Quality & Quantity 35: 173–189, 2001.
© 2001 Kluwer Academic Publishers. Printed in the Netherlands.
Using Single-Equation Models of
Function-of-Functions Type in Sociological
Department of Sociology, Stockholm University, S-106 91 Stockholm, Sweden
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Abstract. This paper argues that single-equation explanatory models of many types of social
phenomena should not be built in accordance with established sociological ways of thinking. In
sociological research, the focus is often on the causal mechanisms behind phenomena, and it is
often interesting to use models that show the hierarchical causal structure, that is, how inﬂuences are
nested in the causal process. I propose such a model with a form that reﬂects a two-step structure.
According to this model, the dependent factor is a product of independent factors that are linear
functions of variables. The model, which should be used with the factor product in unexpanded form,
can be assumed to have wide application. However, the models used in sociological research and
discussed in textbooks are generally very different. They do not have a function-of-functions form,
but take a form in which variables are directly entered. Furthermore, even if they take interaction into
consideration, they are linear in an extended sense because they construe it as one or more terms that
are products of single variables. In comparison with the proposed type of model, these models are
technically simpler. However, this paper argues that the proposed type of model is superior in many
contexts because it better reﬂects the causal process.
Key words: Form of models, hierarchical causal structure, interaction, non-linearity
Broadly speaking, sociology is not very successful as an explanatory discipline.
Certainly, there are many exceptions, but it seems that there are many social phe-
nomena that are unsatisfactorily explained. One reason for this may be that the
mathematical models commonly used to explain phenomena have an inappropriate
form. In this paper I discuss the advantages and disadvantages of using models
with a new form that, in my opinion, are superior to the models traditionally used
in many contexts.
The particular form that mathematical models should take is, of course, im-
possible to deﬁne in a general way since there are many types of social phenomena
that may be explained in many different ways. However, it is possible to say some-
thing about the adequate form of many models, especially when considering the
types of models that are now commonly used. The single-equation models found
in current sociological research often have a very simple form. Most models for