# Interpretation of GEE coefficients

Suppose blood pressure is a continuous outcome variable and you run a linear GEE with following predictors: age (years), weight (lbs), and smoking (yes/no). How would you interpret the coefficients for these predictors? Would it be the same as in "regular" linear regression?

Yes, they are interpreted the same way. The only consideration (and key departure from linear regression) is that these measured effects are considered to be at a "population" level. This is often not a key component of effect interpretation, so your main effect for, say smoking would be, "An expected difference in blood pressure comparing smokers to non-smokers of the same age and weight." Note that I wouldn't say "An expected difference in blood pressure comparing a smoker to a non-smoker of the same age and weight."

• So if you have clusters of people and run the GEE above, the coefficients would still have the same interpretation? The only difference is that GEE incorporates the correlation structure of the data and thus gives more accurate standard errors? Also isn't "regular" linear regression at the population level as well? – guy Apr 22 '14 at 22:45
• Yes, GEE always estimates the marginal effects, even when a correlation structure has been specified (unlike the mixed model). Regular linear regression is not necessarily at the population level. The conditional and marginal effects are the same for linear models, but for correlated data, the mixed model estimates intracluster correlations for weighted LS, and this gives you individual level SE estimates (GEE has population level SE estimates which are generally bigger). – AdamO Apr 22 '14 at 22:50
• But the whole GEE process relies on first specifying r (ICC), from which we gets weights and an estimate of the mean. This is an iterative process which continues until some stopping condition? Also you can compute the standard errors of the coefficients any way you like after the whole process is done? – guy Apr 22 '14 at 22:54
• I think you should refer to Longitudinal Data Analysis, Diggle Heagerty Liang Zeger. They talk in great depth about differences between GEE and Mixed models. The sandwich basically "averages over" all the conditional effects according to the distribution of the model predictors to get that population level effect. Correctly specifying the variance structure only gets you better standard errors for the marginal effect estimates. – AdamO Apr 22 '14 at 22:56
• Adam interesting about the interpretation of the SEs. I hadn't picked up on this. – conjectures Apr 23 '14 at 7:33

For continuous outcome or response you can't apply GEE. GEE can be applied only to categorical outcomes when you want to estimate the parameters marginally (not individually). However, you can apply GEE once you made your response variable (Blood Pressure) categorical. For example high, low, medium.
The interpretation of the coefficients is depending on the link function (identity, logit ...) you applied .

• Incorrect. You certainly can use GEE for continuous outcomes. – not_bonferroni Feb 7 '17 at 19:23
• $\sum_{i=1}^N \frac{\partial \mu_{ij}}{\partial \beta_k} V_i^{-1} \{ Y_i - \mu_i(\beta)\} = 0$ – not_bonferroni Feb 7 '17 at 19:32
• This is the sum over the criterion function for each sampled unit. The fact that it's a sum has nothing to do with whether or not the response is continuous. – not_bonferroni Feb 7 '17 at 19:39
• However, the very notion of a working covariance structure obviously assumes a numeric outcome. Categorical data are accommodated through an arbitrary numeric coding scheme (e.g. 0/1). You trollin' Dejene? – not_bonferroni Feb 7 '17 at 19:40
• Now you're talking about likelihood-based inference. Do you know what GEE is? – not_bonferroni Feb 7 '17 at 19:53