The standard scoring of the CLASS PreK produces three domain scores that are widely used in research, practice and policy. Despite these domains being based on developmental theory and research, limited empirical evidence exists for the three-domain structure as operationalized in the CLASS PreK. Using the 2009 and 2014 Head Start Family and Child Experiences Surveys (FACES), we estimated a series of exploratory and confirmatory bifactor and traditional factor analyses to produce evidence regarding this structure and possible alternatives in nationally representative samples of Head Start classrooms. Replicating and extending the small set of prior factor analytic studies, we found alternative factor structures fit equally well or better than the standard structure in both FACES 2009 and 2014 as well as problems with estimation and fit of a bifactor structure of general and specific factors proposed by the CLASS PreK developers. Across all domain structures, associations with children's academic and social-emotional gains during the Head Start year were uniformly small and generally non-significant. Our findings encourage future refinements of the CLASS PreK and continued development of new measures to better operationalize its conceptually-motivated domains. [The paper was published in "Early Childhood Research Quarterly" v53 p23-39 Mar 2020.]