  In this paper, we apply Vuong's (1989) general approach of model selection to
the comparison of nested and non-nested unidimensional and multidimensional
item response theory (IRT) models. Vuong's approach of model selection is
useful because it allows for formal statistical tests of both nested and
non-nested models. However, only the test of non-nested models has been applied
in the context of IRT models to date. After summarizing the statistical theory
underlying the tests, we investigate the performance of all three distinct
Vuong tests in the context of IRT models using simulation studies and real
data. In the non-nested case we observed that the tests can reliably
distinguish between the graded response model and the generalized partial
credit model. In the nested case, we observed that the tests typically perform
as well as or sometimes better than the traditional likelihood ratio test.
Based on these results, we argue that Vuong's approach provides a useful set of
tools for researchers and practitioners to effectively compare competing nested
and non-nested IRT models.
