Measurement, 6: 213–218, 2008 Copyright © Taylor & Francis Group, LLC ISSN 1536-6367 print / 1536-6359 online DOI: 10.1080/15366360802265987 HMES 1536-6367 1536-6359 Measurement, Vol. 6, No. 3, June 2008: pp. 1–10 Measurement REJOINDER Rejoinder: Continuing the Dialogue on Invariant Measurement REJOINDER Engelhard George Engelhard, Jr. Emory University The major purpose of my focus article was to stimulate discussion regarding the concept of invariant measurement. My intent was to provide a historical lens for considering how our views of invariant measurement have evolved over time through the work of three key measurement theorists: Guttman, Rasch, and Mokken. The commentators have offered a variety of direct and indirect responses to my focus article; they have raised few, if any, issues with which I disagree. However, I would like to take this opportunity to continue the dialogue about invariant measurement. Key words: invariant measurement, Guttman, Rasch, Mokken MILLSAP Millsap (this issue) focuses his comments on the invariance of item calibrations over different populations or subsets of examinees (sample-invariant calibration of items). This is called measurement invariance, and includes research on differ- ential item functioning, factorial invariance, and predictive invariance (Meredith, 2007). He stresses the idea that research workers must make a distinction between invariance properties that are inherent in the structural aspects of the model, and questions of whether or not invariance holds for a particular set of Correspondence should be addressed to George Engelhard, Jr., Department of Educational Studies, Emory University, 1784 North Decatur Road, Atlanta, GA 30322. E-mail: gengelh@emory.edu