proc mixed covariance parameterization in space and time

[JahnDavik]

I am trying to analyse some data from variety trials on forage grasses. The data consist of a range of multi-harvest pasture field experiments. Typically a single experiment would consist of 10-15 cultivars or candidate cultivars in randomized complete block design.  After the year of establishment the experiment is typically harvested the 3 following years.

One, most likely, naïve analysis using Proc Mixed, would be as follows:

data t;

infile ‘TESB.txt’; input field establ engar plot rep cult yield row col harvyr;

run;

proc mixed data=t method = reml;

class rep cult harvyr;

model yield = rep/ ddfm=kr;

random cult harvyr;

run;

The variables to consider here are:

rep – replication

cult – cultivar

yield – yield

row – row number

col – column number

harvyr – harvest year

However, I apparently do not account for the correlations in space and time here, and here is where I need help:

First, how do I account for the spatial covariances among the field plots, e.g., the fact that neighbouring plots are more likely to be positively correlated? I realize that the ‘repeated’ statement is the one to use, but I cannot figure out how. BTW: each plot position is given my the row and col variables.

Second, each plot is harvested in three subsequent years, so I would assume that this would cause positive correlations as well and should be included in the model.

Ideally I would like to see both these covariances included simultaneously.

Would really appreciate feedback here.

Thank you.

[StatsMan]

If you have plots that are spatially correlated and observations on plants within a plot that are temporally correlated, then you can try something like

   random plot / type=ar(1);

   repeated time / subject=plant(plot) type=ar(1);

Unless you have a lot of plots, the estimates of the components of the AR(1) structure of the spatial component of your design are going to be rough at best.  If you have measurements of the plot locations in two dimensions, then you can try TYPE=SP(POW)(x y) on that RANDOM statement to incorporate the two dimensional distance between the plots.