Between-Item Multidimensional IRT: How Far Can the Estimation Methods Go?

Multidimensional item response models are known to be difficult to estimate, with a variety of estimation and modeling strategies being proposed to handle the difficulties. While some previous studies have considered the performance of these estimation methods, they typically include only one or two methods, or a small number of factors. In this paper, we report on a large simulation study of between-item multidimensional IRT estimation methods, considering five different methods, a variety of sample sizes, and up to eight factors. This study provides a comprehensive picture of the methods’ relative performance, as well as each individual method’s strengths and weaknesses. The study results lead us to make recommendations for applied research, related to which estimation methods should be used under various scenarios.

A multidimensional IRT model for continuous and graded responses with error in persons and items

This article proposes two multidimensional extensions of existing DMs: the M-DTCRM, intended for (approximately) continuous responses, and the M-DTGRM, intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the IRT parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates.

A multidimensional IRT model for continuous and graded responses with error in persons and items

This article proposes two multidimensional extensions of existing DMs: the M-DTCRM, intended for (approximately) continuous responses, and the M-DTGRM, intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the IRT parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates.