On the Assessment of Unidimensional Measurement: Internal and External Consistency, and Overall Consistency Criteria

Kumar and Dillon recently presented a conceptual, overall consistency criterion that represents a sufficient condition for consistency. In commenting on their article, the authors (1) clarify the interrelated nature of internal consistency and external consistency, (2) show that the bogus perfect fit example is itself bogus in that it cannot occur in either theory or practice, (3) underscore that the specific overall consistency criterion formula defined by Kumar and Dillon cannot be applied in practice, whereas the internal consistency and external consistency criteria can, and (4) caution against using within-block factor analyses as recommended by Kumar and Dillon, and instead advocate the use of confirmatory factor analysis with multiple-indicator measurement models far assessing unidimensionality. In an addendum, the authors discuss their position on unidimensionality and its assessment, contrasting it with the Kumar and Dillon position on unidimensionality and consistency.