This is a basic question about how to determine when some fixed effect in your model should also be included as a random intercept.
Below are 2 simple basic examples.
Let's say we're testing the effect of some glider on cross-country skiers' performance (tested over multiple races), but the athletes are tested with different equipment (two different types of skis). We know that they generally should be quicker with type 1 skis than type 2 (and let's say for the sake of argument that we don't expect significant individual variabilty in the effect of ski type).
Now consider the following studies:
Let's say we're interested in the effect of the glider on skier performance, but not really interested in the effect of ski type (maybe we tested student skiers from two schools who have slightly different equipment), though we know the ski type will have some influence on results. Then our model should likely be:
performance ~ Glider + (1+SkiType|Subject) + (1|Race)Now, alternatively, let's say we're specifically interested in the interaction between the glider and ski type (e.g., expecting that the use of this glider might counteract the differences in ski type performance). In this case, I would think our model should look like:
performance ~ Glider*SkiType + (1|Subject) + (1|Race)
The question is basically, should SkiType still be included in the random effects structure in study 2 since it's a central fixed effect of interest? Or, if we include SkiType as a random slope, are we then essentially partially controlling away Subject variability with respect to SkiType that we're actually interested in?