# Can nonlinear regression with least squares estimations be used for testing hypotheses with data containing dependent observations?

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?

• When you say the data do not fit the assumptions, do you mean that the data are count data and are therefore not normally distributed? Or do you mean something else?
– Bill
Commented May 4, 2016 at 19:32
• I'm sorry for the unclarity, what I meant to say is that not only the error distribution of the data is non-normal, but the set is also heteroscedastic. Commented May 10, 2016 at 11:05
• OK, great. Now, what is it about the dynamics which are interesting? You want to know if places that started low density have their density increase, relative to the ones that started high density? Or something else?
– Bill
Commented May 17, 2016 at 18:57
• These are the questions I'm working with: (1) does the abundance of my species vary significantly through time (i.e. is there a significant effect of "time" on "count"); (2) is the observed temporal dynamics in abundance affected by the initial density (i.e. is there a significant effect of "starting abundance/density/count at time 0 on "count"); and (3) is the observed temporal dynamics in abundance affected by location (i.e. is there a significant effect of "location" on "count"). If I can check for interactions (e.g. starting count*location), it would be great. Commented May 18, 2016 at 9:11
• I intend on testing increases and decreases through time using Wilcoxon comparisons of sequencial dates with Bonferroni correction of p-values, but this will be a post-hoc if the test above tell me that time has an effect on the dynamics of density. Commented May 18, 2016 at 9:14