Introduction to Mixed Modelling: Beyond Regression and Analysis of Variance, 2nd Edition

Chapter 4Interval estimates for fixed-effect terms in mixed models

4.1 The concept of an interval estimate

We have seen in earlier chapters that the estimates of fixed effects produced by mixed-model analysis are similar to those produced by the more familiar analysis methods. Regression analysis gives coefficients that are interpreted as slopes and intercepts; analysis of variance gives treatment means. Mixed-model analysis, when the same terms are placed in the fixed-effect model, gives similar estimates, which can be interpreted in the same way (Chapter 1—slopes and intercepts; Chapter 2—treatment means). However, the apparent precision of these estimates, indicated by their standard errors (SEs), is affected by the decision to specify other terms in the model as random. In this chapter, we shall explore the precision with which fixed effects are estimated by mixed-model analysis. The single value so far given as the estimate of each model parameter (slope, intercept or mean) is referred to as a point estimate, and the precision of each point estimate is indicated by enclosing it in an interval estimate. This indicates the range within which the true value of the parameter can reasonably be supposed to lie.

Before determining the interval estimates of the various model parameters introduced so far, we need to set out the general principles to be followed when obtaining such an estimate. Consider a model parameter β. The point estimate of this parameter is referred to as ...