Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-07T17:58:56.176Z Has data issue: false hasContentIssue false
  • English
  • Français

A Multidimensional Latent Trait Model for Measuring Learning and Change

Published online by Cambridge University Press:  01 January 2025

Susan E. Embretson
Susan E. Embretson*
Affiliation:
University of Kansas
*
Requests for reprints should be sent to Susan Embretson, Department of Psychology, University of Kansas, Lawrence, KS 66045.
Get access Rights & Permissions [Opens in a new window]

Abstract

A latent trait model is presented for the repeated measurement of ability based on a multidimensional conceptualization of the change process. A simplex structure is postulated to link item performance under a given measurement condition or occasion to initial ability and to one or more modifiabilities that represent individual differences in change. Since item discriminations are constrained to be equal within a measurement condition, the model belongs to the family of multidimensional Rasch models. Maximum likelihood estimators of the item parameters and abilities are derived, and an example provided that shows good recovery of both item and ability parameters. Properties of the model are explored, particularly for several classical issues in measuring change.

Keywords

change measurementRasch modelstest theorysimplex models
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 3 , September 1991 , pp. 495 - 515
Copyright
Copyright © 1991 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ackerman, P. L. (1988). Determinants of individual differences during skill acquisition: Cognitive abilities and information processing. Journal of Experimental Psychology, General, 117, 288–318.CrossRefGoogle Scholar
Anastasi, A. (1988). Psychological testing, New York: Macmillan.Google Scholar
Andersen, E. B. (1985). Estimating latent correlations between repeated testings. Psychometrika, 50, 3–16.CrossRefGoogle Scholar
Anderson, J. E. (1939). The limitations of infant and preschool tests in the measurement of intelligence. Journal of Psychology, 10, 203–212.Google Scholar
Anderson, T. W. (1960). Some stochastic process models for intelligence test scores. In Arrow, K. J., Karlin, S., Suppes, P. (Eds.), Mathematical methods in the social sciences (pp. 151–163). Stanford, CA: Stanford University Press.Google Scholar
Bereiter, C. (1963). Some persisting dilemmas in the measurement of change. In Harris, C. W. (Eds.), Problems in measuring change (pp. 3–20). Madison: University of Wisconsin Press.Google Scholar
Bock, R. D. (1976). Basic issues in the measurement of change. In de Gruijter, D. N. M., van der Kamp, L. J. T. (Eds.), Advances in psychological and educational measurement (pp. 75–96). New York: Wiley.Google Scholar
Carlson, J. S., Weidl, K. H. (1979). Toward a differential testing approach: Testing the limits employing Raven's matrices. Intelligence, 3, 323–344.CrossRefGoogle Scholar
Corballis, M. C. (1965). Practice and the simplex. Psychological Review, 72, 399–406.CrossRefGoogle ScholarPubMed
Cronbach, L. J., Furby, L. (1970). How should we measure change—or should we?. Psychological Bulletin, 74, 68–80.CrossRefGoogle Scholar
Dearborne, D. F. (1921). Intelligence and its measurement: A symposium. Journal of Educational Psychology, 12, 123–147.Google Scholar
Embretson, S. E. (1987). Improving the measurement of spatial ability by a dynamic testing procedure. Intelligence, 11, 333–358.CrossRefGoogle Scholar
Embretson, S. E. (1989). Measuring learning ability by dynamic testing, Lawrence, KS: University of Kansas, Department of Psychology.Google Scholar
Fischer, G. H. (1972). A measurement model for the effect of mass-media. Acta Psychologica, 36, 207–220.CrossRefGoogle Scholar
Fischer, G. H. (1976). Some probabilistic models for measuring change. In de Gruijter, D. N. M., van der Kamp, L. J. T. (Eds.), Advances in psychological and educational measurement (pp. 97–110). New York: John Wiley & Sons.Google Scholar
Fischer, G. H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3–26.CrossRefGoogle Scholar
Fischer, G. H., Formann, A. K. (1972). An algorithm and a Fortran program for estimation of parameters for a linear logistic test model, Vienna, Austria: University of Vienna, Department of Psychology.Google Scholar
Guttman, L. (1955). A generalized simplex for factor analysis. Psychometrika, 20, 173–192.CrossRefGoogle Scholar
Harris, C. W. (1963). Problems in measuring change, Madison: University of Wisconsin Press.Google Scholar
Jones, M. (1970). A two-process theory of individual differences in motor learning. Psychological Review, 77, 353–360.CrossRefGoogle Scholar
Jöreskog, K. G. (1970). Estimation and testing of simplex models. British Journal of Mathematical Statistical Psychology, 23, 121–145.CrossRefGoogle Scholar
Keats, J. A. (1983). Ability measures and theories of cognitive developments. In Wainer, H., Messick, S. (Eds.), Principals of modern psychological measurement (pp. 81–101). Hillsdale, NJ: Erlbaum Publishers.Google Scholar
Lidz, C. (1987). Dynamic testing, Beverly Hills, CA: Guilford Press.Google Scholar
Lord, F. M. (1963). Elementary models for measuring change. In Harris, C. W. (Eds.), Problems in measuring change (pp. 21–38). Madison: University of Wisconsin Press.Google Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
Rasch, G. (1961). On the meaning of measurement in psychology. In Neyman, J. (Eds.), Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, Vol. 5 (pp. 119–147). Berkeley: University of California Press.Google Scholar
Stake, R. E. (1961). Learning parameters, aptitudes and achievements. Psychometric Monographs No. 9, 26, (4, Pt. 2).Google Scholar
Sternberg, R. J. (1985). Beyond IQ: A triarchic theory of intelligence, Cambridge, England: Cambridge University Press.Google Scholar
Takane, Y., de Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393–408.CrossRefGoogle Scholar
Thissen, D., Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567–577.CrossRefGoogle Scholar
Whitely, S. E. (1978). Individual inconsistency: Implications for test reliability and behavioral predictability. Applied Psychological Measurement, 2, 571–579.CrossRefGoogle Scholar
Whitely, S. E., Nieh, K. (1981). Program LINLOG (Tech. Rep. NIE-81-3 for National Institute of Education), Lawrence, KS: University of Kansas.Google Scholar
Wissler, C. (1901). The correlation of mental and physical traits. Psychological Monographs, 3 (6, Whole No. 16).CrossRefGoogle Scholar
Woodrow, H. (1938). The relationship between abilities and improvement with practice. Journal of Educational Psychology, 29, 215–230.CrossRefGoogle Scholar