Approximations of normal IRT models for change.

E.S. Tan, A.W. Ambergen, J. Does, T. Imbos

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)

Abstract

Keywords: closed form estimators, IRT, longitudinal

In this paper, the one parameter Item Response Theory (IRT) model with normal Item Characteristic Curves (ICC) in longitudinal context has been studied. The abilities are structured according to a general mixed effects linear regression model. The items are supposed to be a sample from a large bank of items with constant mean difficulty. If the number of repeated measures is large, then commonly used simultaneous estimation procedures often lead to practical problems with respect to multidimensional numerical integrations. In this article, an approximation of the normal ICC is introduced that leads to simple ability and difficulty estimators with nice asymptotic properties. The relative efficiency and bias of the ability estimator are studied. An illustration with real data shows high relative efficiency within an accaptable range of the domain of the ICC. Moreover, the bias is very small. A simulation study shows the effect of non-normal item parameters on the regression estimates. The results suggest that the proposed procedure is rather robust against departures from normality. However, the estimation of the correlations between regression parameters can be seriously biased.
Original languageEnglish
Pages (from-to)208-223
Number of pages16
JournalJournal of Educational and Behavioral Statistics
Volume24
Issue number2
DOIs
Publication statusPublished - 1 Jan 1999

Cite this

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title = "Approximations of normal IRT models for change.",
abstract = "Keywords: closed form estimators, IRT, longitudinal In this paper, the one parameter Item Response Theory (IRT) model with normal Item Characteristic Curves (ICC) in longitudinal context has been studied. The abilities are structured according to a general mixed effects linear regression model. The items are supposed to be a sample from a large bank of items with constant mean difficulty. If the number of repeated measures is large, then commonly used simultaneous estimation procedures often lead to practical problems with respect to multidimensional numerical integrations. In this article, an approximation of the normal ICC is introduced that leads to simple ability and difficulty estimators with nice asymptotic properties. The relative efficiency and bias of the ability estimator are studied. An illustration with real data shows high relative efficiency within an accaptable range of the domain of the ICC. Moreover, the bias is very small. A simulation study shows the effect of non-normal item parameters on the regression estimates. The results suggest that the proposed procedure is rather robust against departures from normality. However, the estimation of the correlations between regression parameters can be seriously biased.",
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Approximations of normal IRT models for change. / Tan, E.S.; Ambergen, A.W.; Does, J.; Imbos, T.

In: Journal of Educational and Behavioral Statistics, Vol. 24, No. 2, 01.01.1999, p. 208-223.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Approximations of normal IRT models for change.

AU - Tan, E.S.

AU - Ambergen, A.W.

AU - Does, J.

AU - Imbos, T.

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Y1 - 1999/1/1

N2 - Keywords: closed form estimators, IRT, longitudinal In this paper, the one parameter Item Response Theory (IRT) model with normal Item Characteristic Curves (ICC) in longitudinal context has been studied. The abilities are structured according to a general mixed effects linear regression model. The items are supposed to be a sample from a large bank of items with constant mean difficulty. If the number of repeated measures is large, then commonly used simultaneous estimation procedures often lead to practical problems with respect to multidimensional numerical integrations. In this article, an approximation of the normal ICC is introduced that leads to simple ability and difficulty estimators with nice asymptotic properties. The relative efficiency and bias of the ability estimator are studied. An illustration with real data shows high relative efficiency within an accaptable range of the domain of the ICC. Moreover, the bias is very small. A simulation study shows the effect of non-normal item parameters on the regression estimates. The results suggest that the proposed procedure is rather robust against departures from normality. However, the estimation of the correlations between regression parameters can be seriously biased.

AB - Keywords: closed form estimators, IRT, longitudinal In this paper, the one parameter Item Response Theory (IRT) model with normal Item Characteristic Curves (ICC) in longitudinal context has been studied. The abilities are structured according to a general mixed effects linear regression model. The items are supposed to be a sample from a large bank of items with constant mean difficulty. If the number of repeated measures is large, then commonly used simultaneous estimation procedures often lead to practical problems with respect to multidimensional numerical integrations. In this article, an approximation of the normal ICC is introduced that leads to simple ability and difficulty estimators with nice asymptotic properties. The relative efficiency and bias of the ability estimator are studied. An illustration with real data shows high relative efficiency within an accaptable range of the domain of the ICC. Moreover, the bias is very small. A simulation study shows the effect of non-normal item parameters on the regression estimates. The results suggest that the proposed procedure is rather robust against departures from normality. However, the estimation of the correlations between regression parameters can be seriously biased.

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