¹Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. Assistant professor. Email: ammontenegrod@unal.edu.co
²Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. Associate professor. Email: ecepedac@unal.edu.co

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.

Key words: Binary response, Item response theory, Index, Multidimensional data, Synthetic estimator, Latent trait.

Un problema central asociado con los Modelos Multidimensionales de Teoría de Respuesta al Item (TRIM) es la imposibilidad de ordenar a los examinados. En este artículo, se obtienen dos índices sintéticos unidimensionales que son combinaciones lineales óptimas del vector de habilidades. Estos índices sintéticos son semejantes a la composición de referencia comúnmente usada en los modelos TRIM, pero son más fáciles de calcular. Los índices sintéticos se comparan con el parámetro de habilidad obtenido cuando un conjunto de datos multidimensionales es ajustado con un modelo TRI unidimensional.

Palabras clave: respuesta binaria, teoría de respuesta al ítem, índice, datos multidimensionales, estimador sintético, trazo latente.

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