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The Use of an Identifiability-Based Strategy for the Interpretation of Parameters in the 1PL-G and Rasch Models

Published online by Cambridge University Press:  01 January 2025

Paula Fariña Open the ORCID record for Paula Fariña [Opens in a new window] ,
Jorge González  and
Ernesto San Martín
Paula Fariña*
Affiliation:
Universidad Diego Portales
Jorge González
Affiliation:
Pontificia Universidad Católica de Chile
Ernesto San Martín
Affiliation:
Pontificia Universidad Católica de Chile Université catholique de Louvain
*
Correspondence should be made to Paula Fariña, Faculty of Engineering and Science, Universidad Diego Portales, Vergara 432, Santiago, Chile. Email: paula.farina@udp.cl
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Abstract

Using the well-known strategy in which parameters are linked to the sampling distribution via an identification analysis, we offer an interpretation of the item parameters in the one-parameter logistic with guessing model (1PL-G) and the nested Rasch model. The interpretations are based on measures of informativeness that are defined in terms of odds of correctly answering the items. It is shown that the interpretation of what is called the difficulty parameter in the random-effects 1PL-G model differs from that of the item parameter in a random-effects Rasch model. It is also shown that the traditional interpretation of the guessing parameter in the 1PL-G model changes, depending on whether fixed-effects or random-effects versions of both models are considered.

Keywords

parameter interpretationidentifiabilityIRT models
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 2 , June 2019 , pp. 511 - 528
Copyright
Copyright © 2019 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-09659-w) contains supplementary material, which is available to authorized users.

The partial financial support of the ANILLO Project SOC1107 (ended in November 2015) from the Chilean Government is gratefully acknowledged. The first, second and third authors also acknowledge the partial financial support of FONDECYT Projects 11160374, 1150233 and 1181216, respectively.

References

Agresti, A. (2002). Categorical Data Analysis, 2New York: Wiley.CrossRefGoogle Scholar
Andrich, D., Marais, (2014). Person proficiency estimates in the dichotomous rasch model when random guessing is removed from difficulty estimates of multiple choice items. Applied Psycological Measurement, 38, 432–449.CrossRefGoogle Scholar
Andrich, D., Marais, I., Humphry, S. (2012). Using a theorem by Andersen and the dichotomous Rasch model to asses the presence of random guessing in multiple choice items. Journal of Educational and Behavioral Statistics, 37(3), 417–442.CrossRefGoogle Scholar
Andrich, D., Marais, I., Humphry, S. (2016). Controlling guessing bias in the dichotomous Rasch model applied to a large-scale, vertically scaled testing program. Educational and Psycological Measurement, 76, 412–435.CrossRefGoogle ScholarPubMed
Birnbaum, A. (1968). Some latent trait models. In Lord, F., Novick, M. (Eds), Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
De Boeck, P., Wilson, M. (2004). Explanatory item response models: A generalized linear and nonlinear approach, New York: Springer.CrossRefGoogle Scholar
Embretson, S., Reise, S. (2000). Item response theory for psychologists, Mahwah: Lawrence Erlbaum Associates.Google Scholar
Hambleton, R., Cook, L. (1977). Latent trait models and their use in the analyses of educational test data. Journal of Educational Measurement, 14, 75–96.CrossRefGoogle Scholar
Holland, P. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55(4), 577–601.CrossRefGoogle Scholar
Lindsay, B., Clogg, C. C., Grego, J. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of the American Statistical Association, 86(413), 96–107.CrossRefGoogle Scholar
Lord, F. (1968). An analysis of the verbal scholastic aptitude test using Birnbaum’s three-parameter logistic model. Educational and Psychological Measurement, 28, 989–1020.CrossRefGoogle Scholar
Lord, F. (1970). Item characteristic curves as estimated without knowledge of their mathematical form—A confrontation of Birnbaum’s logistic model. Psychometrika, 35, 43–50.CrossRefGoogle Scholar
Maris, G., Bechger, T. (2009). On interpreting the model parameters for the three parameter logistic model. Measurement: Interdisciplinary Research and Perspectives, 7, 75–88.Google Scholar
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. The Danish Institute for Educational Research (Expanded edition, 1980). Chicago: The University Chicago Press.Google Scholar
Rigdom, S., Tsutakawa, R. (1983). Parameter estimation in latent trait models. Psychometrika, 48(4), 567–574.CrossRefGoogle Scholar
Rizopoulos, D. (2006). ltm: An R package for latent variable modeling and item response theory analyses. Journal of Statistical Software, 17(5), 1–25.CrossRefGoogle Scholar
San Martín, E. (2016). Identification of item response theory models. In van der Linden, W. (Eds), Handbook of item response theory, Boca Raton: Chapman and Hall/CRC 127–150.Google Scholar
San Martín, E., De Boeck, P. (2015). What do you mean by a difficult item? On the interpretation of the difficulty parameter in a Rasch Model. In Millsap, R., Bolt, D., van der Ark, L., Wang, W. C. (Eds), Quantitative psychology research, Berlin: Springer International Publishing 1–14.Google Scholar
San Martín, E., Del Pino, G., De Boeck, P. (2006). IRT models for ability-based guessing. Applied Psychological Measurement, 30(3), 183–203.CrossRefGoogle Scholar
San Martín, E., González, J., Tuerlinckx, F. (2009). Identified parameters, parameters of interest and their relationships. Measurement: Interdisciplinary Research and Perspective, 7, 97–105.Google Scholar
San Martín, E., González, J., Tuerlinckx, F. (2015). On the unidentifiability of the fixed-effects 3PL model. Psychometrika, 80(2), 450–467.CrossRefGoogle ScholarPubMed
San Martín, E., Rolin, J., Castro, L. (2013). Identification of the 1PL model with guessing parameter: Parametric and semiparametric results. Psychometrika, 78(2), 341–379.CrossRefGoogle ScholarPubMed
Waller, M. (1974). Removing the effects of random guessing from latent trait ability estimates (Research Bulletin RB-74-32). Educational Test Service, Princeton, NJ.Google Scholar
Weitzman, R. (1996). The Rasch model plus guessing. Educational and Psychological Measurement, 56(5), 779–790.CrossRefGoogle Scholar
Wright, B. (1989). Dichotomous Rasch model derived from counting right answers: Raw scores as sufficient statistics. Rasch Measurement Transactions, 3(2), 62.Google Scholar
Wu, H. (2016). A note on the identifiability of fixed-effect 3PL-models. Psychometrika, 81(4), 1093–1097.CrossRefGoogle Scholar
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