Abstract
The chapter presents a family of multidimensional logistic models for change, which are based on the Rasch model (RM) and on the linear logistic test model (LLTM; see Fischer, this volume), but unlike these models do not require unidimensionality of the items. As will be seen, to abandon the unidimensionality requirement becomes possible under the assumption that the same items are presented to the testees on two or more occasions. This relaxation of the usual unidimensionality axiom of IRT is of great advantage especially in typical research problems of educational, applied, or clinical psychology, where items or symptoms often are heterogeneous. [See Stout (1987, 1990) for a quite different approach to weakening the strict unidimensionality assumption.] Consider, for example, the problem of monitoring cognitive growth in children: A set of items appropriate for assessing intellectual development will necessarily contain items that address a number of different intelligence factors. If we knew what factors there are, and which of the items measure what factor, we might construct several unidimensional scales. This is unrealistic, however, because the factor structures in males and females, above- and below-average children, etc., generally differ, so that there is little hope of arriving at sufficiently unidimensional scales applicable to all children. Therefore, a model of change that makes no assumption about the latent dimensionality of the items is a very valuable tool for applied research.
This research was supported in part by the Fonds zur Forderung der Wissenschaftlichen Förschung, Vienna, under Grant No. P19118-HIS
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References
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika 43, 561–573.
Cox, D.R. (1970). The Analysis of Binary Data. London: Methuen.
Fischer, G.H. (1972). A measurement model for the effect of mass-media. Acta Psychologica 36, 207–220.
Fischer, G.H. (1974). Einführung in die Theorie psychologischer Tests. [Introduction to Mental Test Theory. In German.] Berne: Huber.
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 applications. In H. Spada and W.F. Kempf (Eds), Structural Models of Thinking and Learning (pp. 203–225 ). Berne: Huber.
Fischer, G.H. (1983a). Logistic latent trait models with linear constraints. Psychometrika 48, 3–26.
Fischer, G.H. (1983b). Some latent trait models for measuring change in qualitative observations. In D.J. Weiss (Ed), New Horizons in Testing (pp. 309–329 ). New York: Academic Press.
Fischer, G.H. (1987a). Applying the principles of specific objectivity and generalizability to the measurement of change. Psychometrika 52, 565–587.
Fischer, G.H. (1987b). Heritabilität oder Umwelteffekte? Zwei verschiedene Ansätze zur Analyse von Daten getrennt aufgewachsener eineiiger Zwilinge. [Heritability of environmental effects? Two attempts at analyzing data of monozygotic twins reared apart. In German.] In E. Raab and G. Schulter (Eds), Perspektiven Psychologischer Forschung. Vienna: Deuticke.
Fischer, G.H. (1989). An IRT-based model for dichotomous longitudinal data. Psychometrika 54, 599–624.
Fischer, G.H. (1991). A new methodology for the assessment of treatment effects. Evaluación Psicologica — Psychological Assessment 7, 117–147.
Fischer, G.H. (1993). The measurement of environmental effects. An alternative to the estimation of heritability in twin data. Methodika 7, 20–43.
Fischer, G.H. and Formann, A.K. (1981). Zur Schätzung der Erblichkeit quantitativer Merkmale. [Estimating heritability of quantitative trait variables. In German.] Zeitschrift für Differentielle und Diagnostische Psychologie 3, 189–197.
Fischer, G.H. and Formann, A.K. (1982). Veränderungsmessung mittels linear-logistischer Modelle. [Measurement of change using linear logistic models. In German.] Zeitschrift für Differentielle und Diagnostische Psychologie 3, 75–99.
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 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 Tanzer, N. (1994). Some LBTL and LLTM relationships. In G.H. Fischer and D. Laming (Eds), Contributions to Mathematical Psychology, Psychometrics, and Methodology (pp. 277–303 ). New York: Springer-Verlag.
Haberman, S.J. (1974). The Analysis of Frequency Data. Chicago: The University of Chicago Press.
Hammer, H. (1978). Informationsgewinn und Motivationseffekt einer Tonbildschau und eines verbalen Lehrvortrages. [Information gain and motivation by video show and a verbal teacher presentation. In German.] Unpublished doctoral dissertation. University of Vienna, Vienna.
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.
Jansen, P.G.W. and Roskam, E.E. (1986). Latent trait models and dichotomization of graded responses. Psychometrika 51, 69–91.
Koschier, A. (1993). Wirksamkeit von Kommunikationstrainings. [The efficacy of communication training seminars. In German.] Unpublshed master’s thesis. University of Vienna, Vienna.
Kropiunigg, U. (1979a). Wirkungen einer sozialpolitischen Medienkampagne. [Effects of a sociopolitical media campaign. In German.] Unpublished doctoral dissertation, University of Vienna, Vienna.
Kropiunigg, U. (1979b). Einstellungswandel durch Massenkommunikation. [Attitude change via mass communication. In German.] Österreichische Zeitschrift für Soziologie 4, 67–71.
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.
Rasch, G. (1961). On general laws and the meaning of measurement in psychology. Proceedings of the IV Berkeley Symposium on Mathematical Statistics and Probability (Vol. 4 ). Berkeley: University of California Press.
Rasch, G. (1965). Statistisk Seminar. [Statistical Seminar.] University of Copenhagen, Department of Mathematical Statistics, Copenhagen. ( Notes taken by J. Stene. )
Roskam, E.E. and Jansen, P.G.W. (1989). Conditions for Rasch-dichotomizability of the unidimensional polytomous Rasch model. Psychometrika 54, 317–332.
Schumacher, M. (1980). Point estimation in quantal response models. Bio-metrical Journal 22, 315–334.
Stout, W. (1987). A nonparametric approach for assessing latent trait dimensionality. Psychometrika 52, 589–617.
Stout, W. (1990). A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika 55, 293–325.
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Fischer, G.H., Seliger, E. (1997). Multidimensional Linear Logistic Models for Change. 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_19
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