Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair

Abstract

This chapter introduces a new use of mathematical modelling and a new approach to the modelling of social interaction using difference equation models such as we discussed in Chapter 3. These equations express, in mathematical form, a proposed mechanism of change of marital interaction over time. The modelling is designed to suggest a precise mechanism of change. In much of this book the aim of the methodology is quantitative. That is, on the basis of our psychological understanding we write down, in mathematical form, the causes of change in the dependent variables. In the field of family psychology, however, statistical analysis is the usual analytical approach and, furthermore, generally based on linear models. In recent years it has become increasingly clear that most systems are highly nonlinear. The new approach to studying marital interaction with mathematical models was initiated by J. M. Gottman, based on his extensive studies of family interaction, and J.D. Murray (see the book by Gottman et al. 2002 for considerably more psychological detail and several case studies which have used the modelling technique and philosophy described in this chapter). The material we discuss here is based in large part on the paper by Cook et al. (1995).