Méthodes d'étude de l'adéquation au modèle logistique à un paramètre (modèle de Rasch)
Flieller, André
Mathématiques et Sciences humaines, Tome 128 (1994), p. 19-47 / Harvested from Numdam

Le modèle de Rasch, ou modèle logistique de réponse à l'item à un paramètre, constitue une avancée méthodologique importante, mais l'étude de l'adéquation de données empiriques à ce modèle ne va pas sans problème. Après une brève présentation du modèle de Rasch, l'article discute certains problèmes généraux rencontrés dans les études d'adéquation. Vingt-quatre tests d'adéquation, graphiques et statistiques sont ensuite présentés et évalués. La nécessité d'employer plusieurs méthodes d'évaluation est soulignée dans la conclusion.

Studying model data fit is a problem while employing Rasch model (one-parameter item response model). After a brief presentation of the Rasch model, this article discutes some general problems encountererd in the evaluation of item fit. Then 24 tests of item fit, both graphic and statistical, are presented and evaluated. The necessity of employing several methods of evaluation is enhanced in the conclusion.

Publié le : 1994-01-01
@article{MSH_1994__127__19_0,
     author = {Flieller, Andr\'e},
     title = {M\'ethodes d'\'etude de l'ad\'equation au mod\`ele logistique \`a un param\`etre (mod\`ele de Rasch)},
     journal = {Math\'ematiques et Sciences humaines},
     volume = {128},
     year = {1994},
     pages = {19-47},
     zbl = {0821.62094},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/MSH_1994__127__19_0}
}
Flieller, André. Méthodes d'étude de l'adéquation au modèle logistique à un paramètre (modèle de Rasch). Mathématiques et Sciences humaines, Tome 128 (1994) pp. 19-47. http://gdmltest.u-ga.fr/item/MSH_1994__127__19_0/

Andrich, D. (1988). Rasch models for measurement. Newbury Park (CA): Sage Publications. | MR 982031

Andersen, E.B. (1972, a). The numerical solution of a set of conditional estimation equations. The Journal of the Royal Statistical Society, Series B, 34, 42-54. | MR 331594 | Zbl 0239.62031

Andersen, E.B. (1973, b). Conditional inference in multiple-choice questionnaires. British Journal of Mathematical and Statistical Psychology, 26, 31-44. | MR 451601

Andersen, E.B. (1973, a). A goodness of fit test for the Rasch model. Psychometrika, 38, 123-140. | MR 311064 | Zbl 0276.62048

Baker, F.B. (1987). Methodology review : Item parameter estimation under the one-, two-, and three-parameter logistic models. Applied Psychological Measurement, 11, 111-141.

Bishop, Y.M.M., Fienberg, S.E. & Holland, P.W. (1975). Discrete multivariate analysis : Theory and practice. Cambridge, MA: MIT Press. | MR 381130 | Zbl 0332.62039

Bonis, M. De, Féline, A., Lebeaux, M.-O. & Simon, M. (1994). Evaluation de la sévérité de la dépression : Comparaison des modèles logistique, factoriel et implicite. In M. Huteau (Ed.), Les techniques d'évaluation des personnes (68-70). Paris: E.A.P.

Bock, R.D. & Aitkin, M. (1981). Marginal maximum likehood estimation of item parameters : An application of an EM algorithm. Psychometrika, 46, 443-459. | MR 668311

Cohen A.S. & Kim, S.-H. (1993). A comparison of Lord's χ2 and Raju's area measures in detection of DIF. Applied Psychological Measurement, 17, 39-52.

Dickes, P. (1983). Modèle de Rasch pour items dichotomiques : Théorie, technique et application à la mesure de la pauvreté. Cahiers Economiques de Nancy, 11, 73-116.

Dickes, P. & Hausman, P. (1983). Définir et mesurer la délinquance juvénile. Bulletin de Psychologie, n° 359, 441-455.

Divgi D.R. (1981). Model free evaluation of equating and scaling. Applied Psychological Measurement, 5, 203-208.

Elliot, C.D., Murray, D.J. & Saunders, R. (1977). Goodness of fit to the Rasch model as a criterion of unidimensionality. Manchester: University of Manchester.

Flieller, A. (1988). Application du modèle de Rasch à un problème de comparaison de générations. Bulletin de Psychologie, 42, 86-91.

Fraser, C. & Mcdonald, R.P. (1988). NORHAM : Least squares item factor analysis. Multivariate Behavioral Research, 23, 267-269.

Fischer, G.H. (1974). Einführung in die Theorie psychologischer Tests. Bern: Verlag Hans Huber. | Zbl 0315.92016

Fischer, G.H. & Schleiblechner, H.H. (1970). Algorithmen und Programmen für das probabilistische Testmodel von Rasch. Psychologische Beiträge, 12, 23-51.

Goldstein, H. (1980). Dimensionality, bias, independence and measurement scale problems in latent test score models. British Journal of Mathematical and Statistical Psychology, 33, 234-246. | MR 604075

Goldstein, H. & Wood, R. (1989). Five decades of item response modelling. British Journal of Mathematical and Statistical Psychology, 42, 139-167. | MR 1066347 | Zbl 0718.62261

Gustafsson, J.E. (1980, a). A solution of the conditional estimation problem for long tests in the Rasch model for dichotomous items. Educational and Psychological Measurement, 40, 377-385.

Gustafsson, J.E. (1980, b). Testing and obtaining fit of data to the Rasch model. British Journal of Mathematical and Statistical Psychology, 32, 205-233.

Gustafsson, J.E. & Linblad, T. (1978). The Rasch model for dichotomous items : A solution of the conditional estimation problem for long tests and thome thoughts about item screening procedures. Reports from the Institute of Education, University of Göteborg, n° 67.

Hambleton, R.K. (1969). An empirical investigation of the Rasch test theory model. Unpublished doctoral dissertation, University of Toronto (Canada).

Hambleton, R.K. (1989). Principles and selected applications of item response theory. in R. L. Linn, Educational measurement (3rd ed.) (p. 147-200). New York: Macmillan.

Hambleton, R.K. & Murray, L. (1983). Some goodness of fit investigations for item response models, in R. K. Hambleton (Ed.), Applications of item response theory (p. 71-94). Vancouver: Educational Research Institute of British Columbia.

Hambleton, R.K. & Swaminathan, H. (1985). Item Response Theory. Boston (MA): Kluver-Nihoff Publishing.

Hambleton, R.K. & Swaminathan, H. & Rogers, H.J. (1991). Fundamentals of Item Response Theory. Newbury Park (CA): Sage Publications.

Hattie, J. (1985). Methodology review : Assessing unidimensionality of tests and items. Applied Psychological Measurement, 9, 139-164.

Ludlow, L.H. (1985). A strategy for the graphical representation of Rasch model residuals. Educational and Psychological Measurement, 45, 851-859.

Ludlow, L.H. (1986). Graphical analysis of item response theory residuals. Applied Psychological Measurement, 10, 217-229.

Lord, F. (1980). Applications of Item Response Theory to practical testing problems. Hillsdale (N.J.): Lawrence Erlbaum.

Mcdonald, R., P. (1982). Linear versus nonlinear models of item response theory. Applied Psychological Measurement, 6, 379-396.

Mckinley, R.L. & Mills C.N. (1985). A comparison of several goodness-of-fit statistics. Applied Psychological Measurement, 9, 49-57.

Mclaughlin M.E. & Drasgow, F. (1987). Lord's Chi-Square Test of item bias with estimated and with known person parameters. Applied Psychological Measurement, 11, 161-173.

Mead, R. (1976). Assessment of fit data to the Rasch model. Paper presented at the annual meeting of the American Educational Research Association, San Francisco.

Martin-Löf (1973, oktober). Statistika Modeller. Anteckningar från seminarier Läsaret 1969-1970 utarbetabe av Rolf Sunberg. Stockholm: Instituet för Försäkringsmathematik och Matematisk Statistik vid Stockholms Universitet.

Mislevy, R.J. & Bock, R.D. (1990). Bilog 3 (2nd ed). Mooresville (IN): Scientific Software Inc.

Molenaar, I.W. (1983). Some improved diagnostics for failure of the Rasch model. Psychometrika, 48, 49-72.

Molenaar, I.W. (1990). P.M.L. : User's manual PC version. Groningen: ProGAMMA.

Rasch, G. (1960/1980). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research (1st ed.) / Chicago: University Press (2nd ed.).

Rasch, G. (1977). On specific objectivity : an attempt at formalizing the request for generality and validity of scientific statements. Danish Yearbook of Philosophy, 14, 58-94.

Reiser, M. (1989). An application of the item-response model to psychiatric epidemiology. Sociological Methods and Research, 18, 66-103.

Reuchlin, M. (1992). Introduction à la recherche en psychologie. Paris: Nathan.

Rogers, H.J. & Hattie, J.A. (1987). A Monte Carlo investigation of several person and item fit statitistics for item response models. Applied Psychological Measurement, 11, 47-57.

Stene E. (1969). An exact test for stochastic independence of responses in an item analysis model. Symposium on Rasch models, Køge (Denmark).

Stocking, M.L. (1990). Specifying optimum examinees for item parameter estimation in item response theory. Psychometrika, 55, 461-475.

Swaminathan, H. & Gifford, J.A. (1982). Bayesian estimation in the Rasch model. Journal of Educational Statistics, 7, 175-191.

Thissen, D. (1982). Marginal maximum likehood estimation for the one-parameter logistic model. Psychometrika, 47,175-186. | Zbl 0494.62095

Traub, R.E. & Lam, R. (1985). Latent structure and item sampling models for testing. Annual Review of Psychology, 36, 19-48.

Van Den Vijven, F.R. (1986). The robustness of Rasch estimates. Applied Psychological Measurement, 10, 45-57.

Van Den Wollenberg, A.L. (1979). The Rasch model and time limit tests. Doctoral dissertation. University of Nijmegen (The Netherlands): Student papers.

Van Den Wollenberg, A.L. (1982, a). A simple and effective method to test the dimensionality axiom of the Rasch model. Applied Psychological Measurement, 6, 83-91.

Van Den Wollenberg, A.L. (1982, b). Two new test statistics for the Rasch model. Psychometrika, 47, 123-140. | Zbl 0489.62098

Waller, M.I. (1981). A procedure for comparing latent trait models. Journal of Educational Measurement, 18, 119-125.

Whitely, S.E. (1980). Latent trait models in the study of intelligence. Intelligence, 4, 97-132.

Wright, B.D. (1985). Rasch measurement models. In T.H. Husén & T.N. Postlethwaite (Eds). The International Encyclopedia of Education, 1st ed. (4177-4181). Oxford: Pergamon Press.

Wright, B.D. & Douglas, G.A. (1977). Conditional versus unconditional procedures for sample-free item analysis. Educational and Psychological Measurement, 37, 573-586.

Wright, B.D., Mead, R.J. & Bell, S.R. (1979). BICAL : Calibrating items with the Rasch model. Statistical Research Memorandum N° 23B. Chicago: University of Chicago, School of Education.

Wright, B.D. & Panchapakesan, N. (1969). A procedure for sample-free item analysis. Educational and Psychological Measurement, 29, 23-57.

Wright, B.D. & Stone, M.H. (1979). Best test Design. Chicago: MESA Press.

Yen, W.M. (1981). Using simulation results to choose a latent trait model. Applied Psychological Measurement, 5, 245-262.

Yen W.M. (1987).A comparison of the efficiency and accuracy of bilog and logist. Psychometrika, 52, 275-291.