GEE correlation structure's number of parameters I am kind of confused on GEE correlation structure's number of parameters. Say I have 10 students(or clusters) and I measure their physical strength 10 times for each of them with their corresponding covariates over time. I want to specify GEE's unstructured correlation.
So for each person, I have 9 choose 2 parameters for correlation. That is 36 for each cluster(person). In total, I would have 360 different correlation parameters and I have an non identifiable model.
Is this correct?
Update:
Assume that 1 person got 9 measurements and 2 person got 3 measurements. In this case, there is no reason to assume same correlation structure in each cluster. Can I assume that variances are all the same here? I could have variance in cluster different as well.
 A: No, there will be 10 choose 2 correlation parameters, which are assumed equal across all participants, giving a total of 45. The correlation between measurements at time $t$ and time $t^\prime$ for individual $i$ is $\alpha_{tt^\prime}$, giving correlation matrix
$$
COR(Y,Y) = \begin{pmatrix} 
1 & \alpha_{1,2} & \alpha_{1,3} & ... & \alpha_{1,10}\\
\alpha_{1,2} & 1 & \alpha_{2,3} & ... & \alpha_{2,10}\\
\ldots & \ddots & & & \vdots\\
\alpha_{1,10} & \alpha_{2,10} &  & ... & 1\\
\end{pmatrix}
$$
That is still a lot of $\alpha$ parameters to estimate, but it's sometimes manageable.
This assumes common observation times in the data. But if some participants missed certain observation times that isn't necessarily a problem. For example, imagine that participant 7 was only observed at times 1 and 10, but missed the middle 8 observations. Then $Cor(Y_{7,1}, Y_{7,10}) = \alpha_{1,10}$ is still a reasonable assumption.
If the assumption of a common correlation structure is unsuitable for your data, then these GEE models should not be used. For example, if you have two groups under study where one group has strong correlations in their responses and the other group does not have correlated responses. I think it might be possible to model the correlation parameters as a function of $X$, but I'm not sure.
