Last Wednesday I had a meeting with the folks of the New Zealand Drylands Forest Initiative in Blenheim. In addition to sitting in a conference room and having nice sandwiches we went to visit one of our progeny trials at Cravens. Plantation forestry trials are usually laid out following a rectangular lattice defined by rows and columns. The trial follows an incomplete block design with 148 blocks and is testing 60 *Eucalyptus bosistoana* families. A quick look at survival shows an interesting trend: the bottom of the trial was much more affected by frost than the top.

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# Category: r (Page 17 of 20)

Yesterday morning at 7 am I was outside walking the dog before getting a taxi to go to the airport to catch a plane to travel from Christchurch to Blenheim (now I can breath after reading without a pause). It was raining cats and dogs while I was walking doggyo, thinking of a post idea for Quantum Forest; something that I could work on without a computer. Then I remembered that I told Tal Galili that I would ‘mention r-bloggers’ in a future post. Well, Tal, this is it.

In a previous post I summarily described our options for (generalized to varying degrees) linear mixed models from a frequentist point of view: nlme, lme4 and ASReml-R^{†}, followed by a quick example for a split-plot experiment.

But who is really happy with a toy example? We can show a slightly more complicated example assuming that we have a simple situation in breeding: a number of half-sib trials (so we have progeny that share one parent in common), each of them established following a randomized complete block design, analyzed using a ‘family model’. That is, the response variable (dbh: tree stem diameter assessed at breast height—1.3m from ground level) can be expressed as a function of an overall mean, fixed site effects, random block effects (within each site), random family effects and a random site-family interaction. The latter provides an indication of genotype by environment interaction.

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When working in research projects I tend to fit several, sometimes quite a few, alternative models. This model fitting is informed by theoretical considerations (e.g. quantitative genetics, experimental design we used, our understanding of the process under study, etc.) but also by visual inspection of the data. Trellis graphics—where subsets of data are plotted in different ‘panels’ defined by one or more factors—are extremely useful to generate research hypotheses.

There are two packages in R that have good support for trellis graphics: lattice and ggplot2. Lattice is the oldest, while ggplot2 is probably more consistent (implementing a grammar of graphics) and popular with the cool kids and the data visualization crowd. However, lattice is also quite fast, while ggplot2 can be slow as a dog (certainly way slower than *my* dog).

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This post is one of those ‘explain to myself how things work’ documents, which are not necessarily completely correct but are close enough to facilitate understanding.

## Background

Let’s assume that we are working with a fairly simple linear model, where we only have a response variable (say tree stem diameter in cm). If we want to ‘guess’ the diameter for a tree (y_{i}) our best bet is the average (μ) and we will have a residual (ε_{i}). The model equation then looks like:

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