selecting subjects for random statements in a repeated measures rcbd design

[Hi-Ho-Cherry-O]

Hello All,

I am working with a fertilizer study in apple tree production and I am hoping to get some help regarding my code.

Experimental Design:

• RCBD with 4 blocks (rows)
• 3 trees per plot (row*trt)
• 5 Treatments (fertilizer rates) = (0, 25, 50, 75, and 100 lbs N/acre)
• Measured Yield per tree once every 3 years (2019-2021)

My main interest is in differences per treatments, but I would also like to see how they are affected by time. I have gone back and forth on the code, specifically regarding the random and repeated statements. In my latest edition, I am using proc mixed and the code is as follows:

proc mixed;
class row trt tree year;
model yield = year trt trt*year/ddfm=kr2;
random intercept/subject=row;
random intercept/subject=row*trt;
random intercept/subject=row*trt*tree;
repeated year/subject=row*trt*tree type=ar(1);
lsmeans trt/adjust=tukey;
run;

My main question is, what subjects should I include in my random and repeated statements? I believe I should account for differences within blocks and experimental units, but do I also need to include variance within observational units (row*trt*tree)?

I have also attached the dataset and sas code. I would appreciate any insight.

Thank you!

Eliott

[StatsMan · Accepted solution]

Each RANDOM statement correlates the observations from the same level of the subject effect. So your first RANDOM statement correlates observations from the same level of ROW. Your 2nd correlates observations from the same level of ROW*TRT, and so on. You *might* get more efficiency out of MIXED if you combine the three RANDOM statements into one, using

   random int trt trt*tree / subject=row;

The REPEATED statement further calculates the observations from the same TREE in a ROW*TRT combination using AR(1) across the years. 

If this is what you want, then you have the correct model. It can be informative to use the V and R options on the RANDOM and REPEATED statements respectively to see the correlation structure you have imposed on your data through your model. Use the syntax V= and R= to print only the portion of V or R for a certain subject level. For example, R=5 prints the block of R for the 5th subject. 

[Hi-Ho-Cherry-O]

Thank you so much!