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Fitting Rasch Model using Appropriateness Measure Statistics

Published online by Cambridge University Press:  10 April 2014

José Antonio López Pina  and
M. Dolores Hidalgo Montesinos
José Antonio López Pina*
Affiliation:
University of Murcia
M. Dolores Hidalgo Montesinos
Affiliation:
University of Murcia
*
Correspondence should be addressed to: José A. López Pina, Depto. de Psicología Básica y Metodología, Facultad de Psicología, Campus de Espinardo, 30100-Murcia(Spain). Phone: 968-363478. Fax: 968-364115. E-mail: jlpina@um.es
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Abstract

In this paper, the distributional properties and power rates of the Lz, Eci2z, and Eci4z statistics when they are used as item fit statistics were explored. The results were compared to t-transformation of Outfit and Infit mean square. Four sample sizes were selected: 100, 250, 500, and 1000 examinees. The abilities were uniform and normal with mean 0 and standard deviation 1, and uniform and normal with mean –1 and standard deviation 1. The pseudo-guessing parameter was fixed at .25. Two ranges of difficulty parameters were selected: ±1 logits and ±2 logits. Two test lengths were selected: 15 and 30 items. The results showed important differences between the T-infit, T-outfit, Lz, Eci2z, and Eci4z statistics. The T-oufit, T-infit, and Lz statistics showed poor standardization with estimated parameters because their distributional properties were not close to the expected values. However, the Eci2z and Eci4z statistics showed satisfactory standardization on all conditions. Further, the power rates of Eci2z and Eci4z were 5% to 10% higher than the power rates of Lz, T-outfit, and T-infit to detect items that do not fit Rasch model.

El objetivo de este trabajo fue estudiar la potencia y propiedades distribucionales de tres estadísticos de medida de la adecuación cuando se utilizan como estadísticos de ajuste de los ítems. Los estadísticos sometidos a comparación fueron: Lz, Eci2z y Eci4z. Los resultados obtenidos se compararon con los estadísticos T-outfit y T-infit. Se seleccionaron cuatro tamaños muestrales: 100, 250, 500 y 1000 sujetos. Se sometieron a estudio distintas distribuciones de habilidad: uniforme y normal, con media 0 y desviación típica 1, y uniforme y normal con media –1 y desviación típica 1. El parámetro de pseudo-azar fue fijado en .25. Para los parámetros de dificultad se utilizaron dos distribuciones uniformes de ±1 logits y ±2 logits. Por ultimo, se consideraron dos longitudes de tests: 15 y 30 ítems. Los resultados mostraron que los estadísticos Lz, T-outfit y T-infit no tienden a los valores esperados cuando se calculan con parámetros estimados, mientras que los estadísticos Eci2z y Eci4z mantuvieron mejor las propiedades de sus distribuciones teóricas. Además, la potencia de estos dos últimos estadísticos para detectar ítems no ajustados al modelo de Rasch estuvo entre un 5% y un 10% más que la potencia de los estadísticos Lz, T-outfit y T-infit.

Keywords

Rasch modelitem response theoryappropriateness measureitem fit statisticsmodelo de Raschteoría de la respuesta al ítemmedida de la adecuaciónestadísticos de ajuste de ítems
Type
Articles
Information
The Spanish Journal of Psychology , Volume 8 , Issue 1 , May 2005 , pp. 100 - 110
Copyright
Copyright © Cambridge University Press 2005

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