Computerized adaptive testing (CAT) is widely used, which adapts to the ability of each examinee and greatly shortens testing time. However, few studies have investigated how the response time (RT) recorded in CAT is related to student engagement in exams. Test engagement reflects a student's willingness to actively participate in the testing process. Lack of engagement can undermine test reliability and validity. This study has three goals: handling the missing-by-design issue raised by CAT, estimating student engagement using RT, and exploring how student characteristics affect their engagement. With a sample of 867 participants, preliminary results showed that RT could be used to measure test-taking behaviors via a psychometric method. Bayesian mixed effects models will be used to further explore how student characteristics influence engagement.