correlated variables as fixed effect in mixed effect models I am interested to know whether the count of beetles depends more on precipitation or in minimum temperature in winter.  I currently model as fixed effects: 


*

*altitude (correlated with temperature) 

*minimum temperature,

*temperature (which is correlated with minimum temperature) 

*precipitation


and as random effects 


*

*year (data has been collected over 20 years)

*region

*technician (who did the measurements)


My question is: If the variables treated as fixed effects are correlated, is it better to add them all?
 A: Here's a first cut at the question.
Fixed effects correlated between themselves are not necessarily problematic. Correlation may make it harder to assign variance to different variables, that's actually just reflecting the smaller amount of information in the data.
Fixed effects correlated with random effects are potentially more problematic.  This seems to be your situation.  Specifically I would guess that all the fixed effects are correlated with region.  The Hausmann test tries to see whether this will matter to inferences about your fixed effects, but it seems it's not particularly powerful.  In any case, a traditional way around the problem, due to Mundlak, involves putting group-averaged fixed effect levels as covariates to predict the random effects.  A clear discussion of these issues - not ecology I'm afraid - can be found in 
Bell, A. J. D. and Jones, K. 2015, Explaining Fixed Effects: Random Effects modelling of Time-Series Cross-Sectional and Panel Data. Political Science Research and Methods, vol 3., pp. 133-153 (preprint)
This also emphasises the upsides of the slightly more elaborate modeling this requires.
So, to answer your question: Should you put them all in?  If you want.  The question is more, where and how should you put them in if you do.
