Overall, study findings support the extension of authoritative school climate model to high school and guide further research on the conditions for a positive school climate. The study conducted multilevel multivariate structural modeling in a statewide sample of 48,027 students in 323 public high schools, who completed the Authoritative School Climate Survey. As hypothesized, two measures of structure (Disciplinary Structure and Academic Expectations) and two measures of support (Respect for Students and Willingness to Seek Help) were associated with higher student engagement (Affective Engagement and Cognitive Engagement) and lower peer aggression (Prevalence of Teasing and Bullying) on both student and school levels of analysis, controlling for the effects of school demographics (school size, percentage of minority students, and percentage of low income students). (Publisher abstract modified)