Revista Colombiana de Estadística
Print version ISSN 0120-1751
MONTENEGRO DIAZ, ÁLVARO MAURICIO and CEPEDA, EDILBERTO. Synthesizing the Ability in Multidimensional Item Response Theory Models. Rev.Colomb.Estad. [online]. 2010, vol.33, n.1, pp. 127-147. ISSN 0120-1751.
A central problem associated with Multidimensional Item Response Theory (MIRT) Models is the impossibility of ordering the examinees. In this paper, we obtain two unidimensional synthetic indices that are optimal linear combinations of the ability vector. These synthetic indices are similar to the reference composite commonly used in MIRT models, but they are easier to calculate and interpret. The synthetic indices are compared with the unidimensional ability obtained when a multidimensional data is fitted with an unidimensional IRT (UIRT) model.
Keywords : Binary response; Item response theory; Index; Multidimensional data; Synthetic estimator; Latent trait.