Which non parametric test can be used for multiple repeated measures at the same site?

Question

I have repeated monthly measurements of some variable at several different sites, so that I have 21 data points (21 months) for each site. Now, I want to see if there are significant seasonal differences in each of these sites, e.g., did site 1 differ in four seasons + post hoc test to determine in which seasons it differed significantly.

I am looking for a test that would be suitable for evaluating the differences at each site separately, given that:

• the measurements are taken repeatedly from the same site, so my understanding is that they are non-independent
• the data at each site in each season is not normally distributed
• the data is continuous
• in 3 of the seasons I have 6 observations (in each) and in 1 season only 3 observations

I thought first of using a Kruskal Wallis test, but it requires the data to be independent, which is not the case for repeated measures. Then I came across the Friedman test, but it requires an equal number of data points, which is also violated in my case. And also, it could rather be used to test whether there are seasonal differences across all of my sites, not in each individually, right?

My problem is quite similar to this question, but there is no answer there: Non-parametric test for repeated measures that are not independent

Any leads are greatly appreciated!

Answer 1

The proportional odds model is a generalization of the Wilcoxon test. See fharrell.com/post/rpo for resources. A logical longitudinal generalization of that is a Markov model. See examples in Chapter 7 and in the last chapter of https://hbiostat.org/rmsc