Standardized teaching observation protocols have become increasingly popular in evaluating teaching in recent years. One of such protocols that has gained substantial interest from researchers and practitioners is the Classroom Assessment Scoring System-Secondary (CLASSS). According to the developer, CLASS-S has three domains of teacher-student interactions: Classroom Organization, Emotional Support, and Instructional Support. The goal of this study is to examine the structure of CLASS-S while accounting for the hierarchical multivariate ordinal nature of data collected through this protocol. Data used in this study came from two sources. The first source is the Understanding Teacher Quality (UTQ) study that took place middle schools in three large school systems from the same metropolitan region in the southeastern United States. The second source is the Toward an Understanding of Classroom Context (TUCC) study conducted in middle and high schools in an urban fringe mid-Atlantic school district. The UTQ study includes 458 teachers teaching mathematics (n = 231) or English language arts (n = 227) to sixth, seventh, or eight graders. The TUCC study included 82 teachers in 20 middle and 20 high schools. The authors examined the structure of CLASS-S using a Bayesian hierarchical multivariate ordinal model. Results from this study showed that accounting for the hierarchical multivariate ordinal nature of data does matter for understanding the structure of CLASS-S scores. Figures are appended.