I have an unbalanced panel data set, which covers a set of about 10 variables I am very interested in as controls in a regression. However, only a few of these variables are available in all waves: most of them are only available for a few waves down to two which are only available for 5 waves. Additionally, these variables have high rates of missingness.
If I just create a sample where all variables are available I lose a massive share of observations and years. So I split the sample in several subsamples each depending on the availability of these variables, i.e.
Sample 1 - very small sample but all variables are available for all obs
Sample 2 - somewhere in between
Sample 3 - all waves and observations, but for many individuals observations on the interesting variables not available.
So now a t-test was used to check whether the mean of the dependent variable and some other unaffected key variables differ among these samples. Unfortunately, they do in most cases. I did the t-test in the first instance to prove that for example the dependent variable does not significantly differ between samples.
I am not sure what to do with the information, that they do differ. Is there anything I can do?