As far as I am aware of, decisions to charge or not to charge and how in Portuguese national museums are never based on research. Those who scrap admission fees do it in the name of “democratisation” and “accessibility” and state that the loss of income is not significant (never mentioning how much it is, though). Those who reinstate them usually speak of the need to generate some income.
Although previous research and summative evaluation is not part of our practice in Portugal, this is not the case in other countries. And even though we seem to lack our own specific data, we can always learn from the experience and shared knowledge of others.