Students are most likely to leave science, technology, engineering, and mathematics (STEM) majors during their first year of college. We developed an analytic approach using random forests to identify at-risk students. This method is deployable midway through the first semester and accounts for academic preparation, early engagement in university life, and performance on midterm exams. By accounting for cognitive and noncognitive factors, our method achieves stronger predictive performance than would be possible using cognitive or noncognitive factors alone. We show that it is more difficult to predict whether students will leave STEM than whether they will leave the institution. More factors contribute to STEM retention than to institutional retention. Early academic performance is the strongest predictor of STEM and institution retention. Social engagement is more predictive of institutional retention, while standardized test scores, goals, and interests are stronger predictors of STEM retention. Our approach assists universities to efficiently identify at-risk students and boost STEM retention.