Abstract

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Researchers should cite this work as follows:

• Nielsen, F. (2023). 1981-Nielsen_Francois-Rachel_Rosenfeld-Substantive_Interpretations_of_Differential_Equation_Models. SIMIODE, QUBES Educational Resources. doi:10.25334/81FC-2A33

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Nielsen, Francois and Rachel A. Rosenfeld. 1981. Substantive Interpretations of Differential Equation Models. American Sociological Review. 46: 159-174.

Article Abstract: The use of differential equations models to study social processes has been increasing rapidly. There are, however, ambiguities in the interpretation of the parameters of these models. We suggest that the interpretation of the parameters can best be developed by focusing on the equation for the trajectory over time of the dependent variables (the integral), rather than on the equation for the instantaneous rate of change (the differential equation). The equation for the trajectory can be decomposed into two distinct and substantively meaningful components: one describing the speed of the process away from initial levels of the dependent variable, and one describing factors affecting the value of the dependent variable reached at equilibrium. The interpretation of parameters of dynamic models is illustrated with reference to research on two substantive topics: political mobilization and intragenerational mobility.

This paper offers a rich (albeit captured in 1981) set of materials on using differential equations in sociology.

The examples offered are almost always simple first order or linear systems of first order differential equations. Much discussion centers on the meaning of the coefficients and the qualitative analysis and their interpretations in support of theory.