Within and between estimates in random-effects models: Advantages and drawbacks of correlated random effects and hybrid models

Correlated random-effects (Mundlak, 1978, Econometrica 46: 69–85; Wooldridge, 2010, Econometric Analysis of Cross Section and Panel Data [MIT Press]) and hybrid models (Allison, 2009, Fixed Effects Regression Models [Sage]) are attractive alternatives to standard random-effects and fixed-effects models because they provide within estimates of level 1 variables and allow for the inclusion of level 2 variables. I discuss these models, give estimation examples, and address some complications that arise when interaction effects are included.