Hostname: page-component-5f745c7db-j9pcf Total loading time: 0 Render date: 2025-01-06T22:17:43.169Z Has data issue: true hasContentIssue false
  • English
  • Français

The Application of Latent Class Models in Adaptive Testing

Published online by Cambridge University Press:  01 January 2025

George B. Macready  and
C. Mitchell Dayton
George B. Macready*
Affiliation:
University of Maryland
C. Mitchell Dayton
Affiliation:
University of Maryland
*
Requests for reprints should be sent to George Macready, Department of Measurement, Statistics, and Evaluation, College of Education, University of Maryland, College Park, MD 20742.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper provides a description of a new adaptive testing algorithm based on a latent class modeling framework. The algorithm incorporates a four-stage iterative procedure that conditionally minimizes expected loss in classification of respondents across different content domains. The classification decisions relate to the membership of a person in a category of a latent variable for each of the separate domains considered. The algorithm appears to be particularly effective when latent class membership is related across the various domains of interest, since classification decisions on domains assessed early in the process are used to revise the probabilities for latent class membership on domains for which classification decisions have not yet been made. To assess the effectiveness of the proposed algorithm, a simulation based upon real data was conducted. For this example, the algorithm proved to be relatively efficient, requiring only 40% of the number of items needed under a nonadaptive approach. In addition, the algorithm provided classification decisions which, in 96% of the cases, were consistent with decisions based upon all available items when the maximum acceptable classification error rate was set at 5%.

Keywords

latent class modelslatent structure analysisadaptive testing
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 1 , March 1992 , pp. 71 - 88
Copyright
Copyright © 1992 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

Bergan, J. R. (1983). Latent-class models in educational research. In Gordon, E. W. (Eds.), Review of Research in Education, 10 (pp. 305–360). Washington, DC: American Educational Research Association.Google Scholar
Brown, J. M., & Weiss, D. J. (1977)An adaptive testing strategy for achievement test batteries (RR 77-6). University of Minnesota, Department of Psychology.CrossRefGoogle Scholar
Clogg, C. C. (1977). Unrestricted and restricted maximum likelihood latent structure analysis: A manual for users (Working Paper No. 1977-09). The Pennsylvania State University, Population Issues Research Office.Google Scholar
Clogg, C. C. (1981). New developments in latent structure analysis. In Jackson, D. M., Borgatta, E. F. (Eds.), Factor analysis and measurement in sociological research: A multi-dimensional perspective (pp. 215–246). Beverly Hills, CA: Sage.Google Scholar
Clogg, C. C., Goodman, L. A. (1986). On scaling models applied to data from several groups. Psychometrika, 51, 123–135.CrossRefGoogle Scholar
Dayton, C. M., Macready, G. B. (1976). A probabilistic model for validation of behavioral hierarchies. Psychometrika, 41, 198–204.Google Scholar
Dayton, C. M., Macready, G. B. (1988). Concomitant-variable latent class models. Journal of the American Statistical Association, 83, 173–178.CrossRefGoogle Scholar
Ferguson, R. L. (1971). Computer assistance for individual measurement (RR 71-8). University of Pittsburgh, Learning Research and Development Center.Google Scholar
Goodman, L. A. (1974). The analysis of systems of qualitative variables when some of the variables are unobservable. Part I—A modified latent structure approach. American Journal of Sociology, 79, 1179–1259.CrossRefGoogle Scholar
Goodman, L. A. (1978). Analyzing qualitative/categorical data, Cambridge, MA: Abt Books.Google Scholar
Green, B. F., Bock, R. D., Humphreys, L. G., Linn, R. L., Reckase, M. D. (1984). Technical guidelines for assessing computerized adaptive testing. Journal of Educational Measurement, 21, 347–360.CrossRefGoogle Scholar
Hayek, L. C. (1978). Properties of maximum likelihood estimators for a class of probabilistic models, College Park, MD: University of Maryland.Google Scholar
Kingsbury, G. G., & Weiss, D. J. (1979). An adaptive testing strategy for mastery decisions (RR 79-5). University of Minnesota, Department of Psychology.Google Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
Lord, F. M. (1980). Some how and which for practical tailored testing. In van der Kamp, L., Langerak, W., de Gruijter, D. (Eds.), Psychometrics for educational debates (pp. 189–205). New York: John Wiley & Sons.Google Scholar
Macready, G. B. (1975). The structure of domain hierarchies found within a domain referenced testing system. Educational and Psychological Measurement, 35, 583–598.CrossRefGoogle Scholar
Macready, G. B., Dayton, C. M. (1977). The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 2, 99–120.CrossRefGoogle Scholar
Macready, G. B., Dayton, C. M. (1980). The nature and use of mastery models. Applied Psychological Measurement, 4, 493–516.CrossRefGoogle Scholar
Patterson, H. L., Vierling, J. S. (1970). EDINET instruction series: Individualized mathematics program, Minneapolis, MN: Honeywell Information Systems.Google Scholar
Schafer, W. D. (1980). Assessment of dispersion in categorical data. Educational and Psychological Measurement, 40, 879–883.CrossRefGoogle Scholar
Weiss, D. J. (1982). Improving measurement quality and efficiency with adaptive testing. Applied Psychological Measurement, 6, 473–492.CrossRefGoogle Scholar
Wilcox, R. R. (1979). Achievement tests and latent structure models. British Journal of Mathematical and Statistical Psychology, 32, 61–71.CrossRefGoogle Scholar
Wilcox, R. R. (1982). Some empirical and theoretical results on an answer-until-correct scoring procedure. British Journal of Mathematical and Statistical Psychology, 35, 57–70.CrossRefGoogle Scholar