Multilevel Item Response Model with Heterogeneous Within-Cluster Variances

Within-cluster variance homogeneity is one of the key assumptions of multilevel models; however, assuming a constant (i.e. equal) within-cluster variance may not be realistic. Moreover, existent within-cluster variance heterogeneity should be regarded as a source of additional information rather tha...

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Veröffentlicht in:The Journal of experimental education 2022-07, Vol.90 (4), p.962-980
Hauptverfasser: Kara, Yusuf, Kamata, Akihito
Format: Artikel
Sprache:eng
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Zusammenfassung:Within-cluster variance homogeneity is one of the key assumptions of multilevel models; however, assuming a constant (i.e. equal) within-cluster variance may not be realistic. Moreover, existent within-cluster variance heterogeneity should be regarded as a source of additional information rather than a violation of a model assumption. This study extends the three-level Rasch item response model to estimate cluster-specific variances as random effects adopting the Bayesian approach. Data analysis results provided empirical evidence for the possible violations of the within-cluster variance heterogeneity, as well as the utility of the proposed heterogeneous model. A small-scale simulation study conducted to provide information about the estimation efficiency of the model parameters with varying degrees of within-cluster variance heterogeneity.
ISSN:0022-0973
1940-0683
DOI:10.1080/00220973.2020.1858015