[R-meta] Replicating Three-Level Model with Fixed Effects

[Andrew Loignon]

Hi everyone,

As part of a separate project, I've been familiarizing myself with multi-level meta-analyses. While working through the example provided on the metafor package's website (http://www.metafor-project.org/doku.php/analyses:konstantopoulos2011), I ran into some difficulties replicating the three-level model described by Konstantopolous (2011, "Fixed effects and variance components estimation in
three-level meta-analysis").

Specifically, I can replicate Konstantopolous' two-level model using year as a fixed effect (Table 4 in the research article) using the following code:

m0.ml <- rma.mv(yi, vi,
                random = ~ 1| study,
                mods = ~ I(year-mean(year)),
                method="ML",
                digits=3,
                data=dat.konstantopoulos2011
                )
summary(m0.ml)

However, when I extend the model to include the higher-level nesting variable (i.e., district), the intercept diverges from what Konstantopolous reports (Table 5 in the research article). Right now, I'm using the following code:

m1.ml <- rma.mv(yi, vi,
                random = ~ 1| district/study,
                mods = ~ I(year-mean(year)),
                method="ML",
                digits = 3,
                data=dat.konstantopoulos2011)
summary(m1.ml)

With this model, I find an intercept of .178, while Konstantopolous reports a value of .183.

Any suggestions for how to reconcile these differences would be very much appreciated.

Best,

Andrew
Andrew C. Loignon
Assistant Professor
2716 Business Education Complex
Rucks Department of Management
E. J. Ourso College of Business
Louisiana State University
Baton Rouge, LA 70808
Email: aloignon using lsu.edu<mailto:aloignon using lsu.edu>
Phone: 225-578-6148


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