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Educational and Psychological Measurement
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Application of Multidimensional Item Response Theory Models to Longitudinal Data

Janneke M. te Marvelde

University of Twente, the Netherlands

Cees A. W. Glas

University of Twente, the Netherlands, C.A.W.Glas{at}gw.utwente.nl

Georges Van Landeghem

Catholic University of Leuven, Belgium

Jan Van Damme

Catholic University of Leuven, Belgium

The application of multidimensional item response theory (IRT) models to longitudinal educational surveys where students are repeatedly measured is discussed and exemplified. A marginal maximum likelihood (MML) method to estimate the parameters of a multidimensional generalized partial credit model for repeated measures is presented. It is shown that model fit can be evaluated using Lagrange multiplier tests. Two tests are presented: the first aims at evaluation of the fit of the item response functions and the second at the constancy of the item location parameters over time points. The outcome of the latter test is compared with an analysis using scatter plots and linear regression. An analysis of data from a school effectiveness study in Flanders (Belgium) is presented as an example of the application of these methods. In the example, it is evaluated whether the concepts "academic self-concept," "well-being at school," and "attentiveness in the classroom" were constant during the secondary school period.

Key Words: longitudinal data • repeated measures • panel data • item response theory • generalized partial credit model • multidimensional IRT models • marginal maximum likelihood estimation

Educational and Psychological Measurement, Vol. 66, No. 1, 5-34 (2006)
DOI: 10.1177/0013164405282490
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