Abstract
We consider a latent trait model developed by Rasch for the response time on a set of pure speed tests, which is based on the assumption that the test response times are approximately gamma distributed with known index parameters and scale parameters depending on subject ability and test difficulty parameters. In this chapter, the principle of Lagrange multiplier tests is used to evaluate differential test functioning and subgroup invariance of the test parameters. Two numerical illustrations are given.
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References
Aitchison, J., & Silvey, S.D. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813–828.
Denckla, M.B., & Rudel, R.G. (1974). Rapid automatized naming of picture objects, colors, letters and numbers by normal children. Cortex, 10, 186–202.
Denckla, M.B., & Rudel, R.G. (1976). Rapid automatized naming (RAN): Dyslexia differentiated from other learning abilities. Neuropsychologica, 14, 471–479.
Glas, C.A.W. (1998). Detection of differential item functioning using Lagrange multiplier tests. Statistica Sinica, 8, 647–667.
Glas, C.A.W. (1999). Modification indices for the 2PL and the nominal response model. Psychometrika, 64, 273–294.
Glas, C.A.W. (2001). Differential item functioning depending on general covariates. In A. Boomsma, M.A.J. van Duijn, & T.A.B. Snijders (Eds.), Essays on item response theory (pp. 131–148). New York: Springer-Verlag.
Glas, C.A.W., & Verhelst, N.D. (1995). Testing the Rasch model. In G.H. Fischer & I.W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 69–96). New York: Springer-Verlag.
Gulliksen, H. (1950). The reliability of speeded tests. Psychometrika, 15, 259–269.
Jansen, M.G.H. (1997a). The Rasch model for speed tests and some extensions with applications to incomplete designs. Journal of Educational and Behavioral Statistics, 22, 125–140.
Jansen, M.G.H. (1997b). Rasch’s model for reading speed with manifest exploratory variables. Psychometrika, 62, 393–409.
Kail, R., & Hall, L.K. (1994). Processing speed, naming speed, and reading. Developmental Psychology, 30, 949–954.
Lindgren, B.W. (1968). Statistical theory (2nd ed.). New York: MacMillan.
Louis, T.A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226–233.
Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
Maris, E. (1993). Additive and multiplicative models for gamma distributed random variables, and their applications as psychometric models for response times. Psychometrika, 58, 445–469.
Meredith, W. (1971). Poisson distributions of error in mental test theory. British Journal of Mathematical and Statistical Psychology, 24, 49–82.
Meyer, M.S., Wood, F.B., Hart, L.A., & Felton, R.H. (1998). Selective predictive value of rapid automatized naming in poor readers. Journal of Learning Disabilities, 31, 106–117.
Rao, C.R. (1947). Large sample tests of statistical hypothesis concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society, 44, 50–57.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: The Danish Institute of Educational Research. (Expanded edition, 1980. Chicago: The University of Chicago Press.)
Thissen, D. (1983). Timed testing: An approach using item response theory. In D.J. Weiss (Ed.), New horizons in testing: Latent trait theory and computerized adaptive testing (pp. 179–203). New York: Academic Press.
Van den Bos, K.P., & Lutje Spelberg, H.C.L. (1997). Measuring word identification skills and related variables. In C.K. Leong & L.M. Joshi (Eds.), Cross-language studies of learning to read and spell (pp. 271–281). Boston, MA: Kluwer.
Visser, J.J.C.M. (1997). Lezen op AVI-niveau. De schaling, normering en validering van de nieuwe AVI-toetskaarten [Reading on AVI-level: Scaling, norming and validating the AVI-test]. ’s-Hertogenbosch: KPC.
Wolf, M., Bally, H., & Morris, R. (1986). Automaticity, retrieval processes, and reading: A longitudinal study in average and impaired children. Child Development, 57, 988–1000.
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Jansen, M.G.H., Glas, C.A.W. (2001). Statistical Tests for Differential Test Functioning in Rasch’s Model for Speed Tests. In: Boomsma, A., van Duijn, M.A.J., Snijders, T.A.B. (eds) Essays on Item Response Theory. Lecture Notes in Statistics, vol 157. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0169-1_8
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DOI: https://doi.org/10.1007/978-1-4613-0169-1_8
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