My experimental design causes me some headache. It consists of three sites (A, B, C). Each site contains two treatments (Treat1 and Treat2). Obtained data (resp1 and resp2) were recorded at eight different expositions (E, W, N, S, NE, SW, NW, SE), three replicates each. Not all sites and treatments share the same expositions (please see data file here, password: CrossValidated1.
I am mainly interested in the effect of exposition. But also in treatment. Certainly, there is an effect of year.
So my first idea was to apply a linear mixed effect model with fixed factor exposition and treatment. But the model showed an error of singularity. I found a "solution" here to handle that. But I am not really happy with this, nor I understand correctly. Furthermore I have only few levels in site (=3), treatment (=2) and year (=2).
Which options do I have? Which approach would be appropriate? Thank you.