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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 NSE and 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?

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As far as predictions go:

It is fine to include the two correlated effects. Depending on the extent of the correlation the variable may not improve the model, but it should not hurt it just because they are correlated.

As far as analysis goes:

If your goal is to draw insights from the model, for example through hypothesis testing, the correlation will interfere with this. Because these two variables are describing the same (or similar) variation in the DV, they will share the burden of expressing that variation. Therefore the corresponding parameter estimates will understate the significance of each of the correlated variables.

A good thing to think about is, "what would happen if I just repeated an IV, and retrained my model."

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  • $\begingroup$ The goal is to estimate the LS means of the response for each effect. Can I use separate models including 1 variable at the time? $\endgroup$ – gabboshow Sep 16 '15 at 11:16
  • $\begingroup$ I updated the question $\endgroup$ – gabboshow Sep 16 '15 at 11:32

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