Website measures of engagement captured from millions of users, such as in-page scrolling and viewport position, can provide deeper understanding of attention than possible with simpler measures, such as dwell time. Using data from 1.2M news reading sessions, we examine and evaluate three increasingly sophisticated models of sub-document attention computed from viewport time, the time a page component is visible on the user display. Our modeling incorporates prior eye-tracking knowledge about onscreen reading, and we validate it by showing how, when used to estimate user reading rate, it aligns with known empirical measures. We then show how our models reveal an interaction between article topic and attention to page elements. Our approach supports refined large-scale measurement of user engagement at a level previously available only from lab-based eye-tracking studies.