Background: I am currently analyzing data from an experiment where I fed ant colonies either treated or untreated diet continuously for a month and then measured the weight of individual offspring from each colony at the conclusion of the experiment. Because each colony was only fed one of the diets continuously it seems to me that each colony is nested under treatment.
Question: How I include colony, as a random or fixed effect, nested under treatment has a major implication on the statistical outcome of the analysis (see output). Should [colony nested under treatment] be a fixed or random effect?
While the debate on fixed vs random effect questions seems to be somewhat contentious, the most consistent answer appears to be that nested should always be run as random without much discussion as to why the alternative is ALWAYS wrong:
Why would JMP give the option to include nested as a fixed if it goes against conventional wisdom?
Looking at the dataset globally, it is clear that there is a treatment effect, but it appears that one of the colonies was unaffected by the treatment (see image). This leads me to think that there is a colony by treatment effect and that some colonies are more tolerant to the treatment while others are not. I am aware that with a non-factorial design (no crossing) I cannot prove this statistically. With the fixed model I get significance of the nested colony treatment and the treatment itself. When ran as random I lose the significance of the treatment variable. I don’t understand how randomizing the effect of colony can be separated from the treatment effect in an instance like this. Before I get called out for my non factorial design, let me say that there would be no practical way to cross in this type of study.
Thanks in advance for any advice or suggestions you have!
No, nested effects need not be random. The domains in which 'experts' opined about the impossibility of a fixed nested effect might not offer examples, though.
Yes, if colony represents a sample of a population of colonies, then it should be modeled as a random effect in your case.
Regarding your conclusion, "Looking at the dataset globally, it is clear that there is a treatment effect, but it appears that one of the colonies was unaffected by the treatment (see image)," I think that you are confusing the fixed effects (treatment) and the random effects (colony). The random effect is about variation. The fixed effect is about the mean.
You could divide a sample of ants from each colony and apply the treatment to each split to achieve a crossed structure, no?
Because we are looking at colony offspring in response to developmental exposure, a stable colony with a laying queen is required during the treatment administration. Testing a portion of adult workers would not get at the same question and splitting a colony would ultimately end up requireing two different queens and thus lead to colonies with different genetics . Each colony can only be assigned one treatment (nested) and each colony is also different. The alternatives would be much more complicated (and $$).
Suppose you were instead looking at whether the size of the colony was important. Also assume you only knew the relative colony sizes within each food type. Imagine that you began with two starter colonies, one for each food type and you didn't know their sizes. Then you divided each starter up into 1/2, 1/4, 1/8, ... and assigned each sequence pf colonies to each food type. It would seem to me you would then have a nested ordinal effect within each food type. One could probably make a similar experiment where two continuous measurement devices were used in an experiment and their relative scales were unrelated. This would give you a nested continuous factor. My recollection was that JMP didn't allow continuous factors to be nested.