I previously showed the general form of this autoregressive matrices in this post, and you can see the matrix below. In summary, the residuals have moved from to. In addition, we will have a spatial residual. We will use here a very popular approach, which is to consider two separable (so we can estimate the bloody things) autoregressive processes, one for rows and one for columns, to model spatial association. See previous post for explanation of the bits and pieces. There are a few ways to model environmental trends (AR processes, simple polynomials, splines, etc) that can be accounted for either through the G matrix (as random effects) or the R matrix.
Gratuitous picture: Detail of Mosteiro dos Jerónimos, Belém, Lisboa, Portugal (Photo: Luis). Kind of we could be violating the independence assumption if you haven’t got the hint yet.
SPLIT SPLIT PLOT DESIGN R PROGRAM ASREML TRIAL
Plants ( triffids excepted) do not move, which means that environmental trends within a trial (things like fertility, water availability, temperature, etc) can affect experimental units in a way that varies with space and which induces correlation of the residuals. This chap has put a really nice collection of data sets WITH suggested coding for the analyses, including nlme, lme4, asreml, MCMCglmm and a few other bits and pieces. Kevin is a man of mistery, a James Bond of statisticians-so he keeps a low profile-with a keen interest in experimental design and analyses. Rather than mucking around with typing coordinates we can rely on Kevin Wright’s version of the oats dataset contained in the agridat package. Yates presented a nice diagram of his oats data set in the paper, so we have the spatial location of each data point which permits us playing with within-trial spatial trends.
Where was I? Showing how split-plots look like under the bonnet (hood for you US readers). In the process I ‘discovered’ that I live in the middle of nowhere, as it took me 36 hours to reach my conference destination (Estoril, Portugal) through Christchurch, Sydney, Bangkok, Dubai, Madrid and Lisbon. Disappeared for a while collecting frequent flyer points.
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