Equating is a statistical process used to accomplish score comparability so that the scores from the different test forms can be used interchangeably. One of the most widely used equating procedures is unidimensional item response theory (UIRT) equating, which requires a set of assumptions about the data structure. In particular, the essence of UIRT rests on the unidimensionality assumption, which requires that a test measures only a single ability. However, this assumption is not likely to be fulfilled for many real data such as mixed-format tests or tests composed of several content subdomains: failure to satisfy the assumption threatens the accuracy of the estimated equating relationships.
The main purpose of this dissertation was to contribute to the literature on multidimensional item response theory (MIRT) equating by developing a theoretical and conceptual framework for true-score equating using a simple-structure MIRT model (SS-MIRT). SS-MIRT has several advantages over other complex MIRT models such as improved efficiency in estimation and a straightforward interpretability.
In this dissertation, the performance of the SS-MIRT true-score equating procedure (SMT) was examined and evaluated through four studies using different data types: (1) real data, (2) simulated data, (3) pseudo forms data, and (4) intact single form data with identity equating. Besides SMT, four competitors were included in the analyses in order to assess the relative benefits of SMT over the other procedures: (a) equipercentile equating with presmoothing, (b) UIRT true-score equating, (c) UIRT observed-score equating, and (d) SS-MIRT observed-score equating.
In general, the proposed SMT procedure behaved similarly to the existing procedures. Also, SMT showed more accurate equating results compared to the traditional UIRT equating. Better performance of SMT over UIRT true-score equating was consistently observed across the three studies that employed different criterion relationships with different datasets, which strongly supports the benefit of a multidimensional approach to equating with multidimensional data.