About 65% of students who start engineering programs do not graduate. This situation causes significant economic losses and social problems for families and society and risks achieving social sustainability worldwide. Sometimes, engineering programs focus on enrolling students rather than providing strategies to secure their academic success, which often leads to student dropout. This study proposes a model to explain and predict engineering dropout through pedagogical, sociodemographic, and institutional factors. Using data from 4127 engineering students (cohorts 2005 – 2019), a structural equation model (SEM) and logistic regression demonstrate that institutional, demographic, and pedagogical variables explain and predict dropout in computer, electronic, environmental, and industrial engineering. According to SEM, institutional, sociodemographic, and pedagogical factors confirm the theoretical model. With Logistic regression as a predictable model, we could identify variables that predict almost 74.8% of student dropouts and 72.4% of student success. Our results provide novel insights to engineering programs and Higher Education institutions to implement curricula and pedagogical strategies leading to decreased engineering dropouts and increased student success.