I am reading Introduction into mixed modelling by N.W. Galway. It is partly a repeat of things I know, but I expect to use mixed models quite a lot the coming time, so it is good to repeat these things.
My problem with this book is a sensory example in chapter 2. It is profiling data, but with some twists, as happens in real life. He also makes some odd choices.

Design

The test concerns four hot products (ravioli). Because the products are hot, it was found not feasible to use a proper balanced design within each day (e.g. Williams designs). Within a day each presentation (he used presentation for rounds) has one product, as shown in the table below. Which is fine in a way, I do believe in making designs which be executed in practice. However, I come from a facility where we would at least have tried to solve this with the ‘au-bain-marie’.

Table 1, allocation of products A to D over presentations and days.

Day	Presentation 1	Presentation 2	Presentation 3	Presentation 4
1	B	A	C	D
2	C	D	B	A
3	A	C	B	D

Within each presentation the nine assessors get served portions. It was randomized though not registered who got what serving. Even so, a random variable was created to serve as proxy. I understand this does not make a difference if servings are nested in presentations and days. Still, it removes the option of actually looking at this effect except as nested within servings and days. I can actually imagine that the product served first is different, especially in case of sloppy sensory practices, so it would be nice to be able to check this.

Model

The following effects were used in the model(s)
Table 2. Allocation of effects

Effect	Allocation
Day	Random
Day.Presentation	Random
Day.Presentation.Serving	Random
Product	Fixed
Assessor	Fixed
Product.Assessor	Fixed

Here I got my ax to grind.

• Product.Assessor. To quote: ‘(assessor) ANA perceived Brand B as the least salty, whereas (assessor) GUI perceived Brand  A as the least salty. Such crossover effects may be important: they suggest an obstacle to designing a brand that will please all consumers‘. In my (industry) experience the sensory panel may well be in a different country or even continent as the target market, so that is a bit too strong. Besides, nine assessors is a bit low to segment groups on. Typically segmenting would be done with a consumer group, say 120 persons, in the target market. In my view  sensory is intended to provide an objective measurement. The assessors are representing what a typical human may taste, and are hence random. With assessors random, product.assessor can only be found random too.
• Day.Presentation. To quote: ‘Presentation 1 on Day 1 is not the the same as presentation 1 on day 2‘ and ‘it would therefore not be meaningful to obtain the mean for presentation 1 over days‘. Actually, presentation 1 is the same on day 1 as on day 2 . It is the tasting with a clean palette. While palette cleansing is supposed to make all presentations equal, that does not mean it really does. After all, this is on the trade-off between production (shorter cleaning time) and correctness (longer cleaning time). Looking at this effect is important. I would make it fixed. For round 1 specifically, it represents monadic tasting as in a consumer test. Surely a first impression is important to understand consumer liking, when correlating consumer data and sensory data I might look at solely presentation 1. Having said that, given the design in table 1, I would make presentation random. The information is not there to do anything else. 

Conclusion

I dislike the design, the sensory foundation and interpretation. However, if you ignore that sensory based dislike, the model actually makes sense and is a nice example. On top of that, the book has R code using lme (nlme package), with code on the download site http://www.wiley.com/legacy/wileychi/mixed-modelling/ has both nlme and lme4 examples, so is up to date. I am looking forward to reading the next chapters.