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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?

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The fact that the scoring procedure variable is a group-level variable rather than an individual level one should not be a problem. There should not either be any issue with having two levels of random effect. Modern software should cope with this seamlessly although as far as I can remember it used to be an issue in the old days.

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