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What is a multilevel random effects model?
In a multilevel (random effects) model, the effects of both types of variable can be estimated. Inference to a population of groups: In a multilevel model the groups in the sample are treated as a random sample from a population of groups.
What is cross-classified model?
In cross-classified data, lower level units do not belong to one and only one higher. level unit. Rather, lower level units belong to pairs or combinations of higher level. units formed by crossing two or more higher level classifications with one another.
How are cross-level interactions used in multilevel models?
A cross-level interaction in a multilevel model is an interaction among fixed effects, one of which is measured at level 1 and one of which is at level 2. The fact that you have level 1 and 2 indicates the random effects are nested. For example: students nested within teachers because each student has only one teacher.
When to use a crossed random effect model?
Crossed random effects models are a little trickier than most mixed models, but they are quite common in many fields. Recognizing when you have one and knowing how to analyze the data when you do are important statistical skills.
Is there a third level of crossed random factors?
A third level is possible as well. This would happen if each doctor sees all their patients at one of four hospitals or each field has only one of 5 species. In one kind of 2-level model, there is not one random factor at Level 2, but two crossed factors. Each observation at Level 1 is nested in the combination of these two random factors.
That is each level of a random effect has a one-to-many relation with the levels of the lower random effect. E.g. each class id is unique for a given class in a given school and cannot refer to a class in any other school. This is how we constructed the class2 variable in our data.