A simple way to obtain a rough measure of permissions or full OA (the element of open access that goes beyond free to read, to providing permission to reuse the material in a variety of ways, from downloading and redistributing (including, or not including, commercial re-use), to making derivatives), is to review the DOAJ journals and note which journals use Creative Commons licensing, which license, and which ones use which license. It would be helpful to follow the DOAJ Subject lists for this, as there could be disciplinary differences, and also to note the publishers. BMC uses CC-BY, for example, and is a large enough publisher to impact the percentage of journals using CC-BY in biomedicine. It would be a good idea to download the DOAJ title list on a particular date, and work with that. Otherwise, the ongoing dramatic growth of DOAJ will mean your title list will keep changing as you research.
For a smaller but useful study, just look at one of the DOAJ subject areas, or a few very different subject areas to get some idea of the range. This could be useful information in and of itself, and/or as a pilot project for a larger study.
It is important to note that lack of CC licensing does NOT mean that a journal is not willing to provide permissions-OA, only that the journal has not expressed permissions-OA in this manner.
Another interesting research question would be whether DOAJ journals that are not using Creative Commons licensing consider their journals to be providing some aspect of permissions OA. A survey approach, working cooperatively with DOAJ to distribute the survey to DOAJ journals, might be workable.
I just contributed this idea to the Journal Business Models section of the Open Access Directory.