Inspired by the discussion on StatBlog on open peer review and the idea of viewing every paper as a discussion paper, I would like to take the opportunity to make a short comment on a paper recently published in Stat: Practical marginalized multilevel models by Griswold et al. (2013). This is a very interesting paper reformulating the marginalized multilevel model (MMM; Heagerty and Zeger, 2000) and showing how to fit such a model using existing mixed model computing solutions. The MMM nicely combines marginal and conditional models by specifying both a marginal mean model and a conditional model representing the association structure of longitudinal or other clustered data.

When I was reading Section 4, which describes two real data examples, I looked at the fitted marginal models and wondered how results would look like if the simplest fitting approach had been used: a marginal model with working independence. For example, I analyzed the visual impairment data and used the R gee package (Carey, 2012) to fit a marginal logistic model with working independence. Results are given below. Thanks to Bruce Swihart for providing the data and related information. The data is now also available at http://www.biostat.jhsph.edu/~bswihart/Publications/.

Coefficients: Estimate Naive S.E. Naive z Robust S.E. Robust z (Intercept) -2.4398758 0.04872570 -50.073693 0.05768490 -42.29661 black 0.1005937 0.07096382 1.417535 0.08521642 1.18045

We see that the fitted coefficients differ slightly from those given in the paper’s Table IV. Taking the (robust) standard errors into account, however, these differences cannot be seen as substantial, confirming the results from the paper. The standard errors (both in the paper and above) also indicate that there is no significant marginal effect of race. However, this only due to the fact that other covariates are ignored. In particular when age and education is taken into account, there is a clear effect of race; see, for example, Liang and Zeger (1993).

**References**

- Carey, V. J. (2012).
*gee: Generalized Estimation Equation solver*. R package version 4.13-18; ported to R by Thomas Lumley and Brian Ripley. - Griswold, M. E., B. J. Swihart, B. S. Cao, and S. L. Zeger (2013). Practical marginalized multilevel models.
*Stat 2*, 129-142. - Heagerty, P. J. and S. L. Zeger (2000). Marginalized multilevel models and likelihood inference.
*Statistical Science 15*, 1-19. - Liang, K. Y. and S. L. Zeger (1993). Regression analysis for correlated data.
*Annual Reviews of Public Health 14*, 43-68.