# GEE vs. fitting a simple model to each subject and then test the parameters across subjects

In my experiments, participants (N=50) are asked to play a decision-making game several times. I am interested in testing whether a certain factor "F" (present/absent) influences participants' decisions "D" ("chose D"/"didn't choose D").

I have run a GEE logistic regression in order to account for the repeated measures in the model. The editor of the manuscript isn't very fond of GEE (mostly because he "doesn't understand it very well"). Instead, he suggests we "fit a simple model to each subject and then test the parameters across subjects". To him, this approach is more straightforward. To me it sounds that running N regressions, and then running a t-test on the betas (if this is what he is suggesting) would mean losing a lot of power. I am looking for some evidence for this potential loss of power, or any other argument that indicates that in this situation, GEE is preferable to a two-step random effect analysis. Thanks in advance!

• What software are you using? If R, I may be able to demonstrate how to go about this and address the editor's concerns simultaneously. The editor is right in a certain way. In GEE, you assume that Factor has the same effect for everyone which can be overly constraining. Nov 4, 2018 at 12:54
• Hi! I am working with Stata. Nov 4, 2018 at 13:14

After looking through the Stata manual, you can run two models:

melogit D F || participant_id:
est sto m0 /* store results for future testing */

This is a mixed effects logistic regression model. In this model, you believe that on average, there is a difference at time points when F = 1 versus F = 0. The F before || communicates this belief.

However, you want to adjust for the fact that some time-points come from the same participants. You need some kind of participant identifier after the || to do this. This way, your inference will account for the fact that certain time-points come from the same person. This model is in some regards similar to the GEE model you performed.

Next, you can run:

melogit D F || participant_id: F F0, covariance(unstructured) nocon
est sto m1 /* store results for future testing */

Here, we extend the first model to the situation that the F effect differs by person. For some people, maybe presence has no effect on their decisions. For others, maybe it does. That is what the second F does. F0 is a dummy variable for when F=0. We have to add the nocon option so we can use both dummies. And the covariance(unstructured) allows you to calculate the average correlation between a participant's absent decisions and their present decisions.

Finally, we can run: lrtest m0 m1 to compare the models. The second model is more complicated so if the likelihood ratio test is statistically significant, then there is evidence to suggest that the effect of presence differs by person, and we prefer the second model. Otherwise, the simpler model where we simply account for the fact that the time-points are nested within person suffices.

At the bottom of each melogit model, Stata already provides you with a "conservative" test for whether the mixed effects approach is better than the regular logistic regression approach. If that test, LR test vs. logistic model: chibar2 is statistically significant, it is a simple justification (but in my opinion unnecessary) for taking the mixed effects approach.

I find it unnecessary because I think it is best to just model the structure in the data. If there are repeated rows from each individual, just account for them.