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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.

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**Wiekvoet**.

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