A comment on a paper by H. Wu and M. W. Browne

Abstract

I congratulate Hao Wu and Michael W. Browne (henceforth, WB) on their thought-provoking approach to specification error in moment structure analysis. To my reading, the novel and challenging issue of their paper is to interpret specification error as a (stochastic) second-level variation of the sample covariance matrix, variation that is said to be induced by (physical, real?) "adventitious error" that selects the actual population from where sample data are extracted. Instead of the adage “all models are wrong” [“...but some are useful”], WB imply that each model is wrong in the current population but is true in an hypothetical super-population. The RMSEA emerges as the natural descriptor of the “distance” between the actual and a hypothetical population. My comments elaborate this view and aim to widen the perspective of WB’s paper by relating their approach to alternatives in the literature.