The study revisited the community of inquiry (CoI) instrument for construct revalidation. To that end, the study used confirmatory factor analysis (CFA) to examine four competing models (unidimensional, correlated-factor, second-order factor, and bifactor models) on model fit statistics computed using parameter estimates from a statistical estimator for ordinal categorical data. The CFA identified as the optimal structure the bifactor model where all items loaded on their intended domains and the existence of the general factor was supported, essentially evidence of construct validity for the instrument. The study further examined the bifactor model using mostly model-based reliability measures. The findings confirmed the contributions of the general factor to the reliability of instrument scores. The study concluded with validity and reliability evidence for the bifactor model, supported the model as a valid and reliable representation of the CoI instrument and a fuller representation of the CoI theoretical framework, and recommended its use in CoI-related research and practice in online education.