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

Abstract

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.

Applications of operant demand to treatment selection II: Covariance of evidence strength and treatment consumption

“…The ZBE model extends the framework presented in Hursh and Silberberg (2008) by replacing the log scale with a log-like alternative (Inverse Hyperbolic Sine). Among several differences, the log-like scale used in this model supports a true lower bound at zero (for a discussion of this issue, see Gilroy, 2021), if necessary, and multiple implementations of this model exist (see Eqs. 1-3).…”

Applications of operant demand to treatment selection III: Consumer behavior analysis of treatment choice

“…Specifically, the ZBE model was used to assess caregiver consumption of units of therapy (Q) as a function of price (P) per hour of therapy. This model extends the framework presented in Hursh and Silberberg (2008) by using a modified scale (Inverse Hyperbolic Sine) to support a true lower bound at zero consumption (for a discussion of issues with zero limits, see Gilroy, 2022). The ZBE model also has multiple forms (see Eqs.…”

Using crowdsourcing to study the differential effects of cross-drug withdrawal for cigarettes and opioids in a behavioral economic demand framework.

“…The k span parameter was determined for each drug, one for cigarettes and one for opioids using the GetK function from the beezdemand package (Kaplan et al, 2019), which determines k empirically from the log 10 mean range of consumption +0.5. A constant was added to the span parameter (the default calculation for k in the beezdemand package), which can allow for the model to more closely approximate 0 levels of consumption (see Gilroy, 2022). Drug specific k parameters were used because the consumption for cigarettes was substantially higher than doses of opioids and a distinct k for each drug would allow for appropriate comparisons between withdrawal conditions within a drug.…”