Hidden equivalence in the operant demand framework: A review and evaluation of multiple methods for evaluating nonconsumption.

Operant translations of behavioral economic concepts and principles have enhanced the ability of researchers to characterize the effects of reinforcers on behavior. Operant behavioral economic models of choice (i.e., Operant Demand) have been particularly useful in evaluating how the consumption of reinforcers is affected by various ecological factors (e.g., price, limited resources). Prevailing perspectives in the Operant Demand Framework are derived from the framework presented in Hursh and Silberberg (2008). Few dispute the utility of this framework and model, though debate continues regarding how to address the challenges associated with logarithmic scaling. At present, there are competing views regarding the handling of nonconsumption (i.e., 0 consumption values) and under which situations that alternative restatements of this framework are recommended. The purpose of this report was to review the shared mathematical bases for the Hursh and Silberberg and Koffarnus et al. (2015) models and how each can accommodate nonconsumption values. Simulations derived from those featured in Koffarnus et al. were used to conduct tests of equivalence between modeling strategies while controlling for interpretations of residual error as well as the absolute lower limit. Simulations and proofs were provided to illustrate how neither the Hursh and Silberberg nor Koffarnus et al. models can characterize demand at 0 and how both ultimately arrive at the same upper and lower limits. These findings are discussed, and recommendations are provided to build consensus related to zero consumption values in the Operant Demand Framework.