Bi-Factor MIRT Observed-Score Equating for Mixed-Format Tests

Abstract

The main purposes of this study were to develop bi-factor multidimensional item response theory (BF-MIRT) observed-score equating procedures for mixed-format tests and to investigate relative appropriateness of the proposed procedures. Using data from a large-scale testing program, three types of pseudo data sets were formulated: matched samples, pseudo forms, and simulated data sets. Very minor within-format residual dependence in mixed-format tests was found after controlling for the influence of the primary general factor. The unidimensional IRT and BF-MIRT equating methods produced similar equating results for the data used in this study. When a BF-MIRT model is implemented, we recommend the use of observed-score equating instead of true-score equating because the latter requires an arbitrary approximation or reduction process to relate true scores on test forms.

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