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Teachers' self-efficacy, attitude, and engagement are influenced by various factors, encompassing personal, school contextual, and behavioral aspects. Nevertheless, prior studies have not thoroughly explored the intricate relationship between teachers' self-efficacy, attitudes, and engagement, particularly in the context of teaching science through an integrated STEM approach (ISTEMA). Drawing upon the Social Cognitive Theory and the Theory of Planned Behavior, this study proposes a structural equation model that incorporates school contextual factors: school administrative support and peer or collegial support, along with the personal factor--teachers' STEM discipline knowledge to predict teachers' self-efficacy in teaching science through ISTEMA. It also considers school administrative support and teachers' self-efficacy to teach science through an ISTEMA as predictors for teachers' attitudes and engagement in the implementation of ISTEMA. Additionally, school administrative support, teachers' self-efficacy to teach science through ISTEMA, and teachers' attitude to teach science through ISTEMA are regarded as behavioral factors that predict engagement in the implementation of ISTEMA. The survey was administered to 452 high school teachers hailing from four distinct regions and Phnom Penh City, Cambodia. The results of the full structural equation modeling (SEM) analysis revealed that changes in teachers' STEM discipline knowledge and peer or collegial support may correspondingly lead to changes in teachers' self-efficacy to teach science through an ISTEMA (SE), with an indirect effect of school administrative support (AD) on SE via teachers' STEM discipline knowledge. The enhancement of SE and teachers' attitude to teach science through an ISTEMA (ATT) significantly influences teachers' engagement to teach science through an ISTEMA (EGG), whereas AD has a direct impact on engagement and an indirect one via teachers' self-efficacy and attitude. Furthermore, SE directly and indirectly affects engagement through teachers' attitude. These findings hold profound significance in shaping policies related to teacher training in integrated STEM education and theoretical foundation for future studies.