and Welham et al (2004).…”

Four-way data analysis within the linear mixed modelling framework

“…These estimates were used to calculate the adjusted means for the considered combinations of factors, using the algorithm described by Welham et al (2004). Traditional methods of pairwise comparisons of means in unbalanced data and a large number of levels of factors are not useful.…”

A comparison of winter wheat cultivar rankings in groups of Polish locations

“…The best linear unbiased estimators (BLUEs) for the fixed effects and the best linear unbiased predictors (BLUPs) of the random effects in model (2) were utilized to calculate adjusted GR means on average locations using the algorithm described by Welham et al (2004). The obtained adjusted means were used to determine the cultivar rankings in each region on average locations.…”