Abstract

For polytomous items with m ordered response categories, the nominal response model (NRM; Bock, 1972) allows researchers to estimate m – 1 category “boundary” discrimination (CBD) parameters. These CBD parameters provide important diagnostic information regarding item functioning. Specifically, in ordered polytomous data, a CBD parameter reflects the degree to which a particular response category distinction is useful in discriminating among individuals. Unfortunately, research applying the NRM model to ordered categorical responses is essentially nonexistent. Hence, we illustrate several potentially useful applications of the NRM including exploring whether: a) CBD parameters vary within an item, b) an item contains too many response options, and c) responses options are ordered. We also conducted Monte Carlo simulations to investigate the power of the likelihood-ratio and Wald tests to detect: a) different degrees of within-item variation in CBD parameters, and b) when a single within-item CBD parameter equals zero. Results support the utility of the likelihood-ratio and Wald tests for identifying items where response option choices are differentially discriminating, and for identifying items that contain poorly functioning response options.