Unbiasing the Measurement of Judgment Accuracy: A Hierarchical Extension of the Matching Parameter G of the Lens Model Equation

The G parameter of the lens model equation is a widely used measure of cue-based judgment accuracy, capturing how well individuals align their cue use with ecological validities in probabilistic environments. Despite its popularity across various research domains, the psychological interpretability of G may be severely limited when estimated in the conventional way, that is, based on separate, participant-level regression models. In this paper, we identify core statistical limitations of the conventional approach and demonstrate how these may lead to severely biased conclusions about judgment accuracy across a range of plausible scenarios. To remedy these limitations and increase the meaningfulness of G estimates, we propose a novel hierarchical modeling approach. Through extensive simulation studies, we show that the hierarchical approach yields markedly more accurate and robust G estimates, especially under realistic forms of model misspecification, such as omitted cues, omitted interactions, and misspecified nonlinear relationships. Two empirical illustrations—in the domains of healthiness judgments and metamemory—demonstrate the practical impact of modeling choice, further highlighting the bias in the conventional G parameter when misspecifying model equations. These findings challenge long-held beliefs about human judgment accuracy that were based on the conventional lens model approach. To avoid misleading conclusions due to biased estimates, we advocate for adopting the hierarchical approach as a more valid and reliable tool for measuring cue-based judgment accuracy, thereby strengthening the methodological rigor of judgment and decision-making research.