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 (Lums den, 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 consid ered that includes all item parameters of the three- parameter logistic model (Birnbaum, 1968). In addi tion 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 per son responds differently to items of varying difficulty, and an asymptote parameter measuring a person's pro clivity 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 ac cording to the model and the original simulation parameters. The results seem encouraging, but addi tional empirical study is needed before firm conclu sions can be drawn.