Cogitations on Invariant Measurement

A Memo to Ben Wright on the Perspectives of Rasch and Guttman
  • George EngelhardJr.
Part of the Springer Series in Measurement Science and Technology book series (SSMST)


The purpose of this chapter is to trace the evolution of the concept of invariant measurement as it appears in the work of Guttman and Rasch. The first section of the paper describes the concept of invariance. This section includes a detailed description of the perspectives of Guttman and Rasch on invariant measurement. The next section presents a re-analysis of the Stouffer-Toby data set using Guttman scaling and Rasch measurement theory. Finally, the implications for research, theory and practice of measurement are discussed. An earlier version of this research was presented at the Ben Wright Conference in Chicago (April 2003). I dedicate this chapter to Ben because it represents a continuation of my memos to him on the foundational ideas of measurement.


  1. Andrich, D. A. (1985). An elaboration of Guttman scaling with Rasch models for measurement. In N. B. Tuma (Ed.), Sociological methodology (pp. 33–80). San Francisco: Jossey-Bass.Google Scholar
  2. Andrich, D. A. (1988). Rasch models for measurement. Newbury Park, CA: Sage Publications, Inc..CrossRefGoogle Scholar
  3. Bond, T. G., & Fox, C. M. (2015). Applying the Rasch model: Fundamental measurement in the human sciences (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.Google Scholar
  4. Choppin, B. (1968). Item banking using sample-free calibration. Nature, 219(5156), 870–872.CrossRefPubMedGoogle Scholar
  5. Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Holt, Rinehart and Winston.Google Scholar
  6. Engelhard, G. (1984). Thorndike, Thurstone and Rasch: A comparison of their methods of scaling psychological and educational tests. Applied Psychological Measurement, 8, 21–38.CrossRefGoogle Scholar
  7. Engelhard, G. (2005). Guttman scaling. In K. Kempf-Leonard (Ed.), Encyclopedia of social measurement (Vol. 2, pp. 167–174). San Diego, CA: Academic Press (Elsevier Science).CrossRefGoogle Scholar
  8. Engelhard, G. (2008). Historical perspectives on invariant measurement: Guttman, Rasch, and Mokken [Special issue]. Measurement: Interdisciplinary Research and Perspectives (6), 1–35.Google Scholar
  9. Engelhard, G. (2013). Invariant measurement: Using Rasch models in the social, behavioral, and health sciences. New York: Routledge/Psychology Press/Taylor & Francis.Google Scholar
  10. Guttman, L. (1944). A basis for scaling qualitative data. American Sociological Review, 9(2), 139–150.CrossRefGoogle Scholar
  11. Guttman, L. (1950). The basis for scalogram analysis. In S. A. Stouffer, L. Guttman, E. A. Suchman, P. F. Lazarsfeld, S. A. Star, & J. A. Clausen (Eds.), Measurement and prediction (Vol. IV, pp. 60–90). Princeton: Princeton University Press.Google Scholar
  12. Linacre, J. M. (1989). Many-facet Rasch measurement. Chicago: MESA Press.Google Scholar
  13. Loevinger, J. (1947). A systematic approach to the construction and evaluation of tests of ability. Psychological Monographs, 61, no. 4.Google Scholar
  14. Loevinger, J. (1948). The technic of homogeneous test compared with some aspects of “scale analysis” and factor analysis. Psychological Bulletin, 45, 507–530.Google Scholar
  15. Loevinger, J. (1965). Person and population as psychometric concepts. Psychological Review, 72, 143–1555.CrossRefPubMedGoogle Scholar
  16. Mokken, R. J. (1971). A theory and procedure of scale analysis. The Hague: Mouton/Berlin: De Gruyter.CrossRefGoogle Scholar
  17. Mosier, C. I. (1940). Psychophysics and mental test theory: Fundamental postulates and elementary theorems. Psychological Review, 47, 355–366.CrossRefGoogle Scholar
  18. Mosier, C. I. (1941). Psychophysics and mental test theory II: The constant process. Psychological Review, 48, 235–249.CrossRefGoogle Scholar
  19. Nozick, R. (2001). Invariances: The structure of the objective world. Cambridge, MA: The Belknap Press of Harvard University Press.Google Scholar
  20. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research. (Expanded edition, Chicago: University of Chicago Press, 1980).Google Scholar
  21. Rasch, G. (1961). On general laws and meaning of measurement in psychology. In J. Neyman (Ed.), Proceedings of the fourth Berkeley Symposium on mathematical statistics and probability. Berkeley: University of California Press.Google Scholar
  22. Rasch, G. (1966). An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology, 19(Part 1), 49–57.CrossRefPubMedGoogle Scholar
  23. Stevens, S. S. (1951). Mathematics, measurement and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1–49). New York: Wiley.Google Scholar
  24. Stouffer, S. A., & Toby, J. (1951). Role conflict and personality. The American Journal of Sociology, 56, 395–406.CrossRefGoogle Scholar
  25. van der Linden, W. J. (2016). Handbook of item response theory: volume two, statistical tools. Boca Raton, FL: CRC Press.Google Scholar
  26. Wright, B. D. (1968). Sample-free test calibration and person measurement. In Proceedings of the 1967 invitational conference on testing problems. Princeton, NJ: Educational Testing Service.Google Scholar
  27. Wright, B. D. (1997). A history of social science measurement. Educational Measurement: Issues and Practice, 16(4), 33–45. 52.CrossRefGoogle Scholar
  28. Wright, B. D., & Masters, G. (1982). Rating scale analysis: Rasch measurement. Chicago: MESA Press.Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of GeorgiaAtlantaUSA

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