How to analyze extremly left-skewed data?

Hey everyone,

I am facing some trouble with the data of my master thesis and so I am looking for more general advice on how to deal with this topic:

I am investigating between the % of family ownership in family firms and the acquisition stake (also in %). Therefore, I planned to use a Tobit model (two limits).

However, after finishing my data collection, I end up with a dataset that consists in 319 out of 396 cases of 100 % acquisitions. So only a minority of cases has some variance. In my understanding, this is an extreme case of left skewed-data (mode>median).

So, my question is whether there is a model that is suited to analyze such an extreme case and additionally, whether the results I will get can be used at all.

In a later stage of my thesis, I would also like to investigate possible moderating effects. Is it foreseeable at this point in time whether this will be feasible at all?

The solutions to deal with skewed data were either transforming them using the log or a quantile analysis. However, I do not see how that could help me as the general problem of about 3/4 of the observations having the same value.

I hope I made my problem clear. I am glad for any help or dive since I am not sure how to proceed at this point.

Thank you for your comments and stay healthy in these days!