Robustness of the Polytomous IRT Model to Violations of the Unidimensionality Assumption

The robustness of the polytomous Item Response Theory (IRT) model to violations of the unidimensionality assumption was studied. A secondary purpose was to provide guidelines to practitioners to help in deciding whether to use an IRT model to analyze their data. In a simulation study, the unidimensionality assumption was deliberately violated by using two-dimensional data. The "impact," or change in the error due to violating the assumption, was calculated to assess the effects of the violation on ability estimation. The effects of problematic variables on absolute impacts and their interactions were analyzed, and a factor analysis using the principal component method was conducted to provide guidelines to practitioners on the computer-generated generated data. The precision of the estimated ability was determined in four ways. When the ability estimate was assumed to measure the average ability and the major ability of two unequally important abilities, the procedure was generally robust to the violation. However, when the ability estimate was assumed to measure one of the two equally important abilities and the minor ability of two unequally important abilities, the estimation procedure was not robust. Results from the analysis of variance were consistent with the results from analyzing the relative impacts. (Contains 5 tables and 47 references.) (Author/SLD)