I am looking for opinions/interpretation on a model I'm trying to fit. A disclaimer: I'm an ecologist and not a statistician; and I appreciate everyone's time and opinions! I am generally following Zuur et al. 2009's (using R) recommendations in an attempt to model travel speed as a function of a few environmental covariates, the main one of interest being a 1/0 "treatment" variable.
The data are by nature are hierarchical and I have therefore used a mixed model with a random intercept. The mixed model fits significantly better than the base
gls model. Additionally I included a
varIdent with the mixed model, and that is significantly better than without.
From this point, I have looked at assumptions and diagnostics - the residuals look OK, I think, but I always have a hard time telling if it's "too much" pattern. I think less than 5% of the data are outside of the 2/-2, so I'm good there. The variation doesn't seem to be driven by any points in particular, and the variance of residuals for each group of the "treatment" is close to 1 (using
tapply; I interpret this as minor heterogeneity). A box plot of the residuals by the random effect shows equal spread around zero and minor variation = independence (see below)?
I've looked at residuals vs. fitted (not too bad), residuals vs. each covariate (pattern with one of my covariates, elevation), histogram of the residuals (still quite skewed), and have checked for all potential influential observations.
I just don't know if I'm "done" and can now consider this model an OK fit?
I've included a couple of diagnostic images (response variable can't go below a certain value, and therefore the residual plot shows a sharp "line" in the negative values) - std residuals vs fitted; residuals by random intercept; histogram of residuals (not normalized); residuals by elevation covariate - could be something going on here, but not sure how to deal with it: