Measurement Invariance, Predictive Invariance, and the Duality Paradox

Multivariate Behavioral Research
Roger E Millsap

Abstract

The statistical literature on bias in psychological testing distinguishes at least two forms of bias: measurement bias and predictive bias. Measurement bias concerns group differences in the relationship between a test and the latent variable to be measured. Predictive bias concerns group differences in the relationship between a test and an external criterion. How are these two forms of bias related? For example. if a test is unbiased in the predictive sense, does this fact support the hypothesis that the test is unbiased in the measurement sense? A theorem is given that describes the conditions under which measurement invariance (lack of bias) is consistent with predictive invariance for the linear case. Paradoxically, these two forms of invariance are shown to be inconsistent under realistic conditions. This duality or inconsistency is illustrated in simulated data. The implications of the duality for group differences research are illustrated in real data involving gender and ethnic differences on the SAT. The phenomenon of duality may force a reinterpretation of common empirical findings of test criterion regression slope invariance. and of invariance in test validities. Other implications are discussed.

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Citations

Jan 1, 2013·Multivariate Behavioral Research·Margarita Olivera-Aguilar, Roger E Millsap
Feb 7, 2001·Annual Review of Psychology·L M Hough, F L Oswald
Aug 1, 2014·Psychometrika·Alberto Maydeu-Olivares
Jul 1, 1998·Multivariate Behavioral Research·R E Millsap
Jul 12, 2012·Brain Imaging and Behavior·Paul K CraneUNKNOWN Alzheimer’s Disease Neuroimaging Initiative
Mar 20, 2016·Psychonomic Bulletin & Review·Edgar C Merkle, Ting Wang
Oct 1, 2014·Canadian Journal of Occupational Therapy. Revue Canadienne D'ergothérapie·Manon GuayJohanne Desrosiers
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Aug 8, 2001·Journal of Evaluation in Clinical Practice·C PagliariM Eccles
Aug 16, 2002·Journal of Evaluation in Clinical Practice·Claudia Pagliari, Jeremy Grimshaw

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