Skip to main content
Log in

Psychometrics: From practice to theory and back

15 Years of nonparametric multidimensional IRT, DIF/test equity, and skills diagnostic assessment

  • Articles
  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

The paper surveys 15 years of progress in three psychometric research areas: latent dimensionality structure, test fairness, and skills diagnosis of educational tests. It is proposed that one effective model for selecting and carrying out research is to chose one's research questions from practical challenges facing educational testing, then bring to bear sophisticated probability modeling and statistical analyses to solve these questions, and finally to make effectiveness of the research answers in meeting the educational testing challenges be the ultimate criterion for judging the value of the research. The problem-solving power and the joy of working with a dedicated, focused, and collegial group of colleagues is emphasized. Finally, it is suggested that the summative assessment testing paradigm that has driven test measurement research for over half a century is giving way to a new paradigm that in addition embraces skills level formative assessment, opening up a plethora of challenging, exciting, and societally important research problems for psychometricians.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ackerman, T.A. (1992). A didactic explanation of item bias, item impact, and item validity from a multidimensional perspective.Journal of Educational Measurement, 29, 67–91.

    Google Scholar 

  • Angoff, W.H. (1993). Perspectives on differential item functioning methodology. In P.W. Holland & H. Wainer (Eds.),Differential item functioning (pp. 3–24). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Bolt, D., Froelich, A.G., Habing, B., Hartz, S., Roussos, L., & Stout, W. (in press).An applied and foundational research project addressing DIF, impact, and equity: With applications to ETS test development (ETS Technical Report). Princeton, NJ:ETS.

  • Chang, H., Mazzeo, J., & Roussos, L. (1996). Detecting DIF for polytomously scored items: an adaptation of the SIBTEST procedure.Journal of Educational Measurement, 33, 333–353

    Google Scholar 

  • Chang, H., & Stout, W. (1993). The asymptotic posterior normality of the latent trait in an IRT model.Psychometrika, 58, 37–52.

    Google Scholar 

  • DiBello, L., Stout, W., & Roussos, L. (1995). Unified cognitive/psychometric diagnostic assessment likelihood-based classification techniques. In P. Nichols, S. Chipman, & R. Brennen (Eds.),Cognitively diagnostic assessment (pp. 361–389). Hillsdale, NJ: Earlbaum.

    Google Scholar 

  • Doignon, J.-P., & Falmagne, J.-C. (in press),Knowledge spaces. Berlin Springer-Verlag.

  • Dorans, N.J., & Kulick, E. (1986). Demonstrating the utility of the standardization approach to assessing unexpected differential item performance on the Scholastic Aptitude Test.Journal of Educational Measurement, 23, 355–368.

    Google Scholar 

  • Douglas, J. (1997). Joint consistency of nonparametric item characteristic curve and ability estimation.Psychometrika, 62, 7–28.

    Google Scholar 

  • Douglas, J.A. (2001). Asymptotic identifiability of nonparametric item response models.Psychometrika, 66, 531–540.

    Google Scholar 

  • Douglas J.A., & Cohen A. (2001). Nonparametric ICC estimation to assess fit of parametric models.Applied Psychological Measurement, 25, 234–243.

    Google Scholar 

  • Douglas, J., Kim, H.R., Habing, B., & Gao, F. (1998) Investigating local dependence with conditional covariance functions.Journal of Educational and Behavioral Statistics, 23, 129–151.

    Google Scholar 

  • Douglas, J., Roussos, L., & Stout, W., (1996). Item bundle DIF hypothesis testing: Identifying suspect bundles and assessing their DIF.Journal of Educational Measurement, 33, 465–484.

    Google Scholar 

  • Douglas, J., Stout, W., & DiBello, L. (1996). A kernel smoothed version of SIBTEST with applications to local DIF inference and unction estimation.Journal of Educational and Behavioral Statistics, 21, 333–363.

    Google Scholar 

  • Ellis, J.L., & Junker, B.W. (1997). Tail-measurability in monotone latent variable models.Psychometrika, 62, 495–524.

    Google Scholar 

  • Embretson (Whitely), S.E. (1980). Multicomponent latent trait models for ability testsPsychometrika, 45, 479–494.

    Google Scholar 

  • Embretson, S.E. (1984). A general latent trait model for response processes.Psychometrika, 49, 175–186.

    Google Scholar 

  • Embretson, S. E. (Ed.). (1985),Test design: Developments in psychology and psychometrics (pp. 195–218, chap. 7). Orlando, FL: Academic Press.

    Google Scholar 

  • Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research.Acta Psychologica, 37, 359–374.

    Google Scholar 

  • Froelich, A.G., & Habing, B. (2002, July). A study of methods for selecting the AT subtest in the DIMTEST procedure. Paper presented at the 2002 Annual Meeting of the Psychometrika Society, University of North Carolina at Chapel Hill.

  • Gierl, M.J., Bisanz, J., Bisanz, G., Boughton, K., & Khaliq, S. (2001). Illustrating the utility of differential bundle functioning analyses to identify and interpret group differences on achievement tests.Educational Measurement: Issues and Practice, 20, 26–36.

    Google Scholar 

  • Gierl, M.J., & Khaliq, S.N. (2001). Identifying sources of differential item and bundle functioning on translated achievement tests.Journal of Educational Measurement, 38, 164–187.

    Google Scholar 

  • Gierl, M.J., Bisanz, J., Bisanz, G.L., & Boughton, K.A. (2002, April). Identifying content and cognitive skills that produce gender differences in mathematics: A demonstration of the DIF analysis framework. Paper presented at the annual meeting of the National Council on Measurement in Education, New Orleans, LA.

  • Haberman, S.J. (1977). Maximum likelihood estimates in exponential response models.The Annals of Statistics, 5, 815–841.

    Google Scholar 

  • Habing, B. (2001). Nonparametric regression and the parametric bootstrap for local dependence assessment.Applied Psychological Measurement, 25, 221–233.

    Google Scholar 

  • Haertel, E. (1989). Using restricted latent class models to map the skill structure of achievement items.Journal of Educational Measurement, 26, 301–321.

    Google Scholar 

  • Hartz, S.M. (2002).A Bayesian framework for the Unified Model for assessing cognitive abilities: blending theory with practicality. Unpublished doctoral dissertation, University of Illinois, Urbana-Champaign, Department of Statistics.

    Google Scholar 

  • Holland, P.W. (1990a). On the sampling theory foundations of item response theory models.Psychometrika, 55, 577–601.

    Google Scholar 

  • Holland, P.W. (1990b). The Dutch identity: a new tool for the study of item response models.Psychometrika, 55, 5–18.

    Google Scholar 

  • Holland, P.W., & Rosenbaum, P.R. (1986). Conditional association and unidimensionality in monotone latent variable models.The Annals of Statistics, 14, 1523–1543.

    Google Scholar 

  • Holland, W.P., & Thayer, D.T. (1988). Differential item performance and the Mantel-Haenszel procedure. In H. Wainer & H.I. Braun (Eds.),Test validity (pp. 129–145). Hillsdale, NJ: Lawrence Earlbaum Associates.

    Google Scholar 

  • Jiang, H., & Stout, W. (1998). Improved Type I error control and reduced estimation bias for DIF detection using SIBTEST.Journal of Educational and Behavioral Statistics, 23, 291–322.

    Google Scholar 

  • Junker, B.W. (1993). Conditional association, essential independence, and monotone unidimensional latent variable models.Annals of Statistics, 21, 1359–1378.

    Google Scholar 

  • Junker, B.W. (1999).Some statistical models and computational methods that may be useful for cognitively-relevant assessment. Prepared for the National Research Council Committee on the Foundations of Assessment. Retrieved April 2, 2001, from http://www.stat.cmu.edu/∼brian/nrc/cfa/

  • Junker, B.W., & Ellis, J.L. (1998). A characterization of monotone unidimensional latent variable models.Annals of Statistics, 25(3), 1327–1343.

    Google Scholar 

  • Junker, B. W. & Sijtsma, K. (2001). Nonparametric item response theory in action: an overview of the special issue.Applied Psychological Measurement, 25, 211–220.

    Google Scholar 

  • Koedinger, K.R., & MacLaren, B.A. (2002). Developing a pedagogical domain theory of early algebra problem solving (CMU-HCII Tech. Rep. 02-100). Pittsburgh, PA: Carnegie Mellon University, School of Computer Science.

    Google Scholar 

  • Li, H. & Stout, W. (1996). A new procedure for detecting crossing DIF.Psychometrika, 61, 647–677.

    Google Scholar 

  • Kok, F. (1988). Item bias and test multidimensionality. In R. Langeheine & J. Rost (Eds.),Latent trait and latent models (pp. 263–275). New York, NY: Plenum Press.

    Google Scholar 

  • Linn, R.L. (1993). The use of differential item functioning statistics: A discussion of current practice and future implications. In P.W. Holland & H. Wainer (Eds.),Differential item functioning (pp. 349–364). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lord, F.M. (1980)Applications of item response theory to practical testing problems. Lawrence Erlbaum Associates, Hinsdale, NJ.

    Google Scholar 

  • McDonald, R.P. (1994). Testing for approximate dimensionality. In D. Laveault, B.D. Zumbo, M.E. Gessaroli, & M.W. Boss (Eds.),Modern theories of measurement: Problems and issues (pp. 63–86). Ottawa, Canada: University of Ottawa.

    Google Scholar 

  • Maris, E. (1995). Psychometric latent response models.Psychometrika, 60, 523–547.

    Google Scholar 

  • Mislevy, R.J. (1994). Evidence and inference in educational assessment.Psychometrika, 59, 439–483.

    Google Scholar 

  • Mislevy, R.J. Almond, R.G., Yan, D., & Steinberg, L.S. (1999). Bayes nets in educational assessment: Where do the numbers come from? In K.B. Laskey & H. Prade (Eds.),Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence (pp. 437–446). San Francisco, CA: Morgan Kaufmann.

    Google Scholar 

  • Mislevy, R., Steinberg, L. & Almond, R. (in press). On the structure of educational assessments.Measurement: Interdisciplinary research and perspective. Hillsdale, NJ: Lawrence Erlbaum Associates.

  • Mokken, R.J. (1971).A theory and procedure of scale analysis. The Hague: Mouton.

    Google Scholar 

  • Molenaar, I.W., & Sijtsma, K. (2000).User's manual MSP5 for Windows: A program for Mokken Scale Analysis for Polytomous Items. Version 5.0 [Software manual]. Groningen: ProGAMMA.

    Google Scholar 

  • Nandakumar, R. (1993). Simultaneous DIF amplification and cancellation: Shealy-Stout's test for DIF.Journal of Educational Measurement, 30, 293–311.

    Google Scholar 

  • Nandakumar, R., & Roussos, L. (in press). Evaluation of CATSIB procedure in pretest setting.Journal of Educational and Behavioral Statistics.

  • Nandakumar, R., & Stout, W. (1993). Refinements of Stout's procedure for assessing latent trait unidimensionality.Journal of Educational Statistics, 18, 41–68.

    Google Scholar 

  • O'Neill, K.A., & McPeek, W.M. (1993). Item and test characteristics that are associated with differential item functioning. In P.W. Holland & H. Wainer (Eds.),Differential item functioning (pp. 255–276). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Pellegrino, J.W., Chudowski, N., & Glaser, R (Eds.). (2001).Knowing what students know: The science and design of educational assessment (chap. 4, pp. 111–172) Washington, DC: National Academy Press.

    Google Scholar 

  • Philipp, W. & Stout, W. (1975).Almost sure convergence principles for sums of dependent random variables (American Mathematical Society Memoir No. 161). Providence, RI: American Mathematical Society.

    Google Scholar 

  • Ramsay, J.O. (2000). TESTGRAF:A program for the graphical analysis of multiple choice test and questionnaire data (TESTGRAF user's guide for TESTGRAF98 software). Montreal, Quebec: Author. Versions available for Windows®, DOS, and Unix. The Windows® version was retrived November 11, 2002 from ftp://ego.psych.mcgill.ca/pub/ramsay/testgraf/TestGraf98.wpd

    Google Scholar 

  • Ramsey, P.A. (1993). Sensitivity review: the ETS experience as a case study. In P.W. Holland & H. Wainer (Eds.),Differential item functioning (pp. 367–388). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Rossi, N., Wang, W. & Ramsay, J.O. (in press). Nonparametric item response function estimates with the EM algorithm.Journal of Educational and Behavioral Statistics.

  • Roussos, L., & Stout, W. (1996a). DIF from the multidimensional perspective.Applied Psychological Measurement, 20, 335–371.

    Google Scholar 

  • Roussos, L., & Stout, W. (1996b). Simulation studies of the effects of small sample size and studied item parameters on SIBTEST and Mantel-Haenszel Type 1 error performance.Journal of Education Measurement, 33, 215–230.

    Google Scholar 

  • Roussos, L.A., Stout, W.F., & Marden, J. (1998). Using new proximity measures with hierarchical cluster analysis to detect multidimensionality.Journal of Educational Measurement, 35, 1–30.

    Google Scholar 

  • Roussos, L.A., Schnipke, D.A., & Pashley, P.J. (1999). A generalized formula for the Mantel-Haenszel differential item functioning parameter.Journal of Educational and Behavioral Statistics, 24, 293–322.

    Google Scholar 

  • Shealy, R.T. (1989).An item response theory-based statistical procedure for detecting concurrent internal bias in ability tests. Unpublished doctoral dissertation, Department of Statistics, University of Illinois, Urbana-Champaign.

    Google Scholar 

  • Shealy, R., & Stout, W. (1993a). A model-based standardization approach that separates true bias/DIF from group ability differences and detects test bias/DTF as well as item bias/DIF.Psychometrika, 58, 159–194.

    Google Scholar 

  • Shealy, R., & Stout, W. (1993b). An item response theory model for test bias and differential test functioning. In P. Holland & H. Wainer (Eds.),Differential item functioning (pp. 197–240). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Sijtsma, K. (1998). Methodology review: nonparametric IRT approaches to the analysis of dichotomous item scores.Applied Psychological Measurement, 22, 3–32.

    Google Scholar 

  • Sternberg, R.J. (1985).Beyond IQ: A triarchic theory of human intelligence. New York, NY: Cambridge University Press.

    Google Scholar 

  • Stout, W. (1987). A nonparametric approach for assessing latent trait unidimensionality.Psychometrika, 52, 589–617.

    Google Scholar 

  • Stout, W. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation.Psychometrika, 55, 293–325.

    Google Scholar 

  • Stout, W., Froelich, A.G., & Gao, F. (2001). Using resampling to produce an improved DIMTEST procedure. In A. Boomsma, M.A.J. van Duijn, T.A.B. Snijders (Eds.),Essays on item response theory (pp. 357–376). New York, NY: Springer-Verlag.

    Google Scholar 

  • Stout, W., Habing, B., Douglas, J., Kim, H.R., Roussos, L., & Zhang, J. (1996). Conditional covariance based nonparametric multidimensionality assessment.Applied Psychological Measurement, 20, 331–354.

    Google Scholar 

  • Stout, W., Li, H., Nandakumar, R., & Bolt, D. (1997). MULTISIB—A procedure to investigate DIF when a test is intentionally multidimensional.Applied Psychological Measurement, 21, 195–213.

    Google Scholar 

  • Suppes, P., & Zanotti, M. (1981). When are probabilistic explanations possible?Synthese, 48, 191–199.

    Google Scholar 

  • Tatsuoka, K. K. (1990). Toward an integration of item-response theory and cognitive error diagnosis. In N. Frederiksen, R. Glazer, A. Lesgold, & M.G. Shafto (Eds.),Diagnostic monitoring of skill and knowledge acquisition (pp. 453–488). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Tatsuoka, K. K. (1995). Architecture of knowledge structures and cognitive diagnosis: A statistical pattern recognition and classification approach. In P. Nichols, S. Chipman, & R. Brennen (Eds.),Cognitively diagnostic assessment. Hillsdale, NJ: Earlbaum. 327–359.

    Google Scholar 

  • Thissen, D., & Wainer, H. (2001).Test scoring. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Trachtenberg, F., & He, X. (2002). One-step joint maximum likelihood estimation for item response theory models. Submitted for publication.

  • Tucker, L.R., Koopman, R.F., & Linn, R.L. (1969). Evaluation of factor analytic research procedures by means of simulated correlation matrices.Psychometrika, 34, 421–459.

    Google Scholar 

  • Wainer, H., & Braun, H.I. (1988).Test validity. Hillsdale, NJ: Lawrence Erlbaum Associates. Zhang, J., & Stout, W. (1999a). Conditional covariance structure of generalized compensatory multidimensional items.Psychometrika, 64, 129–152.

    Google Scholar 

  • Whitely, S.E. (1980). (See Embretson, 1980)

  • Zhang, J., & Stout, W. (1999). The theoretical DETECT index of dimensionality and its application to approximate simple structure.Psychometrika, 64, 213–249.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to William Stout.

Additional information

Dedication: I want to dedicate this paper to my wife, Barbara Meihoefer, who was lost to illness in this year of my presidency. For, in addition to all the wonderful things she meant to me personally and the enormous support she gave concerning my career, she truly enjoyed and greatly appreciated my psychometric colleagues and indeed found psychometrics an important and fascinating intellectual endeavor, in particular finding the skills diagnosis area exciting and important: She often took time from her career as a business manager and entrepreneur to attend psychometric meetings with me and to discuss research projects with my colleagues and me. She would have enjoyed this paper.—William Stout

This aricle is based on the Presidential Address William Stout gave on June 23, 2002 at the 67th Annual Meeting of the Psychometric Society held in Chapel Hill, North Carolina.—Editor

I wish to especially thank Sarah Hartz and Louis Roussos for their suggestions that helped shape this paper. I wish to thank all my former Ph.D. students: Without their contributions, the content of this paper would have been vastly different and much less interesting!

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stout, W. Psychometrics: From practice to theory and back. Psychometrika 67, 485–518 (2002). https://doi.org/10.1007/BF02295128

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02295128

Key words

Navigation