Random Intercept model vs. GEE Consider a random intercept linear model. This is equivalent to GEE linear regression with an exchangeable working correlation matrix. Suppose the predictors are $x_1, x_2,$ and $x_3$ and the coefficients for these predictors are $\beta_1$, $\beta_2$, and $\beta_3$. What is the interpretation for the coefficients in the random intercept model? Is it the same as the GEE linear regression except that it is at the individual level?
 A: GEE estimates the average population effects. Random intercept models estimate the variability of these effects. If $\alpha_j=\gamma_0+\eta_j$, $\eta_j\sim\mathcal{N}(0,\sigma^2_\alpha)$, random intercept models estimate both $\gamma_0$ (which is the average population intercept and, in normal linear models, is equal to the one estimated by GEE) and $\sigma^2_\alpha$.
If the intercept is modeled by second-level predictors, e.g. $\alpha_j=\gamma_0+\gamma_1 w_j+\eta_j$, a random intercept model can estimate how the intercepts vary at the individual level, i.d. according to economic, demographic, familiar etc. factors, to the 'group' to which a specific individual belongs.
A: GEE and Mixed Model Coefficients are not usually thought of as the same. An effective notation for this is to denote GEE coefficient vectors as $\beta^{(m)}$ (the marginal effects) and mixed model coefficient vectors as $\beta^{(c)}$ (the conditional effects). These effects are obviously going to be different for non-collapsible link functions since the GEE averages several instances of the conditional link across several iterations. The standard errors for the marginal and conditional effects are also obviously going to be different. 
A third and oft overlooked problem is that of model misspecification. GEE gives you tremendous insurance against departures from model assumptions. Because of robust error estimation, GEE linear coefficients using the identity link can always be interpreted as an averaged first order trend. Mixed models give you something similar, but they will be different when the model is misspecified.
