When you composed your conclusion, the possible reasons for the impact of staff were couched exclusively in terms of an academic intergrative context, such as "a more professional staff builds collections that connect students better to the knowledge that they need" or "library staff encourages students to use the collection"; did you consider socially integrateive aspects as well?
I think of the socially integrative portion in Tinto's model particularly when you mention Gender and Race as predictors. Perhaps, the library is a safe, nonjudgmental atmosphere or, perhaps, it is a safe place to study, a social environment where one can be alone, but feel secure enough with having others around.
I also am curious about if you see a relationship just between number of staff and persistence; or if this is just reflective of more money spent on the library likely creates a better, cleaner, more modern environment and; therefore, is better used because of money not only spent on the collection and on staff, but also on the building itself?
More technology, more collaborative work spaces, more comfy chairs, etc.
I suppose, I see libraries as dwelling in the middle of Tinto's model, uniquely a part of both the Social Integrative experience necessary for student persistence (like students interacting with faculty or librarians, meeting friends for group study, hanging-out between classes, etc.) and the also the necessary Academic Integrative experience (like fostering intellectual curiousity through exhibits, library instruction, life long learning programming, etc.). Some of this is measurable in terms of number of contact hours like through instruction; or, can be qualitatively gathered, through interview after a viewing an exhibit or guest speaker; for example,"are you interested in learning more about this topic?" as a measure of intellectual curiousity. I would think that the number of staff promotes both the academic integrative and the socially integrative in this context.
Cheers, Wil