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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