Multidimensionality and IRT‐Based Item lnvariance Indexes: The Effect of Between‐Group Variation in Trait Correlation

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Abstract
Using a bidimensional two‐parameter logistic model, the authors generated data for two groups on a 40‐item test. The item parameters were the same for the two groups, but the correlation between the two traits varied between groups. The difference in the trait correlation was directly related to the number of items judged not to be invariant using traditional unidimensional IRT‐based unsigned item invariance indexes; the higher trait correlation leads to higher discrimination parameter estimates when a unidimensional IRT model is fit to the multidimensional data. In the most extreme case, when rθ1 θ2= Ofor one group and r θ1 θ2= 1.0 for the other group, 33 out of 40 items were identified as not invariant. When using signed indexes, the effect was much smaller. The authors, therefore, suggest a cautious use of IRT‐based item invariance indexes when data are potentially multidimensional and groups may vary in the strength of the correlations among traits.