What is the proper way to define random variable in GLIMMIX?

[jsquirre]

Hi -I'm a biologist and am trying to improve my statistical skills and understanding.  And I am brand new to this forum.  I have what I'm sure is a fairly basic question, but I want to be sure I am setting up my model correctly in GLIMMIX. I am interested in assessing how a drug treatment impacts the immune response in zebrafish larvae, so my comparison of interest is drug vs no drug.

The experimental design is quite simple. 

The larvae are either treated or not treated with a drug and 24 hours later the area occupied by a particular immune cell type is measured.  This experiment repeated 3 times in its entirety, on different days with completely different larvae. So the experimental days are independent.  There are NO repeated measures.

I want to account for the random effect of experimental day and have considered 2 ways of including it and am wondering which way is best.  I would also appreciate any explanation of why one way is better than the other in which circumstances so that I can improve my understanding.  These are the two codes that I have been working with for this experiment.  I am using SAS 9.3.

1) Experimental day ("exptday") alone as the random variable, with "treat" as the independent variable and "area" as the dependent variable:

proc glimmix plots=ResidualPanel; 
class exptday treat;
model area = treat;
random  exptday;
lsmeans treat / pdiff cl;
output out=out1 pred=p resid=r;
title 'Analysis of area by treatment';
run;

2) Experimental day also included as an "interaction" with treatment

proc glimmix plots=ResidualPanel; 
class exptday treat;
model area = treat;
random  exptday exptday*treat;
lsmeans treat / pdiff cl;
output out=out1 pred=p resid=r;
title 'Analysis of area by treatment';
run;

Any assistance or feedback would be appreciated as I am eager to learn!  Thank you.

[SteveDenham]

This is a randomized block design, where exptday is the blocking factor.  With multiple observations per day and treatment, inclusion of the treatment by exptday interaction will result in the correct degrees of freedom for the test of treatment effect differences.  If you do not include it, then the residual error with the residual degrees of freedom would be used.

SteveDenham

[jsquirre]

Hi Steve -

Thank you for taking the time to answer my query.  As you suggested, I will include the

random  exptday exptday*treat;

term in my analysis code.  As I mentioned, I am new at this and still struggle with identifying the correct degrees of freedom for a given experimental design.  I appreciate your explanation.

Sincerely, 

Jayne