# What are the criteria to be a random factor in a multilevel model?

In multilevel data, observations are correlated in different levels and when we model the data we consider these levels as random variables.

Suppose we have only 6 regions in my data and the observations are nested within the regions. The population from which the data is drawn just has exactly 6 regions. Now, the question is can I use this variable (region) as a level i.e. a random effect or I should use this as a fixed effect?

Total sample size is 8753 and each region contains:

Region 1 -   977
Region 2 - 1750
Region 3 - 1445
Region 4 -   982
Region 5 - 1083
Region 6 - 1107

• How big is your sample and how many readings you have for each region? In general, 5-6 level factors are really pushing the idea of a random effect but it not a completely right-off. Remember you essentially estimate a standard deviation. Do you feel comfortable estimating a standard deviation out of 6 points? If yes, you are good to go! :) Feb 16, 2016 at 20:37
• Thank you for the clarifications. See my answer below. For future reference: If you edit a message following a user comment consider commenting back using the @ sign (so something like @usεr11852 in this case). I did not see your edit, it just happened that I saw gung's later edit. Feb 18, 2016 at 2:53

Yes, it is reasonable to use region as a random factor in your case.
In any case I would strongly suggest that you bootstrap your model to get confidence intervals about the standard deviation of your observed random effect. Assuming you are using R and the package lme4 the function confint(method="boot", ...) is what you want to use at first instance. Note that ultimately the inclusion or exclusion of a random factor is a design question; if you really think that the factor region is something you test against then it should be a fixed effect; if it is (almost) an nuisance parameter or something you do not really have control over then it is plausible to treat as a random effect.