Bayesian estimation of multidimensional polytomous item response theory models with Q-matrices using Stan

Autor(es)

da Silva, Marcelo A. ^[1] ; Liu, Ren ^[2] ; Huggins-Manley, Anne Corinne ^[3] ; Bazan, Jorge L. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Luiz de Queiroz Coll Agr ESALQ, BR-13418900 Piracicaba - Brazil

^[2] Univ Calif Merced, Sch Social Sci Humanities & Arts, Merced, CA - USA

^[3] Univ Florida, Coll Educ, Gainesville, FL - USA

^[4] Univ Sao Paulo, Inst Math & Comp Sci, Sao Carlos - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION; SEP 2021.
• Citações Web of Science: 0

Resumo

The Q-matrix is commonly used in diagnostic classification models and has recently been incorporated into the multidimensional item response theory (MIRT) models to add information about the relationship between items and dimensions of the latent trait. The reformulation of the MIRT models with Q-matrix (MIRT-Q) has presented to improve the precision of the parameters of these models and to provide a simple and intuitive method for users to define the item-trait relationship. This paper aims to explore the incorporation of the Q-matrix in the formulation of MIRT models for polytomous item responses. Specifically, we introduce the incorporation of the Q-matrix into two of the polytomous MIRT models most known and used: the multidimensional graded response (MGR) model, hereinafter called MGR-Q, and the multidimensional generalized partial credit (MGPC) model, hereinafter called MGPC-Q. We provide readers the code of the MGR-Q and MGPC-Q models in Stan, a Bayesian estimation software, and we conduct a simulation study in order to evaluate the parameter recovery of the estimation method. To illustrate the use of both models in practice, we fit them to an operational dataset from 2400 individuals on 13 items and demonstrate the estimation of MGR-Q and MGPC-Q using the Stan program. (AU)

• Processo FAPESP: 17/15452-5 - Novos modelos de regressão para dados com resposta binária e/ou limitada
• Beneficiário: Jorge Luis Bazan Guzman
• Modalidade de apoio: Bolsas no Exterior - Pesquisa