Qual Quant (2013) 47:811–816
Note on differential weight averaging models
in functional measurement
Published online: 24 August 2011
© Springer Science+Business Media B.V. 2011
Abstract Averaging Models have a large diffusion in several different areas of
psychological and social research. They consist of a two parameters representation: a scale
value for the subjective location of the stimulus on the response dimension and a weight
for its importance in the integrated response. In the present paper we suggest a light but
significant modiﬁcation of the traditional formula used to represent the model in order to
make clear some relevant properties of the model, which are essential to obtain unique and
unbiased parameter estimations when a differential-weight averaging model is considered.
This representation favors a superior understanding of the distinction between scale-values
and importance-weights in order to realize what differences in weight could mean when we
analyze empirical data coherent with an Averaging Model.
Keywords Averaging · Functional measurement · Integration · Valuation
Anderson (1981, 1982) has developed Information Integration Theory (IIT) around three
interlaced conceptualizations: stimulus valuation and integration, cognitive algebra, and func-
Behavior depends upon the join action of multi-stimuli conditions and IIT is mainly
concerned with the processes to extract information from observable stimuli conditions
(valuation) and to assemble this information to produce a response (integration).
Cognitive algebra relates to algebraic models, which are very common in cognitive sci-
ences, starting from the assumption that when two or more variables are integrated, coherently
with some algebraic model, the pattern of response can unveil the structure of the covert rules
of the model (Anderson 1996).
G. Vidotto (
Department of General Psychology, University of Padua, Via Venezia 8, 35131 Padova, Italy