How to interpret the output of R's glmer() with quadratic terms
A couple of points.
- Coefficients of non-linear model terms do not have a straightforward interpretation and you should make effect plots to be able to communicate the results from your analyses. You may use
effectPlotData()
from theGLMMadaptive
package to do this. Refer to this page for more information. - To be able to appraise whether including a quadratic effect of
dist_settlements
improves the model fit, you should fit a model without the squared term (i.e. only the linear effect ofdist_settlements
) and a model with the squared term. Then perform a likelihood ratio test to appraise whether inclusion of complex terms improves the model fit. In case of LMMs, make sure to fit both models using maximum likelihood, not REML. For GLMMs, you don't have to borther about (RE)ML. - The variance of the random intercepts is rather close to 0, which may require your attention. Refer to this answer and this section of Ben Bolker's github for more information on this topic.
You may want to take a look at this great lecture series by Dimitris Rizopoulos for more information on (G)LMMs.