Abstract
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.
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References
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.
Andrich, D. A. (1988). Rasch models for measurement. Newbury Park, CA: Sage Publications, Inc..
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.
Choppin, B. (1968). Item banking using sample-free calibration. Nature, 219(5156), 870–872.
Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Holt, Rinehart and Winston.
Engelhard, G. (1984). Thorndike, Thurstone and Rasch: A comparison of their methods of scaling psychological and educational tests. Applied Psychological Measurement, 8, 21–38.
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).
Engelhard, G. (2008). Historical perspectives on invariant measurement: Guttman, Rasch, and Mokken [Special issue]. Measurement: Interdisciplinary Research and Perspectives (6), 1–35.
Engelhard, G. (2013). Invariant measurement: Using Rasch models in the social, behavioral, and health sciences. New York: Routledge/Psychology Press/Taylor & Francis.
Guttman, L. (1944). A basis for scaling qualitative data. American Sociological Review, 9(2), 139–150.
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.
Linacre, J. M. (1989). Many-facet Rasch measurement. Chicago: MESA Press.
Loevinger, J. (1947). A systematic approach to the construction and evaluation of tests of ability. Psychological Monographs, 61, no. 4.
Loevinger, J. (1948). The technic of homogeneous test compared with some aspects of “scale analysis” and factor analysis. Psychological Bulletin, 45, 507–530.
Loevinger, J. (1965). Person and population as psychometric concepts. Psychological Review, 72, 143–1555.
Mokken, R. J. (1971). A theory and procedure of scale analysis. The Hague: Mouton/Berlin: De Gruyter.
Mosier, C. I. (1940). Psychophysics and mental test theory: Fundamental postulates and elementary theorems. Psychological Review, 47, 355–366.
Mosier, C. I. (1941). Psychophysics and mental test theory II: The constant process. Psychological Review, 48, 235–249.
Nozick, R. (2001). Invariances: The structure of the objective world. Cambridge, MA: The Belknap Press of Harvard University Press.
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).
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.
Rasch, G. (1966). An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology, 19(Part 1), 49–57.
Stevens, S. S. (1951). Mathematics, measurement and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1–49). New York: Wiley.
Stouffer, S. A., & Toby, J. (1951). Role conflict and personality. The American Journal of Sociology, 56, 395–406.
van der Linden, W. J. (2016). Handbook of item response theory: volume two, statistical tools. Boca Raton, FL: CRC Press.
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.
Wright, B. D. (1997). A history of social science measurement. Educational Measurement: Issues and Practice, 16(4), 33–45. 52.
Wright, B. D., & Masters, G. (1982). Rating scale analysis: Rasch measurement. Chicago: MESA Press.
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Engelhard, G. (2017). Cogitations on Invariant Measurement. In: Wilson, M., Fisher, Jr., W. (eds) Psychological and Social Measurement. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-67304-2_2
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