This is a really interesting question and I would like to hear some more answers as well.

Zurr et al. (2003) says more or less that both GEE and GLMM are used when the assumption of independence is violated. In GLMMs we basically say that observations from a given source or group (subject, farm, plot, nest...) are correlated but there is not any specific correlation pattern between observations from that source (eg. temporal, spatial, etc). Instead, for GLMMs the variance of the distribution (usually taken as normal) of the effects of the source is calculated.

On the other hand GEEs don't make any estimation of the "distributional properties" of the source (subject, farm,...). This means that the model for the mean response depends only in the covariates and not in the random effects. Then, the advantage of a GEE (as opposed to a GLMM) is that you can specify several types of within group correlation: unstructured, autoregressive (AR-1), exchangeable or compound-symmetry (the one used on GLMM), stationary, auto-correlation, ante-dependence, and some other correlation structures.

I'm not sure I understand completely your experiment, I imagine your 'random effect' will be spider. So in your case, because you don't seem to have several longitudinal repeated measurements (over time or space) data, I would just stick to a GLMM.

In selecting the method, we need to ask three things. (1) Is it a survey with explicit sampling plan? (2) Is it unbalanced design (unbalanced = # of patients differs from one hospital to another)? (3) Is # of clusters sufficiently large? If the survey was conducted with explicit sampling plan, you should use survey analysis methods (survey commands in SAS, Stata, or R). If not (if it was a simple random sample), you can use hierarchical model (random-effects model), GEE, or clustered robust SE. If the data are unbalanced design, random-effects model or GEE are the way to go (these two methods can handle unbalanced design), and clustered robust SE may not be a good option. If you're dealing with the balanced data, all 3 methods can be used. In general, random-effects (20-30 clusters for fixed effects, 100 clusters necessary for variance component estimate) model and GEE (50-100 clusters) require a fair number of clusters just to get the procedure to run (# of clusters is more important than # of units within each cluster!). However, clustered robust standard errors also need a fair number of clusters in order to be reliably computed.

References:

http://www.ats.ucla.edu/stat/stata/library/cpsu.htm

http://annals.org/article.aspx?articleid=716858&resultClick=3

http://www.ucl.ac.uk/pcph/research-groups-themes/thin-pub/research_presentations/GEE

http://www.modeling.uconn.edu/m3c/assets/File/Mcneish_small%20number%20of%20clusters.pdf

If you have 50+ clusters, you can use both GEE and random-effects model. If you have less than 50, I suggest you use random-effects model. GEE is robust to misspecification of working correlation only when the number of clusters is large. If the number of clusters is not sufficiently large, you need to be considerate about which correlation matrix to use (I suggest you use many correlation matrices as sensitivity analysis). In general, the estimates you will get from running hierarchical model (aka random-effects model) and GEE should not make a huge difference (so far as you are not making wrong assumptions).

Reference: http://annals.org/article.aspx?articleid=716858

I sugest you run both GEE and random-effects model (GLMM) and see if your findings are sensitive to the model specification.

A very interesting question, which has generated a lot of confusion in the past 20 years! Historically, GEEs were introduced when it was not yet possible to fit GLMMs in a robust way (and in fact it is still a hard problem today). However, I have the impression than many pepole stick to GEEs due to historical reasons, and not because it is the correct or best way to do an analysis. I did a thorough literature resarch in the past 2 months and found tons of papers about the difference between marginal models (usually, but not exclusively, fitted by GEEs) and conditional models (GLMMs).

I find the following reference useful:

Lindsey, J. K. and P. Lambert (1998). On the appropriateness of marginal models for repeated measurements in clinical trials. Statistics in Medicine 17, 447–469.

Particulary, on p. 465 you find the following text:

"[...] in most situations if we start directly from a simple

model for the marginal distribution of the responses, a complex

and unrealistic conditional relationship between the responses

and the explanatory variables is implicitly generated [...]. The

biological validity of such a model will generally be questionable,

although it will obviously have to be considered case by case.

All models are wrong [...] but we are arguing that models di-

rectly constructed to have simple marginals will be more wrong

than those beginning with a reasonably simple conditional rela-

tionship. They will tend to yield biased conclusions about the

questions under study. Nevertheless, [...] marginal inference

techniques often assume that some simple marginal regression

equation for the mean is correct. Generally, this cannot be the

case."

I guess one really has to decide FIRST, if a marginal or a conditional model correctly answers the research question. If it is a conditional model, one should use a GLMM. If it is a marginal model, one can either use a GEE directly, or integrate the result from the GLMM (which I think is the way to go).

I agree with Stefanie.

Before clicking on any software button or running SAS, R or SPSS code, make clear to yourself what you wish to analyse, what assumptions are beyond GLMM and GEE, and you are done. For any general question there is a general answer, but in general it will not fit your particular question.And my favorite quite from Ludrook:"Even during the planning stage of a study it is very important to seek the advice of a qualified biostatistician."

Although it is an old thread, could the attached paper be of interest?

It reiterates how GLMM and GEEs differ. I personally cannot recommend GEEs, because using them is in some sense equivalant to

- Omitting important covariates

- The Simpson paradox

- Berkson measurement error in a covariate

That's the message of the attached paper.

Dear Stefanie,

Thanks for the recommended paper. I was wondering what is suggested to chose instead of GEE if I am interested in robust inference, violated assumptions of RE/FE models in my data and in the case I am purely interested in a population based inference. Any recommendation?

Dear Claudia

Thanks for your question. I probably should qualify my above answer a bit: There can be situations when GEEs are fine, namely when you have reasons to assume that the marginal relationship you formulate is ok. Lindsey and Lambert, whom we cite in the paper mentioned above, say that

"All models are wrong [...] models directly constructed to have simple

marginals will be more wrong than those beginning with a

reasonably simple conditional relationship."

I would say that it is, however, yet another question If your assumptions regarding the FE/REs are violated, in which case transformations might help. Alternatively, you can perform individual-specific analyses and then look at the distribution of the results, but I understand that that's not what you are interested in, right?

Best,

Steffi

Since you have a longitudinal model I am attaching an excellent discussion that compares GEEs with the GLMM approach as well as discusses the entire topic by Prof. Marie Davidian of NC State University and past president of the American Statistical Association who is a leading expert on these topics. I suggest you take a look at this material and perhaps contact her. HTH. Best wishes, David Booth

Here is the link:

https://www4.stat.ncsu.edu/~davidian/st732/notes.html