## ABSTRACT

Imagine a situation in which an innocent researcher wishes to explain variance in some critical criterion variable. For expedience, he uses only a single predictor in his validation study. After data collection, the researcher observes a rather unimpressive correlation (e.g., rxy = .10 ). The researcher then explains in his Discussion section that his model is perfect because, if he had measured all relevant variables, his “model” would have explained all the variance in the criterion. Absurd, you say! Ridiculous! J’accuse! How can one argue for the integrity of a model based on unmeasured variables and/ or unexpected relationships? Despite the lunacy of the preceding example, a similar practice occurs with some frequency in applications of structural equation modeling (SEM). Specifically, the practice of allowing for correlated residuals among indicators in SEM is, in many cases, tantamount to capitalizing on “what could have been” and serves as the focus of the current chapter.