I counted the number of animals of a certain species in 6 fixed locations on a monthly basis for 18 months. I now would like to test the effects of location, starting density, and time on the dynamics of those counts. Normally I would use repeated measures ANOVA, but the data does not fit the assumptions, warranting the use of nonparametric alternatives. After much reading I'm considering doing a nonlinear regression using least squares estimation. Two models are made explaining count as a function of time with data subsetted by location, then the two models are compared with ANOVA. Two more are made with the data subsetted by starting density class (high density of animals vs low), and again compared with ANOVA. That is the plan.
Now the question: Can I disregard the dependency between observations when performing NLS regression?