ANOVA or GLM or ?

[Caroline Ritter]

Hello,
I have trouble identifying the correct statistical test and hope you can help me
For my study, I have 10 observations each from 15 different individuals. The outcome measure is count data (e.g., how often they perform a specific behaviour), which is not normally distributed but right skewed. However, after log transformation, the data follows a Gaussian distribution pretty closely. The dataset looks like this.

Individual	Observation	Behaviour (Count)
1	1	0
1	2	3
1	3	6
[...]
2	1	1
2	2	8
2	3	0
[...]

I now want to assess whether there is a difference between individuals regarding the frequency of the behaviour. I thought about 1-way ANOVA but I don't know if the "nesting" of situations within individuals is a problem.
Alternatively, I thought about generalized linear mixed models. However, because I do not have a predictor other than the individual (which would be my random effect), I don't know what that model would look like.
Any help is highly appreciated.

Thanks!

[Clyde Schechter]

I thought about 1-way ANOVA but I don't know if the "nesting" of situations within individuals is a problem.

It most certainly is a problem. Or, at least you have to start out with the assumption that it's a problem.

However, because I do not have a predictor other than the individual (which would be my random effect), I don't know what that model would look like.

So you will not get what you need with -glm- either, because you have two level data (repeated measurements within individuals). There are a couple of ways you can proceed. If you are satisfied that the log count is reasonably normal, and if you are not going to be plagued with heteroscdeasticity, you could do a repeated measures ANOVA.

But what I think would be more congenial is to do a random effects model for count data such as -xtpoisson- or -xtnbreg-. So it might be as simple as:

xtset individual
xtpoisson behavior, re