Advertisement

Psychometrika

, Volume 67, Issue 4, pp 485–518 | Cite as

Psychometrics: From practice to theory and back

15 Years of nonparametric multidimensional IRT, DIF/test equity, and skills diagnostic assessment
  • William Stout
Articles

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.

Key words

nonparametric IRT NIRT latent unidimensionality latent multidimensionality essential unidimensionality monotone locally independent unidimensional IRT model MLI1 item pair conditional covariances DIMTEST HCA/CCPROX DETECT CONCOV Mokken scaling generalized compensatory model approximate simple structure DIF differential item functioning differential bundle functioning DBF valid subtest multidimensional model for DIF MMD SIBTEST MultiSIB Mantel-Haenszel PolySIB CrossingSIB skills diagnosis formative assessment Unified Model reparameterized Bayes Unified Model MCMC evidence centered design ECD PSAT Score Report Plus 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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
  2. 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
  3. 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.Google Scholar
  4. Chang, H., Mazzeo, J., & Roussos, L. (1996). Detecting DIF for polytomously scored items: an adaptation of the SIBTEST procedure.Journal of Educational Measurement, 33, 333–353Google Scholar
  5. Chang, H., & Stout, W. (1993). The asymptotic posterior normality of the latent trait in an IRT model.Psychometrika, 58, 37–52.Google Scholar
  6. 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
  7. Doignon, J.-P., & Falmagne, J.-C. (in press),Knowledge spaces. Berlin Springer-Verlag.Google Scholar
  8. 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
  9. Douglas, J. (1997). Joint consistency of nonparametric item characteristic curve and ability estimation.Psychometrika, 62, 7–28.Google Scholar
  10. Douglas, J.A. (2001). Asymptotic identifiability of nonparametric item response models.Psychometrika, 66, 531–540.Google Scholar
  11. Douglas J.A., & Cohen A. (2001). Nonparametric ICC estimation to assess fit of parametric models.Applied Psychological Measurement, 25, 234–243.Google Scholar
  12. 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
  13. 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
  14. 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
  15. Ellis, J.L., & Junker, B.W. (1997). Tail-measurability in monotone latent variable models.Psychometrika, 62, 495–524.Google Scholar
  16. Embretson (Whitely), S.E. (1980). Multicomponent latent trait models for ability testsPsychometrika, 45, 479–494.Google Scholar
  17. Embretson, S.E. (1984). A general latent trait model for response processes.Psychometrika, 49, 175–186.Google Scholar
  18. Embretson, S. E. (Ed.). (1985),Test design: Developments in psychology and psychometrics (pp. 195–218, chap. 7). Orlando, FL: Academic Press.Google Scholar
  19. Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research.Acta Psychologica, 37, 359–374.Google Scholar
  20. 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.Google Scholar
  21. 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
  22. 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
  23. 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.Google Scholar
  24. Haberman, S.J. (1977). Maximum likelihood estimates in exponential response models.The Annals of Statistics, 5, 815–841.Google Scholar
  25. Habing, B. (2001). Nonparametric regression and the parametric bootstrap for local dependence assessment.Applied Psychological Measurement, 25, 221–233.Google Scholar
  26. 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
  27. 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
  28. Holland, P.W. (1990a). On the sampling theory foundations of item response theory models.Psychometrika, 55, 577–601.Google Scholar
  29. Holland, P.W. (1990b). The Dutch identity: a new tool for the study of item response models.Psychometrika, 55, 5–18.Google Scholar
  30. 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
  31. 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
  32. 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
  33. Junker, B.W. (1993). Conditional association, essential independence, and monotone unidimensional latent variable models.Annals of Statistics, 21, 1359–1378.Google Scholar
  34. 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/Google Scholar
  35. Junker, B.W., & Ellis, J.L. (1998). A characterization of monotone unidimensional latent variable models.Annals of Statistics, 25(3), 1327–1343.Google Scholar
  36. 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
  37. 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
  38. Li, H. & Stout, W. (1996). A new procedure for detecting crossing DIF.Psychometrika, 61, 647–677.Google Scholar
  39. 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
  40. 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
  41. Lord, F.M. (1980)Applications of item response theory to practical testing problems. Lawrence Erlbaum Associates, Hinsdale, NJ.Google Scholar
  42. 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
  43. Maris, E. (1995). Psychometric latent response models.Psychometrika, 60, 523–547.Google Scholar
  44. Mislevy, R.J. (1994). Evidence and inference in educational assessment.Psychometrika, 59, 439–483.Google Scholar
  45. 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
  46. Mislevy, R., Steinberg, L. & Almond, R. (in press). On the structure of educational assessments.Measurement: Interdisciplinary research and perspective. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  47. Mokken, R.J. (1971).A theory and procedure of scale analysis. The Hague: Mouton.Google Scholar
  48. 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
  49. Nandakumar, R. (1993). Simultaneous DIF amplification and cancellation: Shealy-Stout's test for DIF.Journal of Educational Measurement, 30, 293–311.Google Scholar
  50. Nandakumar, R., & Roussos, L. (in press). Evaluation of CATSIB procedure in pretest setting.Journal of Educational and Behavioral Statistics.Google Scholar
  51. Nandakumar, R., & Stout, W. (1993). Refinements of Stout's procedure for assessing latent trait unidimensionality.Journal of Educational Statistics, 18, 41–68.Google Scholar
  52. 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
  53. 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
  54. 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
  55. 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.wpdGoogle Scholar
  56. 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
  57. Rossi, N., Wang, W. & Ramsay, J.O. (in press). Nonparametric item response function estimates with the EM algorithm.Journal of Educational and Behavioral Statistics.Google Scholar
  58. Roussos, L., & Stout, W. (1996a). DIF from the multidimensional perspective.Applied Psychological Measurement, 20, 335–371.Google Scholar
  59. 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
  60. 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
  61. 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
  62. 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
  63. 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
  64. 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
  65. Sijtsma, K. (1998). Methodology review: nonparametric IRT approaches to the analysis of dichotomous item scores.Applied Psychological Measurement, 22, 3–32.Google Scholar
  66. Sternberg, R.J. (1985).Beyond IQ: A triarchic theory of human intelligence. New York, NY: Cambridge University Press.Google Scholar
  67. Stout, W. (1987). A nonparametric approach for assessing latent trait unidimensionality.Psychometrika, 52, 589–617.Google Scholar
  68. Stout, W. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation.Psychometrika, 55, 293–325.Google Scholar
  69. 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
  70. 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
  71. 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
  72. Suppes, P., & Zanotti, M. (1981). When are probabilistic explanations possible?Synthese, 48, 191–199.Google Scholar
  73. 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
  74. 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
  75. Thissen, D., & Wainer, H. (2001).Test scoring. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  76. Trachtenberg, F., & He, X. (2002). One-step joint maximum likelihood estimation for item response theory models. Submitted for publication.Google Scholar
  77. 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
  78. 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
  79. Whitely, S.E. (1980). (See Embretson, 1980)Google Scholar
  80. Zhang, J., & Stout, W. (1999). The theoretical DETECT index of dimensionality and its application to approximate simple structure.Psychometrika, 64, 213–249.Google Scholar

Copyright information

© The Psychometric Society 2002

Authors and Affiliations

  1. 1.Educational Testing ServiceUSA
  2. 2.Department of StatisticsUniversity of IllinoisChampaign

Personalised recommendations