In 2014, Heather O’Brien, E. Yom-Tov and I published a 100+ pages article on measuring user engagement:
M. Lalmas, H. O’Brien and E. Yom-Tov. Measuring User Engagement, Synthesis Lectures on Information Concepts, Retrieval, and Services, Morgan & Claypool Publishers, 2014
A pre-prodcution PDF version can be found here. Enjoy.