I am experiencing linear mixed models and I have a fundamental questions:
Is it allowed to have correlated fixed effects?
I.e. I measure the activity performed during a day in
step and I want to relate it to the quality of sleep measured as total time slept
TTS, number of sleeping epochs
NSE and duration of sleeping epochs
DSE. These variables are ordinal variables representing 4 interval ranges. Each subject is assessed several days.
My model would be
Step ~ TTS + NSE + DSE + (1|Subject)
but I know that
DSE are correlated: i.e. the higher number of sleeping epochs the shorter these sleeping epochs will be.
Can Effect2 (NSE) and Effect3 (DSE) be correlated? (0.8) What is the proper way to deal with this situation? What if I have more than 2 correlated effects?
Should I fit 2 separate models (one for each of the correlated effects)? Should I include more random effects?