I am working on a problem which revolves around individual axons / nerve cells in two treatment conditions. All relevant questions are clearly on the axon level, and dependent on properties (size, myelination, etc) of individual axons. However, I think that treating each axon as an independent observations without considering which animals they belong to would be cheating. Hence I would like to use a two-level approach with axons nested within animals.
Reading up on this it seems to me that I could use either a nested anova (
aov in R with animal_id as a random effect) or a multilevel linear model (
lme4 with a random intercept). But I'm having a hard time deciding between them (in practise, both actually produce fairly similar results).
Here's what I've learned so far:
I understand that
lme4use maximum likelihood methods which should make them more suitable for unbalanced designs but I do not think that this is a particularly big problem in my case.
I have also heard suggestions that nested anovas may be more suitable for smaller sample sizes. Is this true?
Finally, the developers of
lme4seems to be vehemently against the idea of assigning p values to their results. if I understand correctly this is because "degrees of freedom" is not a very straight forward concept in mixed linear models. But whenever I see people make this argument they also seem to be opposed to p values and null hypothesis testing in general. Is there a better case for trusting the p values in nested
I am very grateful for any answer or comment.