# Nested Anova vs Multilevel Linear Models

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 (nlme / 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 nlme / lme4 use 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 lme4 seems 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 aov compared to lme4?

I am very grateful for any answer or comment.

Thank you

After having spent a few days in the library, I still feel far from understanding all implications of the two options. However, I have learned a few things and if anyone else is in the same boat, I would very much recommend the book "Multilevel Analysis" by Snijders and Bosker to guide your decision. It is by far the best text on this topic that I could find and spans from nested ANOVAs to very complicated multilevel linear models.

For me, it provided some clarification for my three points above:

1) Even though I have fairly balanced groups, my group sizes are small enough that changing a few values on the micro level can have a significant effect on the group variance. Multilevel linear models should be more stable in this situation because group effects of one group inform those of other groups. S&B emphasize that this effect may be particularly noticeable for groups with <50 individuals. [+1 MLM]

2) S&B suggest having at least 10, ideally 20+ groups in an MLM analysis. I am definitely at the low end of this spectrum. [+1 ANOVA?]

3) Yes, F-tests for nested ANOVAs are definitely much more straight-forward. S&B seem to believe that there is a case for p-values in MLMs, too but reading the book makes very clear why it is a lot more complicated. [+1 ANOVA]

I hope this helps someone. I am still very much unsure how to proceed so if anyone has a comment I'd be really happy to read it.

Cheers