Mathematics of marital conflict: Qualitative dynamic mathematical modeling of marital interaction.

Rebecca C. Tyson · Jane White · Regina H. Rushe · John Mordechai Gottman · James Murray

90 citations0/0 files storedJournal of Family Psychology

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Attachment and Relationship Dynamics Family Dynamics and Relationships Counseling, Therapy, and Family Dynamics

Abstract

This article presents a new nonstatistical mathematical approach to modeling marital interaction by means of nonlinear difference equations. The application made of this modeling process in this article is to generate theory in order to understand J. M. Gottman and R. W. Levenson's (1992) report of the ability of one variable derived from a balance view of marital interaction to predict marital dissolution in a prospective study. Parameters are introduced that reflect uninfluenced husband and wife set points, emotional inertia, and influence function. These parameters are subjected to various examinations of validity with other data that reflect patterns of marital interaction and the cascade toward marital dissolution. Results suggest the hypothesis that unstable marriages are characterized at Time 1 by a mismatch in husband and wife influence functions. The modeling method makes it possible to fit a couple's equations under one set of conditions, then to simulate the couple's interaction under different conditions, and then to conduct experiments to test the validity of these simulations. The method provides a new approach toward the building of theory in family psychology. This article introduces a new approach to the modeling of social interaction using the mathematics of difference and differential equations. These equations express, in mathematical form, a proposed mechanism of change over time. They do not represent a statistical approach to modeling; rather they are designed to suggest a precise mechanism of change. This method has been used with great success in the biological sciences (Murray, 1989). The method is usually a quantitative approach that requires the modeler to be able to write down in mathematical form, on the basis of some theory, the causes of change in the dependent variables. For example, in the classic predator-prey problem, a modeler writes down that the rate of change in the population densities is some function of the current densities (e.g., Murray, 1989). Although this

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References

1978Facial Action Coding System 1975Pragmatics of Human Communication 1982Marital Interaction: Experimental Investigations.1992Marital processes predictive of later dissolution: Behavior, physiology, and health.1993The roles of conflict engagement, escalation, and avoidance in marital interaction: A longitudinal view of five types of couples.1995What Predicts Divorce?1973Defensive and supportive communications in normal and deviant families.1971Marital Interaction Coding System.

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