Drawing valid inferences from modern measurement models is contingent upon a good fit of the data to the model. Violations of model-data fit have numerous consequences, limiting the usefulness and applicability of the model. As Bayesian estimation is becoming more common, understanding the Bayesian approaches for evaluating model-data fit models…

In their seminal paper, Edwards and Parry (1993) presented the polynomial regression as a better alternative to applying difference score in the study of congruence. Although this method is increasingly applied in congruence research, its complexity relative to other methods for assessing congruence (e.g., difference score methods) was one of the…

Applied simple difference and regression methods for determining discrepancies between Intelligence Quotient (IQ) and achievement to second- and fifth-grade IQ, reading and math achievement scores. Simple difference discrepancies covaried with IQ and produced disproportionate ethnic representation for both grades in reading and for second graders…