I am working on the analysis for a field experiment testing the effect of a slow-release granular fertilizer (which is supposed to be activated by plant roots) on soil phosphorus (P) concentration over time. The overall experiment is a split-plot with 3 complete blocks of main plots. Main plots are fertilizer type (the slow-release fertilizer, a standard fertilizer, and unfertilized control) and subplots are the presence or absence of plants. The fertilizer dissolves slowly enough that residual granules can be detected in soil, even months after application. So, to separate the contribution of the residual granules (fertilizer not yet dissolved) vs. the soil itself (fertilizer dissolved) to the soil test for phosphorus, we came up with a sampling scheme in which a pair of samples is collected side by side within each subplot (essentially two sub-sub-plots). Then, one sample has the residual fertilizer granules removed and the other has the granules retained before being tested for soil P. However, this sampling scheme does not work for the standard fertilizer, because those granules dissolve quickly and cannot be removed; this means that the standard treatment only has the "granules retained" treatment. In the unfertilized control, there were never any granules present, so this treatment lacks the additional split as well. I have been treating this design as a 2x2 factorial ("plant x granule") plus two controls (unfertilized; standard fertilizer with granules retained). However, the two controls each have both levels of the "plant" factor - just not the "granule" factor, so it is a little different from other factorial+controls codes I have seen. Sampling was completed on 7 dates (weeks 1, 2, 3, 4, 6, 8, 16) to see how the slow-release fertilizer dissolves over time.
The dependent variable is "log_P" - the log of the soil P concentration measured by the soil test. The log transformation was required to satisfy the assumptions of normally distributed residuals. Even with the log transformation, the variance among fertilizer types is not equal, which is why I've included the random _residual_ and covtest statements.
I am using SAS Studio v 9.4.
My question is about the proper nesting of the "granule" factor within the other factors. It seems to me that "granule" should only be nested within "fert" (fertilizer type), since fertilizer type is the factor that is missing some treatments (see sample code below). However, because it is a split-plot with"plant" as the subplot, perhaps "granule" also needs to be nested with the "plant" subplot factor? And I am not at all sure whether "granule" should be nested within "week". All samples were collected for all weeks, on the same day each week, so "week" can be considered a crossed factor (not nested).
proc glimmix data=soil order=data plots=residualpanel plots=studentpanel;
Class block fert plant granule week;
Model log_P = plant|granule(fert)|week / ddfm=kr;
Random block block*plant;
random _residual_ / group=fert;
covtest 'Common variance' homogeneity;
random week / residual subject=plotno type=cs ;
Also, note that I have so far been using the "type=cs" for the repeated measures even though the dates are not equally spaced, since the model would not converge with a spatial power covariance structure. Any advice on this would also be welcome.
Thank you in advance for any help you can provide!
