There can also be student self-selection effects as well. For example, Berkeley and Michigan offer more pre-professional majors (e.g. engineering majors and business) than Chicago does. Also, students in liberal arts majors may have different levels of pre-professional-ness at different schools. These may affect both entry to PhD programs and completion of PhD programs for those who enter them (more pre-professional-oriented students may just go to work after BA/BS (or may target professional schools like MD or JD programs), even if they would be admitted to PhD programs).