Abstract
For the measurement and statistical assessment of individual gain scores based on item sets that satisfy the assumptions of the Rasch, Rating Scale, or Partial Credit Models, a conditional maximum likelihood estimator, Clopper-Pearson confidence intervals, uniformly most accurate confidence intervals, and uniformly most powerful unbiased tests of the hypothesis of no change are presented. All methods are grounded on the exact conditional distribution of the gain score, given the total score for both time points, so that no asymptotic approximations are required. Typical applications of the methods are mentioned.
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References
Andersen, E.B. (1972). The numerical solution of a set of conditional estimation equations. Journal of the Royal Statistical Society, Series B, 34, 42–54.
Andersen, E.B. (1990). The statistical analysis of categorical data. Heidelberg: Springer-Verlag.
Andersen, E.B. (1995). Polytomous Rasch models and their estimation. In G.H. Fischer & I.W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 271–291). New York: Springer-Verlag.
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.
Bereiter, C. (1963). Some persisting dilemmas in the measurement of change. In C.W. Harris (Ed.), Problems in measuring change (pp. 3–20). Madison, WI: University of Wisconsin Press.
Cronbach, L.J., & Furby, L. (1970). How should we measure change, or should we? Psychological Bulletin, 74, 68–80.
Embretson, S.E. (1991). A multidimensional latent trait model for measuring learning and change. Psychometrika, 56, 495–515.
Fischer, G.H. (1987). Applying the principles of specific objectivity and generalizability to the measurement of change. Psychometrika, 52, 565–578.
Fischer, G.H. (1995). Some neglected problems in IRT. Psychometrika, 60, 459–487.
Fischer, G.H., & Ponocny, I. (1995). Extended rating scale and partial credit models for assessing change. In G.H. Fischer & I.W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 351–370). New York: Springer-Verlag.
Fischer, G.H., & Ponocny-Seliger, E. (1998). Structural Rasch modeling: Handbook of the usage of LPCM-WIN 1.0 [Software manual]. Groningen: ProGAMMA.
Guttmann, G., & Etlinger, S.C. (1991). Susceptibility to stress and anxiety in relation to performance, emotion, and personality: The ergopsychometric approach. In Ch. Spielberger, I.G. Sarason, J. Strelau, & J.M.T. Brebner (Eds.), Stress and anxiety (pp. 23–52). New York: Hemisphere.
Hoijtink, H., & Boomsma, A. (1996). Statistical inference based on latent ability estimates. Psychometrika, 61, 313–330.
Holtzman, W.H. (1963). Statistical models for the study of change in the single case. In C.W. Harris (Ed.), Problems in measuring change (pp. 199–211). Madison, WI: The University of Wisconsin Press.
Huber H. (1977). Zur Planung und Auswertung von Einzelfalluntersuchungen [On the planning and analysis of single case studies]. In L.J. Pongratz (Ed.), Handbuch der Psychologie: Vol. 8. Klinische Psychologie (pp. 1153–1199). Göttingen: Hogrefe.
Klauer, K.C. (1991a). An exact and optimal standardized person test for assessing consistency with the Rasch model. Psychometrika, 56, 213–228.
Klauer, K.C. (1991b). Exact and best confidence intervals for the ability parameter of the Rasch Model. Psychometrika, 56, 535–547.
Klauer, K.C. (1995). The assessment of person fit. In G.H. Fischer & I.W. Molenaar (Eds.), Rasch Models: Foundations, recent developments, and applications (pp. 97–110). New York: Springer-Verlag.
Liou, M. (1993). Exact person tests for assessing model-data fit in the Rasch model. Applied Psychological Measurement, 17, 187–195.
Liou, M., & Chang, C.-H. (1992). Constructing the exact significance level for a person fit statistic. Psychometrika, 47, 169–181.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.
Meijer, R.R., & Sijtsma, K. (in press). A review of methods for evaluating the fit of item score patterns on a test. Applied Psychological Measurement.
Mellenbergh, G.J., & Van den Brink, W.P. (1998). The measurement of individual change. Psychological Methods, 3, 470–485.
Molenaar, I.W., & Hoijtink, H. (1990). The many null distributions of person fit indices. Psychometrika, 55, 75–106.
Mood, A.M., Graybill, F.A., & Boes, D.C. (1974). Introduction to the theory of statistics. Singapore: McGraw-Hill.
Ponocny, I. (2000). Exact person fit indexes for the Rasch model for arbitrary alternatives. Psychometrika, 65, 29–42.
Ponocny, I., & Ponocny-Seliger, E. (1999). T-Rasch 1.0 [Software program]. Groningen: ProGAMMA.
Prieler, J. (2000). Evaluation eines Ausleseverfahrens für Unteroffiziere, beim Österreichischen Bundesheer [Evaluation of a selection procedure for noncommissioned officers in the Austrian army]. Unpublished dissertation, University of Vienna, Department of Psychology.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: The Danish Institute of Educational Research. (Expanded edition, 1980. Chicago: University of Chicago Press.)
Rasch, G. (1965). MÃ¥lingsmodellerne og deres principielle baggrund [Models for measurements and their fundamental background]. (Notes taken by J. Stene at the statistical seminar.) Copenhagen: Department of Statistics, University of Copenhagen.
Santner, T.J., & Duffy, D.E. (1989). The statistical analysis of discrete data. New York: Springer-Verlag.
Willett, J.B. (1989). Some results on reliability for the longitudinal measurement of change: Implications for the design of studies of individual growth. Educational and Psychological Measurement, 49, 587–602.
Williams, R.H., & Zimmerman, D.W. (1996). Are simple gain scores obsolete? Applied Psychological Measurement, 20, 59–69.
Witting, H. (1985). Mathematische Statistik I [Mathematical statistics I]. Stuttgart: Teubner.
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Fischer, G.H. (2001). Gain Scores Revisited Under an IRT Perspective. 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_3
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DOI: https://doi.org/10.1007/978-1-4613-0169-1_3
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