Fixed Effects Regression Models Allison Pdf 43
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3. REWB models are sometimes called mixed regression models but, in a technical sense, this is incorrect. It is better to think of them as models that relate fixed effects to random effects. For a more detailed discussion of this point, see Barrientos and Trivedi (2018).
2. Both Mundlak and REBW models assume that the correlation between the residuals in the two equations is zero. If the residuals are correlated the equations might be better fit by fitting each equation separately. In this case, the between and within covariance matrices will be estimated from the results of the two regression equations.
4. Howard's (2011) point is that the mean of the continuous explanatory variable is not always separable into between and within effects. However, the Mundlak model does separate the within and between effects.
Despite the advantages mentioned above, the REWB models have also attracted criticism. Howard (2011) argues that they overestimate the size of the between effects. Howard's (2015) critique of RE models more generally is similar to ours. In one of our recent studies using the RE model, we argue that the REWB model is more robust to outliers and non-normality than the RE model (Barrientos and Trivedi 2018). It is our hope that this discussion of the REWB models will help clarify how we view this class of models and some of the debates around them. We have also avoided some debates that might be better suited for another venue, such as discussions of the gender pay gap. We return to the topic of the gender pay gap in the concluding remarks.
1. This is a basic illustration of the REWB model and incorporates only two explanatory variables, each of which is dichotomous (zero or one). The equations for the Mundlak and RE models with continuous explanatory variables are very similar. See Howard (2015) for a detailed description of the Mundlak model. The Mundlak can be extended to include interaction terms as a matter of convenience. However, if the interaction terms were coded as continuous variables, the Mundlak would be identical to the REWB model. The standard RE model can be extended to include interaction terms by dichotomizing the continuous variables.
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