Parsimonious item response theory modeling with the negative log-log link: The role of inflection point shift.

Abstract

In item response theory (IRT) modeling, the magnitude of the lower and upper asymptote parameters determines the degree to which the inflection point shifts above or below P = 0.50. The current study examines the one-parameter negative log-log model (NLLM), which is characterized by a downward shift in the inflection point, among other distinctive psychometric properties. After detailing the statistical foundations of the NLLM, we present a series of simulation studies to establish item and person parameter estimation accuracy and to demonstrate that this parsimonious model addresses the "slipping" effect (i.e., unexpectedly incorrect answers) via an inflection point < 0.50 rather than through computationally difficult estimation of the upper asymptote. We then provide further support for these simulation results through empirical data analysis. Finally, we discuss how the NLLM contributes to recent methodological literature on the utility of asymmetric IRT models.