I have a regression in which I try to understand how much variance of the metric dependent variable each of the regressors explains. I use the package R relaimpo (Grömping, 2006) for that purpose, that allocates $R^2$ shares to each regressor using the LMG metric. The hypothesis is that the regressors differ drastically in their $R^2$ contribution.
If I had a cross-sectional sample of $N=6000$, things would be dandy. Unfortunately, I only have $N=2000$, but 3 measurement points (weeks 0, 6, 12). Both the dependent variable and regressors are time-varying, that is, they are assessed at each measurement point.
Currently I run the analyses separately for each measurement point and find large differences between relative importance estimates between regressors (0% to 25%), and I find that the ranking of regressors and the explained variance is surprisingly stable over time (at least from a qualitative perspective, plotting the explained variance of each of the 14 regressors for each measurement point).
For a scientific paper, there are two reasons why I want to do this in one regression instead of 3. (1) 3 different analyses take up a lot of space in the paper and obfuscate the main message a bit (regressors differ drastically in their relative importance). (2) $N=2000$ isn't all that much when disentangling the relative contributions of 14 correlated regressors (the CIs are rather large).
Therefore, I wondered whether there are ways to "pool" all subjects into one regression that would not lead to an outcry of anybody with some statistical background ("you severely violated the assumption of statistical independence!!"). In the best case I would simply have one regression that covers all 3 time points.
The method has to be a regression (ie., not using NLE or LME packages), because that is what the
relaimpo package uses as baseline model to then calculate unique $R^2$ contributions of regressors.
What are my options?