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

Chapter 6More advanced mixed models for more elaborate data sets

6.1 Features of the models introduced so far: A review

The mixed models introduced in the examples presented so far are reviewed in Table 6.1. These examples illustrate several features of the range of mixed models that can be specified. Each model term may be a variate, like ‘latitude’, in which each observation can have any numerical value, or a factor, like ‘town’, in which each observation must come from a specified set of levels. Each part of the model (the fixed-effect model and the random-effect model) may have more than one term, as in the random-effect model ‘block + line’. Factors may be crossed, as in the model ‘brand*assessor’, which is equivalent to

Alternatively, they may be nested, as in the model ‘day/presentation/serving’, which is equivalent to

Crossing and nesting of factors is specified using the notation of Wilkinson and Rogers (1973).

Table 6.1 Mixed models introduced in earlier chapters.

Example	Response variable	Fixed-effect model	Random-effect model	Design illustrated	Where discussed
Effects on house prices in England	logprice	latitude	town	Regression analysis on grouped data	Chapter 1; Sections 3.18 and 4.2
Sensory evaluation of ravioli	saltiness	brand*assessor	day/presentation/serving ...