# Goodness of fit for possibly dependent data

My data consists of about a hundred animal visits to three different feeding zones, and I'm trying to determine if there was a preference for one zone over the others.

Each animal visits between one and about a hundred zones (think hummingbirds and feeders).

The problem is that 1) the sequence of zones a given animal visits are likely not independent because each individual animal may have its own preferences, and 2) the visits of different animals are likely not independent, because it is possible (likely) that, say, the first animal and the fifth are the same (they are not identifiable), so the two sequences of visits to zones by the first and fifth may be highly correlated.

If everything was independent, then I could use a chi square test.

Any suggestions?

Edits based on the comments: The data is like:

bird1<-c(1,2,1,1,3,2,1,2)
bird2<-c(3,2,1,2,1,2,3,2,1,3,2,3,2,1)
bird3<-c(1)


...

birdn<-c(2,3,1)


where 1,2 & 3 are labels for the zones visited before the bird left the area.

Now any bird may have its own preferences. And bird1 may be bird3, because once they leave the area, if they come back we have no way of knowing it was the same bird (once it is out of eyesight).

The null hypothesis would be that the three zones are equally preferred; the alternative hypothesis would be that some zone is preferred.

If everything was independent, I could do a chi-square test comparing the observed frequencies to c(1/3,1/3,1/3), but there may be dependence here, and simulations may prove difficulty because there is no obvious model for the dependence.