3 weeks ago
I'm looking for some help nesting factors.
I have the following experiment design:
Four pens per treatment
Four sampled animals per pen
3 samples measured per animal, sometimes just two samples measured, at the same time point.
Previously, I have only take one sample per animal, and my mode and random statement with nesting looks something like
Model = Treatment / cl;
I'm wondering how I could work Animal into that statement. Maybe Animal*Pen(Treatment), or Animal (Pen Treatment) ?
Furthermore, when I write out a linear model equation, I would represent the Pen(Treatment) as uij
u for random effect of j pen for i treatment
How would I properly state it if I incorporated Animal?
uija, with a for animal maybe?
I look forward to any thoughts on this would be appreciated. Apologies if my stats language is a bit imprecise. Too much veterinary medicine and not enough math in my life.
3 weeks ago - last edited 3 weeks ago
Assuming that treatment is the only fixed effect:
class treatment pen animal;
model y = treatment; random pen(treatment) animal*pen(treatment);
Given how SAS expands syntax, there are equivalent ways to identify a random effect in this model:
"pen(treatment)" == "pen*treatment"
"animal*pen(treatment)" == "animal*pen*treatment" == "animal(pen treatment)"
Equation-wise, something like (without going to the trouble of proper symbols)
y_ijkm = mu + t_i + p_ij + a_k(ij) + e_m(ijk)
where i indexes treatment t
j indexes pen p
k indexes animal a
m indexes sample e (residual error)