Abstract
This chapter gives an overview of a family of unidimensional Rasch models where the item parameters are linearly decomposed into certain “basic” parameters. The latter are attached—depending on the particular kind of application—to cognitive operations required for solving the items, to testing situations, or to treatments given to the persons between testing occasions. Typical applications (see below) have sought to assess the difficulty of cognitive operations as elements of the solution process, but the models can just as well be used for measuring the effects of experimental conditions on item difficulty, or the impact of educational treatments on an ability, of therapies on a personality trait, or of communication on an attitude. Such models are available both for cases of dichotomous and for polytomous items.
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References
Andrich, D. (1978a). A rating formulation for ordered response categories. Psychometrika 43, 561–573.
Andrich, D. (1978b). Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement 2, 581–594.
Arrer, S. (1992). Unterschiede zwischen Computer-and Papier-BleistiftVorgabe des 3D W. [Differences Between Computerized and Paper—Pencil Forms of the 3DW. In German] Unpublished master’s thesis, University of Vienna, Vienna.
Baker, F.B. (1993). Sensitivity of the linear logistic test model to misspecification of the weight matrix. Applied Psychological Measurement 17, 201–210.
Embretson, S.E. (1985). Introduction to the problem of test design. In S.E. Embretson, Test Design: Developments in Psychology and Psychometrics (pp. 3–18 ). Orlando: Academic Press.
Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica 37, 359–374.
Fischer, G.H. (1976). Some probabilistic models for measuring change. In D.N.M. de Gruijter and L.J.Th. van der Kamp (Eds), Advances in Psychological and Educational Measurement (pp. 97–110 ). New York: Wiley.
Fischer, G.H. (1977a). Some probabilistic models for the description of attitudinal and behavioral changes under the influence of mass communication. In W.F. Kempf and B. Repp (Eds), Mathematical Models for Social Psychology (pp. 102–151). Berne: Huber and New York: Wiley.
Fischer, G.H. (1977b). Linear logistic latent trait models: Theory and application. In H. Spada and W.F. Kempf (Eds), Structural Models in Thinking and Learning (pp. 203–225 ). Berne: Huber.
Fischer, G.H. (1981). On the existence and uniqueness of maximum-likelihood estimates in the Rasch model. Psychometrika 46, 59–77.
Fischer, G.H. (1983). Logistic latent trait models with linear constraints. Psychometrika 48, 3–26.
Fischer, G.H. (1995a). The linear logistic test model. In G.H. Fisher and I.W. Molenaar (Eds), Rasch Models, Foundations, Recent Developments, and Applications (pp. 131–155 ). New York: Springer-Verlag.
Fischer, G.H. (1995b). Linear logistic models for change. In G.H. Fischer and I.W. Molenaar (Eds), Rasch Models, Recent Developments, and Applications (pp. 158–180 ). New York: Springer-Verlag.
Fischer, G.H. and Formann, A.K. (1982). Some applications of logistic latent trait models with linear constraints on the parameters. Applied Psychological Measurement 4, 397–416.
Fischer, G.H. and Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of change. Psychometrika 56, 637–651.
Fischer, G.H. and Pendl, P. (1980). Individualized testing on the basis of the dichotomous Rasch model. In L.J. Th. van der Kamp, W.F. Langerak, and D.N.M. de Gruijter (Eds), Psychometrics for Educational Debates (pp. 171–188 ). New York: Wiley.
Fischer, G.H. and Ponocny, I. (1994). An extension of the partial credit model with an application to the measurement of change. Psychometrika 59, 177–192.
Fischer, G.H. and Ponocny, I. (1995). Extended rating scale and partial credit models for assessing change. In G.H. Fisher and I.W. Molenaar (Eds), Rasch Models, Foundations, Recent Developments, and Applications (pp. 353–370 ). New York: Springer-Verlag.
Fischer, G.H. and Tanzer, N. (1994). Some LLTM and LBTL relationships. In G.H. Fischer and D. Laming (Eds), Contributions to Mathematical Psychology, Psychometrics, and Methodology (pp. 277–303 ). New York: Springer-Verlag.
Formann, A.K. (1973). Die Konstruktion eines neuen Matrizentests und die Untersuchung des Lösungsverhaltens mit Hilfe des linear logistischen Testmodells. [The Construction of a New Matrices Test and the Investigation of the Response Behavior by Means of the Linear Logistic Test Model. In German.] Unpublished doctoral dissertation, University of Vienna, Vienna.
Formann, A.K. and Piswanger, K. (1979). Wiener Matrizen-Test. Ein Rasch-skalierter sprachreier Intelligenztest. [Viennese Matrices Test. A Rasch-Scaled Culture-Fair Intelligence Test. In German.] Weinheim: Beltz-Test.
Gittler, G. (1990). Dreidimensionaler Wiirfeltest (3DW). Ein Rasch-skalierter Test zur Messung des räumlichen Vorstellungsvermögens. [The Three-Dimensional Cubes Test (3DW). A Rasch-Scaled Test for Spatial Ability. In German.] Weinheim: Beltz-Test.
Gittler, G. (1994). Intelligenzförderung durch Schulunterricht: Darstellende Geometrie und räumliches Vorstellungsvermögen. [The promotion of intelligence via teaching: Mechanical geometry and spatial abilities. In German.] In G. Gittler, M. Jirasko, U. Kastner-Koller, C. Korunka, and A. Al-Roubaie (Eds), Die Seele ist ein weites Land (pp. 103–122 ). Vienna: WUV-Universitätsverlag.
Gittler, G. and Wild, B. (1988). Der Einsatz des LLTM bei der Konstruktion eines Item-pools für das adaptive Testen. [Usage of the LLTM for the construction of an item pool for adaptive testing. In German.] In K.D. Kubinger (Ed), Moderne Testtheorie (pp. 115–139 ). Weinheim and Munich: Beltz Test Gesellschaft/Psychologie Verlags Union.
Hillgruber, G. (1990). Schätzung von Parametern in psychologischen Testmodellen. [Parameter estimation in psychological test models. In German] Unpublished master’s thesis, University of Cologne, Cologne.
Hornke, L.F. and Habon, M.W. (1986). Rule-based item bank construction and evaluation within the linear logistic framework. Applied Psychological Measurement 10, 369–380.
Hornke, L.F. and Rettig, K. (1988). Regelgeleitete Itemkonstruktion unter Zuhilfenahme kognitionspsychologischer Überlegungen. [Rule-based item construction using concepts of cognitive psychology. In German.] In K.D. Kubinger (Ed), Moderne Testtheorie (pp. 140–162 ). Weinheim: Beltz.
Kempf, W. (1972). Probabilistische Modelle experimentalpsychologischer Versuchssituationen. Psychologische Beiträge, 14, 16–37.
Kempf, W. (1977). Dynamic models for the measurement of “traits” in social behavior. In W. Kempf and B.H. Repp (Eds), Mathematical Models for Social Psychology (pp. 14–58 ). Berne: Huber.
Kubinger, K.D. (1979). Das Problemlöseverhalten bei der statistischen Auswertung psychologischer Experimente. Ein Beispiel hochschuldidaktischer Forschung. [The task-solving behavior in the statistical analysis of psychological experiments. An example of research in didactics. In German.] Zeitschrift für Experimentelle und Angewandte Psychologie 26, 467–495.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika 47, 149–174.
Micko, H.C. (1969). A psychological scale for reaction time measurement. Acta Psychologica 30, 324–335.
Micko, H.C. (1970). Eine Verallgemeinerung des Messmodells von Rasch mit einer Anwendung auf die Psychophysik der Reaktionen. [A generalization of Rasch’s measurement model with an application to the psychophysics of reactions. In German.] Psychologische Beiträge 12, 4–22.
Mislevy, R.J. (1981). A general linear model for the analysis of Rasch item threshold estimates. Unpublished doctoral dissertation, University of Chicago, Chicago.
Mohammadzadeh-Koucheri, F. (1993). Interkultureller Vergleich mit einer variierten Form des Matrizentests von Formann. [Cross-cultural comparisons using a variation of the matrices test of Formann. In German.] Unpublished master’s thesis, University of Vienna, Vienna.
Nährer, W. (1980). Zur Analyse von Matrizenaufgaben mit dem linearen logistischen Testmodell. [On the analysis of matrices items by means of the linear logistic test model. In German.] Zeitschrift für Experimentelle und Angewandte Psychologie 27, 553–564.
Pfanzagl, J. (1994). On item parameter estimation in certain latent trait models. In G.H. Fischer and D. Laming (Eds), Contributions to Mathematical Psychology, Psychometrics, and Methodology (pp. 249–263 ). New York: Springer-Verlag.
Piswanger, K. (1975). Interkulturelle Vergleiche mit dem Matrizentest von Formann. [Cross-cultural comparisons by means of the matrices test of Formann. In German.] Unpublished doctoral dissertation, University of Vienna, Vienna.
Rasch, G. (1965). Statistisk Seminar. [Statistical Seminar.] Copenhague: University of Copenhague, Department of Mathematical Statistics. ( Notes taken by J. Stene. )
Scheiblechner, H. (1971). CML-parameter-estimation in a generalized multifactorial version of Rasch’s probabilistic measurement model with two categories of answers, Research Bulletin No. 4. Vienna: Department of Psychology, University of Vienna.
Scheiblechner, H. (1972). Das Lernen und Lösen komplexer Denkaufgaben. [The learning and solving of complex reasoning tasks. In German] Zeitschrift fur Experimentelle und Angewandte Psychologie 3, 456–506.
Smith, R.M., Kramer, G.A., and Kubiak, A.T. (1992). Components of difficulty in spatial ability test items. In M. Wilson (Ed), Objective Measurement: Theory into Practice, Vol. 1 (pp. 157–174 ). Norwood, NJ: Ablex.
Spada, H. (1976). Modelle des Denkens and Lernens. [Models of Thinking and Learning. In German.] Berne: Huber.
Spada, H. and Kluwe, R. (1980). Two models of intellectual development and their reference to the theory of Piaget. In R. Kluwe and H. Spada (Eds), Developmental Models of Thinking (pp. 1–30 ). New York: Academic Press.
Spada, H. and May, R. (1982). The linear logistic test model and its application in educational research. In D. Spearritt (Ed), The Improvement of measurement in Education and Psychology (pp. 67–84 ). Hawthorne, Victoria: Australian Council for Educational Research.
van de Vijver, F.J.R. (1988). Systematizing item content in test design. In R. Langeheine and J. Rost (Eds), Latent Trait and Latent Class Models (pp. 291–307 ). New York: Plenum.
Verhelst, N.D. and Glas, C.A.W. (1993). A dynamic generalization of the Rasch model. Psychometrika 58, 395–415.
Verhelst, N.D. and Glas, C.A.W. (1995). Dynamic generalizations of the Rasch model. In G.H. Fischer and I.W. Molenaar (Eds), Rasch Models, Foundations, Recent Developments, and Applications (pp. 181–201 ). New York: Springer-Verlag.
Whitely, S.E. and Schneider, L.M. (1981). Information structure for geometric analogies: A test theory approach. Applied Psychological Measurement 5, 383–397.
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Fischer, G.H. (1997). Unidimensional Linear Logistic Rasch Models. In: van der Linden, W.J., Hambleton, R.K. (eds) Handbook of Modern Item Response Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2691-6_13
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