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This study refines the Community of Inquiry (CoI) survey by revisiting its underlying dimensions. Under bifactor modeling, the study proposes a general CoI factor which, together with the original, three subscale factors, jointly influences the items of the instrument. Both the bifactor and the original correlated-factor models are analyzed under confirmatory factor analysis and compared on model fit. Although both models provide adequate model fit, the bifactor model is evidently better supported by multiple model fit statistics and by model-based reliability indices demonstrating the presence of the general factor leads to substantially improved reliability estimates of scale/subscale scores. In the end, the study concludes with strong empirical evidence for the bifactor model as a fuller representation of the CoI framework.