A generalized logistic item response model parameterizing test score inappropriateness

Abstract

The person response curve has been suggested as a possible model for test score inappropriateness (Lumsden, 1977, 1978; Weiss, 1973). The two-parameter person response curve proposed by Lumsden includes a person slope parameter but abandons the notion of differential item relatedness to the underlying trait. As an alternative, a generalized logistic model is considered that includes all item parameters of the three-parameter logistic model (Birnbaum, 1968). In addition to the usual person location parameter, the model has extra person parameters representing two possible characterizations of test score inappropriateness: a slope parameter indicating the degree to which a person responds differently to items of varying difficulty, and an asymptote parameter measuring a person’s proclivity to engage in effective guessing or to omit items in the presence of partial information. To assess the model’s feasibility, statistical comparisons were made between parameter estimates from data simulated according to the model and the original simulation parameters. The results seem encouraging, but additional empirical study is needed before firm conclusions can be drawn.