Multidimensional linking for tests with mixed item types

Lihua Yao*, Keith Boughton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Numerous assessments contain a mixture of multiple choice (MC) and constructed response (CR) item types and many have been found to measure more than one trait. Thus, there is a need for multidimensional dichotomous and polytomous item response theory (IRT) modeling solutions, including multidimensional linking software. For example, multidimensional item response theory (MIRT) may have a promising future in subscale score proficiency estimation, leading toward a more diagnostic orientation, which requires the linking of these subscale scores across different forms and populations. Several multidimensional linking studies can be found in the literature; however, none have used a combination of MC and CR item types. Thus, this research explores multidimensional linking accuracy for tests composed of both MC and CR items using a matching test characteristic/response function approach. The two-dimensional simulation study presented here used real data-derived parameters from a large-scale statewide assessment with two subscale scores for diagnostic profiling purposes, under varying conditions of anchor set lengths (6, 8, 16, 32, 60), across 10 population distributions, with a mixture of simple versus complex structured items, using a sample size of 3,000. It was found that for a well chosen anchor set, the parameters recovered well after equating across all populations, even for anchor sets composed of as few as six items.

Original languageEnglish (US)
Pages (from-to)177-197
Number of pages21
JournalJournal of Educational Measurement
Issue number2
StatePublished - Jun 2009

ASJC Scopus subject areas

  • Education
  • Developmental and Educational Psychology
  • Applied Psychology
  • Psychology (miscellaneous)


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