Using the testlet response model as a shortcut to multidimensional item response theory subscore computation

Abstract

In the past decade, computational advances have made application of multidimensional item response theory (MIRT) models a somewhat practical endeavor. Within the context of “diagnostic assessment,” MIRT provides a way to compute subscores on a test as estimates of the latent variables, and its use for that purpose has been proposed. However, the model dimensionality desired for subscores may be too high for straightforward MIRT computation, even with contemporary algorithms and computers. The fact that the testlet response model (TRM) is a computationally convenient reparameterization of a higher-order factor model can be used as the basis of a “shortcut” to MIRT subscore estimation in some cases: Because the TRM is a constrained bifactor model, its item parameters can be estimated using two-dimensional numerical integration, regardless of the total dimensionality of the complete model. After those item parameters are estimated, they can be converted to become the parameters of the corresponding higher-order factor model, and that model can, in turn, be used to compute MIRT subscores. This presentation illustrates the process.