# Difference between random effect and random intercept model

I am looking at clustered data and because I was trained in economics I tend to look at fixed effects and random effects as solutions. An alternative would clearly be multi-level modelling. However, for me the clustering is just a nuisance, so I only care about "controlling it out".

However, looking at the equation of a random intercept model, I cannot see the difference to my random effect model. So I was wondering whether there just might be different names for the same thing, due to differences between disciplines? But then why can you (in Stata) estimate them differently?

• RIM: xtreg y x, i(id) mle
• RE: xtreg y x, re

However, the equation for both seems to be:

$$y_{ij}= b_{0} + b_{1}x1_{ij}+ u_{j} + e_{ij}$$

(Don't know how to format it nicely, but Google gives examples of RE and RIM equations, which look the same to me easily:

• Since an intercept is sort of an effect, a random intercept model is a special case of a random effect model. But you are right, there are many different terms for the same methodology. – Michael M Jul 16 '14 at 14:30
• Could you elaborate on how it is a special case or give me a reference? When I google I only find descriptions of either, but so far no comparison. All I read on RIM could (in my opinion) also be said about RE and vice versa. For example in RIM the group intercepts are the overall intercept+ the cluster error, but RE also has an overall intercept and cluster error? – John Gonway Jul 16 '14 at 14:51
• E.g. I wouldn't call a random effects model with random slopes a random intercept model. I don't know a reference of my first comment though. – Michael M Jul 16 '14 at 15:04
• It is worth explicitly pointing out here that these terms vary importantly & confusingly across disciplines (eg econometrics vs biostatistics). See here: What is a difference between random effects-, fixed effects-, and marginal model?, & here: Concepts behind fixed/random effects models. – gung Jul 17 '14 at 3:18