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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?

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Luke W. Johnston
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1 Answers1

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The betas are very similar in interpretation to those from OLS, but for a population average. For a one unit increase in Cortisol Stress, you'd expect, on average, a 9.5 unit increase in blood pressure, holding all other variables constant. You can also interpret these as slopes associated with the predictor.

The time component in your model is just another controlling factor that you've added into your model. The beta associated with CortisolStress is the slope associated with CortisolStrees while holding time constant (chose any time frame you like -- so it's more akin to your "at any give time" interpretation) as well as the other independent variables in your model. It does not say anything about changes over time. If you wanted to say something about Weight and if/how it changes over time, you'd need to include an interaction term in your model: (i.e. + Time*Weight)

By the way you should not be interpreting GEE coefficients as relating to individuals -- GEE models are marginal models and so the conclusions you draw from them are population-based. See the following discussion I've commented on regarding interpretation: Conditional vs. Marginal models

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StatsStudent
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  • Could you expand on the 'slopes associated with the predictor` part? I'm still getting what that means.. – Luke W. Johnston Jul 25 '15 at 20:50
  • I'm still **not** getting, I mean. – Luke W. Johnston Jul 25 '15 at 20:57
  • 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 02:27
  • 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 02:31
  • Hm, yes, I understand what the slope is in that context. I have edited my question to hopefully make it clearer what I am getting confused about. Basically, I am not understanding the time component. Does the beta say anything about changes over time? Or is it *only* about the *at any given time* interpretation. – Luke W. Johnston Jul 26 '15 at 18:48
  • The time component here is just another controlling factor that you've added into your model. The beta associated with CortisolStress is the slope associated with CortisolStrees while holding time $constant$ (chose any time frame you like -- so it's more akin to your "at any give time" interpretation) as well as the other independent variables in your model. It does not say anything about changes over time. If you wanted to say something about Weight and if/how it changes over time, you'd need to include an interaction term in your model: (i.e. + Time*Weight). – StatsStudent Jul 26 '15 at 19:29
  • By the way you should not be interpreting GEE coefficients as relating to individuals -- GEE models are marginal models and so the conclusions you draw from them are population-based. – StatsStudent Jul 26 '15 at 19:29
  • Excellent, thank you for clearing that up for me! If you just incorporate your comments into your answer I will accept it! – Luke W. Johnston Jul 26 '15 at 19:35
  • Thanks, @Luke. I have made the changes as you requested. – StatsStudent Jul 26 '15 at 19:45
  • +1, However, note that in this case the OP has a normal (`family = gaussian`) model. This is a special case in which the marginal interpretation & the interpretation conditional on the observation are identical. – gung - Reinstate Monica Jul 26 '15 at 20:32
  • Good point, @gung. I didn't look carefully enough at the code -- you are right on here. – StatsStudent Jul 26 '15 at 22:03