Comparison of Three Unidimensional Approaches to Represent a Two-Dimensional Latent Ability Space

All test data represent the interaction of examinee abilities with individual test items. It has been argued that for most tests these interactions result in, either unintentionally or intentionally, multidimensional response data. Despite this realization, many standardized tests report a single score which follows from fitting a unidimensional model to the response data. This process is justified with the understanding that the response data, when analyzed, say for example by a principal component analysis, have a strong, valid, and content identifiable first component and weaker minor inconsequential components. It is believed that the resulting observed score scale represents primarily a valid composite of abilities that are intended to be measured. This study examines three approaches which estimate unidimensional item and ability parameters based on the parameters obtained from a two-dimensional calibration of the response data. The goal of this study is to compare the results of the different approaches to see which best captures the results of the two-dimensional calibration.