Relation of lecture mandatory attendance and lecture quality
In fact there are many studies undertaken in this topic. Below you may find the link to some of these papers.


Classroom attendance: Factors and perceptions of students and faculty in US schools of pharmacy
Student nurse absenteeism in higher education: An argument against enforced attendance
Student and teacher attendance: The role of shared goods in reducing absenteeism 
Why do students miss lectures? A study of lecture attendance amongst students of health science
Does lecture attendance affect academic performance? Panel data evidence for introductory macroeconomics
The impact of charter school attendance on student performance


You can find tons of papers in this topic. Look at this link and her

Hope it helps