We need to score a combined test of English + Maths + Science. Would prefer to take IRT route to classical scoring as want to identify top 0.5% performers. Looked into multidimensional models as an possible solution.

The literature on MIRT talks about loading on multiple skills but could not find any actual use case similar to what I need to do.

Is there any theoretical/empirical guidance on how disparate the skills can be. Is MIRT only used for a subject and subskills within that or multiple subjects can be merged?


In IRT, it is differentiated between between-item multidimensionality and within-item multidimensionality (e.g., Adams, Wilson, & Wang, 1997, doi:10.1177/0146621697211001). That means, every item is either only indicative of single trait (between), or some (or even all) of the items may be indicative of more than one trait (within). You may use MIRT in both cases.

Apart from that, MIRT may be used with uncorrelated or correlated traits (it may not make much sense if your traits correlated in the .90s, but apart from that, there is no restriction). Moreover, second (/higher) order item response models have been developed (e.g., Huang, Wang, Chen, & Su, 2013, doi:10.1177/0146621613488819) for traits that have a hierarchical structure, and bi-factor IRT models are available as well.


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