Abstract
The Rasch model (Rasch, 1960) and the linear logistic test model (LLTM, Fischer, 1973, 1977) are two commonly used item response models. Both models are discussed in Chapter 2. The Rasch model assumes item indicators as predictors, so that each item has a specific effect, the weight of the corresponding item indicator. The LLTM explains these effects in terms of item properties, or in other words item properties are used as item predictors. Therefore, the LLTM may be considered an item explanatory model, in contrast with the Rasch model which is descriptive.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bechger, T.M., Verhelst, N.D., & Verstralen, H.H.F.M. (2001). Identifiability of nonlinear logistic test models. Psychometrika, 66, 357–371.
Bechger, T.M., Verstralen, H.H.F.M., & Verhelst, N.D. (2002). Equivalent linear logistic test models. Psychometrika, 67, 123–136.
Birnbaum, A. (1968). Some latent trait models. In F.M. Ford & M.R. Novick (Eds), Statistical Theories of Mental Test Scores (pp. 397–424). Reading: Addison-Wesley.
Butter, R. (1994). Item response models with internal restrictions on item difficulty. Unpublished doctoral dissertation, K.U.Leuven (Belgium).
Butter, R., De Boeck, P., & Verhelst, N.D. (1998). An item response model with internal restrictions on item difficulty. Psychometrika, 63, 1–17.
Embretson, S.E. (1991). A multidimensional latent trait model for measuring learning and change. Psychometrika, 56, 495–515.
Fischer, G.H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 37, 359–374.
Fischer, G.H. (1977). Linear logistic trait models: Theory and applications. In H. Spada & W.F. Kempf (Eds), Structural Models of Thinking and Learning (pp. 203–225). Bern, Switzerland: Huber.
Maris, G., & Bechger, T. (2003). Equivalent MIRID models. Measurement and Research Department Report 2003–2. Arnhem, The Netherlands: CITO.
McCulloch, C.E., & Searle, S.R. (2001). Generalized Linear, and Mixed Models. New York: Wiley.
Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen, Denmark: Danish Institute for Educational research.
Smits, D.J.M., & De Boeck, P. (2003). A componential model for guilt. Multivariate Behavioral Research, 38, 161–188.
Smits, D.J.M., De Boeck, P., Verhelst, N., & Butter, R. (2001). The MIRID program (version 1.0) (Computer program and manual). K.U.Leuven, Belgium.
Smits, D.J.M., De Boeck, P., & Verhelst, N.D. (2003). Estimation of the MIRID: A program and a SAS based approach. Behavior Research Methods, Instruments, and Computers, 35, 537–549.
Verhelst, N.D., & Glas, C.A.W. (1995). One parameter logistic model. In G.H. Fischer & I.W. Molenaar (Eds), Rasch Models: Foundations, Recent Developments and Applications (pp. 215–238). New York: Springer.
Verhelst, N.D., Glas, C.A.W., & Verstralen, H.H.F.M. (1994). One Parameter Logistic Model (Computer program and manual). Arnhem, The Netherlands: CITO.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Smits, D.J.M., Moore, S. (2004). Latent item predictors with fixed effects. In: De Boeck, P., Wilson, M. (eds) Explanatory Item Response Models. Statistics for Social Science and Public Policy. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3990-9_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3990-9_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2323-3
Online ISBN: 978-1-4757-3990-9
eBook Packages: Springer Book Archive