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INSERTING THE Q-MATRIX INTO MULTIDIMENSIONAL ITEM RESPONSE THEORY MODELS
Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. Practical situations may require a flexible multidimensional structure, different from the usual structure where all items evaluate the multiple latent traits considered. Existing MIRT models do not have in their composition a practical way for the user to define the items that evaluate each of the latent traits considered. To present and evaluate the idea of incorporating Q-matrices in MIRT models, we first formulate the multidimensional 2 parameter logistic model with the Q-matrix (M2PL-Q model). Then, we performed two simulation studies. The first simulation study examined the parameter recovery of the M2PL-Q, and the second simulation study examined the impact of the misspecified Q-matrix on the parameter estimates. In order to explore the effects on the estimation of the parameters caused by the incorporation of the Q-matrix in MIRT models, we performed an applied study with a real dataset with 2,922 individuals who answered 28 items on the Examination for the Certificate of Proficiency in English (ECPE). Incorporating the Q-matrix into the composition of IRT models provides some practical benefits. First, relationships between items and latent traits can be specified directly during test development and incorporated into the model through the Q-matrix in a user-friendly manner. In addition, these constraints provided by the Q-matrix decrease the number of discrimination parameters of the model, simplify the estimation process, increase the accuracy of latent trait estimates, and considerably shorten the estimation time as compared to a fully unrestricted MIRT.
item response theory; MIRT models; Q-matrix; diagnostic measurement; flexible multidimensional structure; multidimensional two-parameter model
Teoria da Resposta ao Item
Marcelo Andrade da Silva, Ren Liu, Jorge Luis Bazán, Anne Corinne Huggins-Manley