# Interpreting a longitudinal generalized estimating equations beta cofficients

I've been struggling with wrapping my head around the GEE beta coefficients and I don't think I fully get it. There are other questions on CrossValidated that ask about GEE in the binary context (Generalized estimating equations output in SPSS and Interpretation of GEE coefficients) and while helpful do not help me understand continuous variables in a longitudinal setting.

Here is an example longitudinal analysis:

geeglm(BloodPressure ~ CortisolStress + Time + Sex + Age + Weight,
id = SubjectID,
family = gaussian,
corstr = 'ar1', data = dataset1)


The data are sorted as:

> Time, SubjectID, ...
> 1, 100, ...
> 2, 100, ...
> 3, 100, ...
> 1, 101, ...
> 2, 101, ...
> ...


The beta coefficient for the CortisolStress is, e.g., 9.50 (SE = 2.3). From what I understand, that means for individuals with a one unit increase in CortisolStress have at any given timepoint a 9.50 unit increase in BloodPressure and that there is a 9.50 unit increase in BloodPressure averaged over time (longitudinal interpretation). Or said another way, as time increases there is a 9.50 unit increase in BloodPressure as CortisolStress increases. This second part, the longitudinal part, is where I'm getting tripped up.

Am I understanding this correctly?

• Sure. You can simply interpret each of the betas as a slope corresponding to the predictor with which it is associated. For example, Let's say the $\hat\beta$ associated with weight in your model was 3.5 and weight was measured in lbs. Then 3.5 is simply the slope associated with weight while holding the other variables constant -- in order words for a 1 pound increase (rise) in weight we can expect a 3.5 increase in blood pressure (run). So 3.5 is simply a slope (rise/run). – StatsStudent Jul 26 '15 at 2:27
• Another way to think about this in terms of slopes from my previous comment is to consider fixed values for CortisolStress, Time, Sex, and Age. If you fix these values and multiple each by their corresponding beta, you can then group all of these terms into a constant term, say $b$. Then you are left with the $\hat\beta \times Weight$ on the RHS. You then have the familiar equation of a line in "slope intercept form" $y = mx+b$ where $m = \hat\beta$ and $x=Weight$. Here $m=\hat\beta$ is the slope associated with weight. – StatsStudent Jul 26 '15 at 2:31