Just as mixed modelling is an extension of the linear-modelling methods comprised in regression analysis and analysis of variance, mixed modelling itself can be further extended in several directions, to give even more versatile and realistic models. This chapter reviews the various contexts in which we have seen that mixed modelling is preferable to a simple regression or analysis of variance approach, then outlines the ways in which the concepts of mixed modelling can be developed further. Fuller accounts of such advanced uses of mixed modelling are given by Brown and Prescott (2006) and by Pinhero and Bates (2000). Brown and Prescott demonstrate the use of the statistical software SAS to fit the models, whereas Pinhero and Bates use the statistical computer language S (of which the software R is one implementation – see Section 1.11). Both books place much more emphasis on the underlying mathematical theory than is given here.

A mixed-model analysis provides a fuller interpretation of the data than a simple regression or analysis of variance approach, and permits wider inferences about the observations to be expected in future, in the following situations:

- When one or more of the factors in a regression model is a random-effect term, and should therefore contribute to the standard errors (SEs) of estimates of effects of other terms. Examples include
- the variation in house prices among towns, which ...

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