Published On: 26/10/2012|Categories: 2008–2012, Vol.33 (2012), Vol.33 (3)|
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An important open issue in Functional Measurement is whether the three most important models of cognitive algebra are sufficient to describe the great majority of possible response behaviors. Generally speaking, the individual response R is a function of the subjective scale values sk and can be imagined as a continuous manifold. First and second order terms of a Taylor series are often used to locally approximate the shape of such a generic function. In this work we suggest that almost any response surface can be approximated by an additive, multiplicative or averaging model, considering that the Taylor expansion is cut at the second order at most. In particular, additive and multiplicative models appear to hold as global approximations, while the averaging model appears to be a connection of local approximations.

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