I'm looking at how the scoring procedure influences individual behaviour in competitions. The independent variable (scoring procedure) is measured on the competition level, while the dependent variable (behaviour of contestant in a competition) is measured on the individual level. The data is partially crossed, as individuals participate in multiple competitions but are not present in all of the existing competitions.
Given this case, is it reasonable to estimate a mixed effects model with random intercepts for individuals and competitions? The problem I see is that a certain competition only has one specific scoring procedure. There is thus only a single value of the independent variable (scoring procedure) for each competition, i.e. there is no variation in the independent variable on the group level. Is it possible to estimate a random intercept for competitions under these circumstances?