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Fitting Logistic IRT Models: Small Wonder

Published online by Cambridge University Press:  10 April 2014

Miguel A. García-Pérez
Miguel A. García-Pérez*
Affiliation:
Complutense University of Madrid
*
Correspondence concerning this article should be addressed to Dr. Miguel A. García-Pérez, Departamento de Metodología. Facultad de Psicología.Universidad Complutense. Campus de Somosaguas. 28223 Madrid (Spain). Phone: (+34) 91 394 3061. Fax: (+34) 91 394 3189. E-mail: miguel@psi.ucm.es
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Abstract

State-of-the-art item response theory (IRT) models use logistic functions exclusively as their item response functions (IRFs). Logistic functions meet the requirements that their range is the unit interval and that they are monotonically increasing, but they impose a parameter space whose dimensions can only be assigned a metaphorical interpretation in the context of testing. Applications of IRT models require obtaining the set of values for logistic function parameters that best fit an empirical data set. However, success in obtaining such set of values does not guarantee that the constructs they represent actually exist, for the adequacy of a model is not sustained by the possibility of estimating parameters. This article illustrates how mechanical adoption of off-the-shelf logistic functions as IRFs for IRT models can result in off-the-shelf parameter estimates and fits to data. The results of a simulation study are presented, which show that logistic IRT models can fit a set of data generated by IRFs other than logistic functions just as well as they fit logistic data, even though the response processes and parameter spaces involved in each case are substantially different. An explanation of why logistic functions work as they do is offered, the theoretical and practical consequences of their behavior are discussed, and a testable alternative to logistic IRFs is commented upon.

La función de respuesta al ítem (FRI) asumida en los modelos al uso en teoría de respuesta al ítem (TRI) es, en la práctica, exclusivamente la función logística. Las funciones logísticas cumplen los requisitos de que su rango es el intervalo [0, 1] y son monótonamente crecientes, pero imponen un espacio paramétrico cuyas dimensiones sólo tienen una interpretación metafórica en el contexto de la evaluación mediante pruebas objetivas. La aplicación de modelos TRI requiere la estimación de los parámetros logísticos que mejor describen unos datos empíricos. Sin embargo, el éxito en la obtención de estos parámetros no garantiza que los constructos representados mediante ellos existan en realidad, puesto que la validez de un modelo no queda establecida sólo por la posibilidad de estimar sus parámetros. Este trabajo muestra que la adopción mecánica de funciones logísticas como FRI en modelos TRI produce estimaciones y ajustes estereotipados. Como prueba, se presentan resultados de un estudio de simulación en el que el modelo logístico produjo un patrón de estimaciones y ajustes de datos no logísticos que fue indistinguible del patrón obtenido para datos logísticos, a pesar de que los datos no logísticos se generaron de acuerdo con un modelo que implica un proceso de respuesta y un espacio paramétrico marcadamente diferentes del logístico. El trabajo termina con unas reflexiones acerca de las razones por las que los modelos logísticos se comportan así y de las consecuencias teóricas y prácticas de ese comportamiento, y también se describe una alternativa empíricamente falsable a las FRI logísticas.

Keywords

goodness of fitparameter estimationitem response theorylogistic modelsfinite state polynomic modelsBILOGbondad de ajusteestimación de parámetrosteoría de respuesta al ítemmodelos logísticosmodelos polinómicos de estados finitosBILOG
Type
Spanish research trends
Information
The Spanish Journal of Psychology , Volume 2 , May 1999 , pp. 74 - 94
Copyright
Copyright © Cambridge University Press 1999

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