Abstract
Some properties of the Linear Logistic Test Model (LLTM) are discussed. Two prerequisites should be met in order to test a cognitive model by means of the LLTM. First, the items used in testing the cognitive model should make up a Rasch homogeneous scale. Second, the population under consideration should be homogeneous with regard to the cognitive strategy employed in solving items representing the task at hand. For a task consisting of solving balance problems it is demonstrated that the second prerequisite is not fulfilled As a consequence the LLTM does not fit for the whole population. By dividing the population into four strategy homogeneous subpopulations a fitting LLTM could be found within one of these subpopulations. Consequently, it is recommended that in using the LLTM for testing cognitive models the population under consideration should be investigated with respect to different cognitive strategies.
This is a modified version of a paper earlier published in Dutch: Het Lineair Logistisch Test Model en heterogeniteit van cognitieve strategieën bij balansproblemen. Tijdschrift voor onderwijsresearch 13(1988), 301–310.
Bitnet/EARN: LVMAANEN @ HGRRUG5, UUCP: {... ! mcvax !} guvaxin ! guicce ! leo
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andersen, E.B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38, 123–140.
Baron, J. (1978). Intelligence and general strategies. In G. Underwood (Ed.), Strategies in Information Processing. London: Academic Press.
Been, P.H., Jorna, R.J. & Sijtsma, K. (1984). Over kijken, meten en modellen bij breukrekentaken. In P.G. Vos, K.B. Koster Sc J. Kingma (Eds.). Rekenen. Balans van standpunten in theorievorming en empirisch onderzoek. Lisse: Swets & Zeitlinger.
Bergan, J.R., Towstopiat, O., Cancelli, A.A. & Karp, C. (1982). Replacement and component rules in hierarchically ordered mathematics rule learning tasks. Journal of Educational Psychology, 74, 32–38.
Broadbent, D.E. (1984). The Maltese cross, a new simplistic model for memory. The Behavioral and’ Brain Sciences, 7, 55–95.
Brown, J.S. & VanLehn, K. (1980). Repair theory: a generative theory of bugs in procedural skills. Cognitive Science, 2, 379–426.
Butterfield, E.C. & Belmont, J.M. (1971). Relations of storage and retrieval strategies as short-term memory processes. Journal of Experimental Psychology, 89, 319–328.
Cooper, L.A. (1982). Strategies for Visual Comparison and Representation: Individual Differences. In R.J. Sternberg (Ed.). Advances in the Psychology of Human Intelligence. Hillsdale (N.J.): Lawrence Erlbaum.
Feldt, L.S. (1965). The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty. Psychometrika, 30, 357–370.
Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 37, 359–374.
Fischer, G.H. (1974). Einfiihrung in die Theorie psychologischer Tests. Bern: Huber.
Fischer, G.H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3–26.
Fischer, G.H. & Formann, A.K. (1982). Some applications of logistic latent trait models with linear constraints on the parameters. Applied Psychological Measurement, 6, 397–416.
Groen, G.J. & Parkman, J.M. (1972). A chronometric analysis of simple addition, Psychological Review, 72, 329–343.
Haeussler, P. (1977). Investigation of mathematical reasoning in science problems. In H. Spada & W.F. Kempf (Eds.). Structural Models of Thinking and Learning. Bern: Huber.
Hunt, E.B., Frost, N. & Lunneborg, C.L. (1973). Individual differences in cognition: A new approach to intelligence. In G. Bower (Ed.). The Psychology of Learning and Motivation. New York: Academic Press.
Hunt, E.B., (1974). Quote the Raven? Nevermore! In L. Gregg (Ed.). Knowledge and Cognition. Hillsdale (N.J.): Lawrence Erlbaum.
Kubinger, K.D. (1979). Das Problemlöseverhalten bei der statistischen Auswertung psychologischer Experimente. Ein Beispiel hochschuldidaktischer Forschung. Zeitschrift für experimentelle und angewandte Psychologie, 26, 467–495.
Kubinger, K.D. (1980). Die Anwendung von Fischers linear logistischen Test Modell zur Leistungssteigerung in Lehrveranstaltungen — Einige neuere Ergebnisse. Archiv für Psychologie, 133, 69–79.
Lewis, C. (1981). Skill in Algebra. In J.R. Anderson (Ed.). Cognitive skills and their acquisition. Hillsdale (N.J.): Lawrence Erlbaum.
MacLeod, C.M., Hunt, E.B. & Mathews, N.N. (1978). Individual differences in the verification of sentence-picture relationships. Journal of Verbal Learning and Behavior, 17, 493–507.
Nährer, W. (1980). Zur Analyse von Matrizenaufgaben mit dem linearen logistischen Testmodell. Zeitschrift für experimentelle und angewandte Psychologie, 27, 553–564.
Newell, A. (1973). You can’t play 20 questions with nature and win. In W.G. Chase (Ed.). Visual Information Processing. New York: Academic Press.
Scheiblechner, H. (1972). Das Lernen und Lösen komplexer Denkaufgaben. Zeitschrift für experimentelle und angewandte Psychologie, 19, 476–506.
Siegler, R.S. (1976). Three aspects of cognitive development. Cognitive Psychology, 8, 481–520.
Siegler, R.S. & Klahr, D. (1982). When do children learn? In R. Glaser (Ed.). Advances in Instructional Psychology, vol 2. Hillsdale (N.J.): Lawrence Erlbaum.
Sijtsma, K. (1982). Een lineair logistisch model ter verklaring van de moeilijkheidspa-rameters van breukrekenitems. In J.G.L.C. Lodewijks & P.R.J. Simons (Eds.). Strategieén in leren en ontwikkeling. Lisse: Swets & Zeitlinger.
Spada, H. (1976). Modelle des Denkens und Lernens. Bern: Huber.
Sternberg, R.J. & Weil, E.M. (1980). An Aptitude x Strategy Interaction in Linear Syllogistic Reasoning. Journal of Educational Psychology, 72, 226–239.
Svenson, O. & Hedenborg, M.L. (1980). Strategies used by children when solving simple subtractions. Acta Psychologica, 4, 1–13.
Underwood, G. (1978). Strategies of Information Processing. New York: Academic Press.
van de Vijver, F.J.R. (1988). Systematizing the item content in test design. In R. Langeheine & J. Rost (Eds.). Latent Trait and Latent Class Models. New York: Plenum Press.
Whitely, S.E. & Schneider, L.M. (1981). Information structure for geometric analo-gies: A test theory approach. Applied Psychological Measurement, 5, 383–397.
Wishart, D. (1978). CL USTAN 1C. Utrecht: Centrum voor Data-Analyse, Rijksuniversiteit Utrecht.
Wollenberg, A.L. van den (1982). A simple and effective method to test the dimensionality axiom of the Rasch model. Applied Psychological Measurement, 6, 83–91.
Wood, R. (1978). Fitting the Rasch model — A heady tale. British Journal of Mathematical and Statistical Psychology, 31, 27–32
Young, R.M. (1978). Strategies and the structure of cognitive skill. In G. Underwood (Ed.). Strategies of Information Processing. New York: Academic Press.
Zwarts, M.A. (1983). Criteriumtoetsen bij aansluiting van primair en secundair onderwijs. (unpublished dissertation). Rijksuniversiteit Utrecht.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
van Maanen, L., Been, P., Sijtsma, K. (1989). The Linear Logistic Test Model and heterogeneity of cognitive strategies. In: Roskam, E.E. (eds) Mathematical Psychology in Progress. Recent Research in Psychology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83943-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-83943-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51686-6
Online ISBN: 978-3-642-83943-6
eBook Packages: Springer Book Archive