Theoretical note: Quantity and concentration as co-determinants of the reinforcing value of sucrose: A re-analysis of some previously published data

According to the Multiplicative Hyperbolic Model of reinforcer value (MHM), the overall value of a reinforcer may be defined by the multiplicative combination of a set of hyperbolic functions, each of which defines the impact of a particular feature of the reinforcer (e.g., quantity, immediacy of delivery). A previous experiment found that the relationship between the indifference volumes (q_A(50)) of reinforcer A (a 0.4-M sucrose solution) and the fixed volume (q_B) of reinforcer B (a 0.2-M sucrose solution: 32 – 256 μl) was consonant with this model. This paper describes a re-analysis of those data in an attempt to identify the nature of the effect of concentration on the two parameters of the size/value hyperbola (asymptote, ε, and sensitivity, Q). Comparison of two versions of the model in which (i) both parameters were free to vary as a function of q_B and (ii) only ε was free to vary, showed that the latter model provided a satisfactory account of the data and that the inclusion of Q as an additional free parameter was not justified. Implications for the development of MHM are discussed.