In praise of the hyperbola

Following a recent review by Killeen (2024) on the utility of hyperbolic functions in the experimental analysis of behavior, this article discusses recent developments of the multiplicative hyperbolic model (MHM) of reinforcer value, according to which "value" is defined as a dimensionless intervening variable derived from the multiplicative combination of separate hyperbolic functions that represent the influence of particular features of a reinforcing event (e.g. quantity, immediacy). The data reviewed here pertain to the choice behavior of rats responding for soluble reinforcers, such as sucrose solutions. Three main areas are covered: the determinants of the maximal value attainable with a particular reinforcer, the incorporation of concentration as a hyperbolic term in the definition of value, and the values of mixtures of appetitive and aversive tastants. It is argued that MHM is fundamentally a descriptive model; value is dimensionless, and its subordinate intervening variables, which define the individual hyperbolic functions, are either dimensionless or share the same scale of measurement as their respective independent variables. Therefore, it would be a mistake to identify any part of the model with any underlying biological entity. A comparison is drawn between MHM and its algebraically close analogue, classical pharmacological receptor theory.