Model Selection of Nested and Non-Nested Item Response Models using Vuong Tests
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In this paper, we apply Vuong's (1989) general approach of model selection to the comparison of both nested and non-nested unidimensional and multidimensional item response theory (IRT) models. This approach is especially useful because it allows for formal statistical tests of non-nested models, and, in the nested case, it offers statistics that are highly competitive with the traditional likelihood ratio test. After summarising the statistical theory underlying the tests, we study the tests' performance in the context of IRT, using simulation studies and real data. We find that, in the non-nested case, the tests can reliably distinguish between the graded response model and the generalized partial credit model. In the nested case, the tests often perform better than the likelihood ratio test.
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