OJAppS  Vol.4 No.8 , July 2014
Effects of Differential Item Discriminations between Individual-Level and Cluster-Level under the Multilevel Item Response Theory Model
This study attempted to interpret differential item discriminations between individual and cluster levels by focusing on patterns and magnitudes of item discriminations under 2PL multilevel IRT model through a set of variety simulation conditions. The consistency between the mean of individual-level ability estimates and cluster-level ability estimates was evaluated by the correlations between them. As a result, it was found that they were highly correlated if the patterns of item discriminations were the same for both individual and cluster levels. The magnitudes of item discriminations themselves did not affect much on correlations, as far as the patterns were the same at the two levels. However, it was found that the correlation became lower when the patterns of item discriminations were different between the individual and cluster levels. Also, it was revealed that the mean of the estimated individual-level abilities would not be necessarily a good representation of the cluster-level ability, if the patterns were different at the two levels.

Cite this paper
Patarapichayatham, C. and Kamata, A. (2014) Effects of Differential Item Discriminations between Individual-Level and Cluster-Level under the Multilevel Item Response Theory Model. Open Journal of Applied Sciences, 4, 425-432. doi: 10.4236/ojapps.2014.48039.
[1]   Kamata, A. (2001) Item Analysis by the Hierarchical Generalized Linear Model. Journal of Educational Measurement, 38, 79-93.

[2]   Adams, R.J., Wilson, M. and Wu, M. (1997) Multilevel Item Response Models: An Approach to Errors in Variables Regression. Journal of Educational and Behavioral Statistics, 22, 47-76.

[3]   Fox, J.P. and Glas, C.A.W. (2001) Bayesian Estimation of a Multi-Level IRT Model Using Gibbs Sampling. Psychometrika, 66, 271-288.

[4]   Fox, J.-P. (2004) Applications of Multilevel IRT Modeling. School Effectiveness and School Improvement, 15, 261-280.

[5]   Fox, J.-P. (2005) Multilevel IRT Using Dichotomous and Polytomous Response Data. British Journal of Mathematical and Statistical Psychology, 58, 145-172.

[6]   Mislevy, R.J. (1983) Item Response Models for Grouped Data. Journal of Educational Statistics, 8, 271-288.

[7]   Natesan, P. (2007) Estimation of Two-Parameter Multilevel Item Response Models with Predictors: Simulation and Substantiation for an Urban School District. Unpublished Doctoral Dissertation, Texas A&M University, College Station, TX.

[8]   Tate, R.L. (1995) Robustness of the School-Level IRT Model. Journal of Educational Measurement, 32, 145-162.

[9]   Tate, R. (2000) Robustness of the School-Level Polytomous IRT Model. Educational and Psychological Measurement, 60, 20-37.