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Imagine collecting data in two locations at three points in time. The same 500 or so people are interviewed repeatedly, a year apart, in each place. There are many things being asked but of interest to me right now is a binary Yes/No answer to one particular question.

I want to know whether the rate of Yes answers in each location increases over time and whether that increase (if it exists) differs between the locations. A secondary question is whether the two locations differ overall.

For purposes of discussion, let's imagine the question to be "Do you shop at Walmart?" and the two locations being one urban area and one out in the suburbs. The actual data is slightly different but along those lines.

I am almost completely inexperienced with Generalized Estimating Equations but from what I've been reading this is sort of classic example of the population average effects that GEE's are designed to produce. Is that a correct idea?

That's my question, what follows is the technique I'm more familiar with and will use if the GEE approach is not appropriate...

When I use a random-intercepts mixed model (because of the repeated measures on each subject) to get time-by-group estimates of proportion Yes answers, I have to use a method of standardizing two estimates back to the entire study population. [see https://academic.oup.com/ije/article/43/3/962/763470 for details]

If I understand these things correctly, a GLMM like that with the random intercepts is meant to offer subject-level estimation, which is why a marginal standardization technique is required to convert everything back to the population level.

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    $\begingroup$ One reason I am exploring GEE or other models not requiring random intercepts is my GLMM-estimated random intercepts exhibit a pattern of large negative logit value for the mean intercept and large SD of the intercepts. It's the sort of thing Carlin, et. al. mention in the Discussion of this paper stat.columbia.edu/~gelman/research/published/397.pdf and I think it arises from having so many people who never at any point in time give a Yes response. $\endgroup$ – Brent Hutto Jan 24 '19 at 15:03
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It's not purely that GEE deals with population marginal effects. Think about the older and still excellent way of analyzing serial data: generalized least squares assuming multivariate normality. Like GEE, GLS does not have subject level intercepts. They can both estimate mean trajectories over subjects. But by not having varying intercepts, they assume that differences between subjects represent ordinary randomness from sampling variability, and that there is not a group of subjects who are "truly on their own course". When intercepts have a very large variance, GEE and GLS will be biased and will produce marginal estimates, otherwise they can be competitive, especially GLS. GEE, unlike GLS or GLMM which are full likelihood models, does not withstand nonrandom dropout of subjects over time. GEE also requires a fairly large sample size to give accurate inference. GLS and GLMM assume missing at random. GEE assumes missing completely at random, in Rubin's missing data parlance.

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  • $\begingroup$ One of my concerns about applying GEE here is definitely the missing data. About 7% of our data is missing due to subjects moving away from the targeted locations. For all I know that may be MCAR (we can not find any ways in which the lost-to-followup people are different) but it's a mighty strong assumption that can't be really put to bed, so to speak. Regarding the GLS, isn't that linear models thing rather than for binary outcomes? $\endgroup$ – Brent Hutto Jan 24 '19 at 14:09
  • $\begingroup$ Yes I should have clarified GLS is for continuous outcomes - it's the generalization of OLS (ordinary linear models). Mixed effects models would be one good choice for binary outcomes. Bayesian hierarchical models even better. And there are models that model binary Y dependence differently but they are not all full likelihood models. $\endgroup$ – Frank Harrell Jan 24 '19 at 18:40
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    $\begingroup$ If I may go off-topic for just one comment...I chuckled when you mentioned Generalized Least Squares. My self-study project for learning R involves, among other things, working my way through Julian Faraway's "Linear Models With R" textbook. It was literally two days ago that I did the Section 8.1 on GLS and that was the first time I'd even thought about the topic in years. Then you mention it here! $\endgroup$ – Brent Hutto Jan 24 '19 at 22:53
  • $\begingroup$ People forgot that GLS existed when SAS PROC MIXED came out and SAS had no way to do GLS. GLS was developed in the 1950s under "growth curve analysis". $\endgroup$ – Frank Harrell Jan 24 '19 at 23:15

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