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Mathematical models and methods 567
After Thurstone, one of the pioneers of this type of research is Hotelling.
In particular, the latter showed that, assuming certain classical hypotheses
(generalizations of the hypotheses of Spearman), the eigenvalues of the correlation
matrix measure the relative importance of factors F,, Fz ... Fn, while
the eigenvectors of this matrix measure the ‘saturations’ (a coefficients). Recently,
dimensional models which are less restrictive in the hypotheses which they
introduce have been propounded by researchers such as Guttman and Shepard.36
There has been much discussion of the compass of these methods of dimensional
analysis. As in the case of measurement models, we find, at least initially,
a tendency to interpret the results of these models in a literal, absolute sense,
the object being deemed, as Thurstone himself put it, to achieve a scientific
identification of the mental ‘faculties’ beloved of scholastic philosophy. Nowadays,
the quality mainly seen in these analyses is that of descriptive models
usable, as the case may be, on problems of grouping or of classification or over
the construction of typologies. This new epistemological attitude probably
derives at least partly from the fact that these methods, used only in psychometric
contexts to begin with, have since been used in other fields (classification
of groups, geographical regions, etc.) working on an assemblage of observable
characteristics.
To conclude it should beInoted that it is probably not by chance that the
principal development of classification and measurement models should have
been in the frame of reference of psychology and sociology. The reason is that
most of the variables used in these disciplines are at once qualitative, and not
directly observable. In economics, on the other hand, the variables are usually
quantitative by nature. This is why, whereas psychology and sociology have
constructed what might be called a general theory of measurement, economics
has concentrated above all on the measurement problems posed by specific
concepts, such as ‘utility’.
C. Inductive models
In relation to the two preceding classes, inductive models are in some sort a
residual class. The characteristic they have in common is that of being ver$iabZe
theories. It is here that they differ, say, from game theory or from the formal
theory of grammar, which are theories inspired by real situations but are not
verifiable in the true sense of the term.
Among the inductive models several sub-categories can be distinguished :
some have a predictive, and others an explanatory bias. Some are adjuncts of
experimentation and others of observation. Some are ‘structural’, others are
not.
The distinction between the first two types is not always easy to make.
Nevertheless, a large number of models can be cited whose sole function is
predictive, as with the electoral models associated with names such as Ithel de
Sola Pool and Rosenthal.37 These models use well established information such
as the variation of voting behaviour with age, sex, religious predilections, socio-