文摘
We empirically assessed the utility of separable (two-stage) models varying in functional form for describing supra-threshold magnitude scaling using joint magnitude estimation (JME). We obtained the raw data from a JME experiment conducted by Ramsay (1979). In that experiment, participants were shown a pair of irregular polygons, whose areas were systematically varied across trials. Participants were asked to assign a number to the combined area of the two polygons. We compared sixteen separable models formed through a factorial combination of functional forms for both the input and output stages. Model selection was based on minimum description length (MDL), and information criteria measures. The MDL results showed that models having linear or power functions were commonly selected, and that the position of the power stage (input or output) varied across participants. However, the information criteria measures showed that models including the Prelec form for the weighting function were chosen for the majority of participants. Both model selection methods supported separable models, which is inconsistent with the traditional view of Stevens that numeric responses are subjective magnitudes.
