KRISTIN RAE SWANSON, PhD
Departments of Pathology and Applied Mathematics
Laboratory of Neuropathology, Department of Pathology
Harborview Medical Center, 325 - 9th Avenue, Box 359791
Seattle, Washington 98104-2499
Office Location: UW Medical RR848
Phone: 206-221-6577
Fax: 206-731-8240
Website with downloadable publications:
http://www.amath.washington.edu/~swanson
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Our presentation will be based primarily on the concents of our
recent book, The Mathematics of Marriage: Dynamic Nonlinear Models,
published by MIT Press in 2003. More information about our book
can be found at:
http://www.amath.washington.edu/~swanson/papers.html
and
http://www.amath.washington.edu/~swanson/reviews.html
EXTENDED ABSTRACT
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Based on the hypothesis that without a theoretical understanding of the processes related to
marital or relationship stability and dissolution, it is difficult to design and evaluate effective
relationship therapies. Using a psychological coding system to “score” each partner in a conflict
conversation, the resultant time series can visually describe the ebb and flow of the interaction,
similar to a “Dow-Jones” industrial average for a relationship conversation. To study these time
series’ for couples’ interactions, we translated a scientific theory for relationships into
mathematical equations combining these dominant features:
Emotional inertia - an individual’s tendency to remain at their present level of affect.
Uninfluenced steady state - what the individual brings to the relationship from their history together.
Influence of one partner on the other including the general tendency for increasing levels of affect to
be responded to with increasing levels of affect.
Repair and damping of influence at extreme levels of affect; i.e., when one partner perceives that the
conversation has become too negative, he/she attempts to repair things by increasing their level
of affect. For example, telling a joke when the conversation has become particularly negative. A
similar mechanism, termed damping, is in effect for highly positive levels of affect.
For each couple, the time series data from each partner is used to estimate the parameters in the
mathematical equations. Although each couple has a unique relationship quantified by their own
characteristic model parameters, an analysis of our longitudinal studies of couples found five
dominant couple’s styles - validating, volatile, conflict-avoiding, hostile, hostile-detached. Only 2
of these styles are stable, typically resulting in long-term happy relationships.
The ability to predict the longitudinal course of marital relationships using this modeling, with an
average of over 90% accuracy, has now been reported in our laboratories in four separate
longitudinal studies (see Gottman, 1993, 1994; Gottman, Coan, Swanson, & Carrere, 1998;
Jacobson et al., 1996). It has also been extended to the study of violent marriages, and the study
of committed cohabiting gay male and lesbian relationships (Gottman et al., 2003a, 2003b).
Another major advantage of this type of modeling is that it permits and even encourages the
simulation of the couple's interaction under new conditions. For example, suppose we observe a
couple having an argument, code their interaction, and then fit a model to it, with specific
parameter values. We can then change one parameter value, such as how positive the husband
is at the start of the conversation, leaving all other parameters the same, and then simulate the
“new” interaction. That is, the model allows one to imagine how this couple may interact under
conditions different from those in which they were first observed. The modeling thus leads to
"what if” thought experiments that can be used to help design new intervention strategies.
Ultimately, this mathematical modeling approach provides a new language for not only talking
about relationships but designing new, scientifically-based, interventions.
REFERENCES:
J. M. Gottman (1993). The roles of conflict engagement, escalation, or avoidance in marital
interaction: A longitudinal view of five types of couples. Journal of Consulting and Clinical
Psychology, 61,6-15.
J.M. Gottman (1994) What predicts divorce? Hillsdale, NJ: Lawrence Erlbaum.
J. M. Gottman, J. Coan, C. Swanson, & S. Carrère. (1998). Predicting marital happiness and
stability from newlywed interactions. Journal of Marriage and the Family, 60, 5-22.
J. M. Gottman, J. D. Murray, C. C. Swanson, R. Tyson, K. R. Swanson. (2002)
The Mathematics of Marriage: Dynamic Nonlinear Models. Bradford Books, MIT Press.
J. Gottman, R. Levenson, C. Swanson, K. R. Swanson, R. Tyson, and D. Yoshimoto. (2003)
Observing Gay, Lesbian and Heterosexual Couples' Relationships: Mathematical Modeling of
Conflict Interaction, Journal of Homosexuality, 45(1):65-91
SHORT BIOGRAPHIES
John M. Gottman, Ph.D. is the Executive Director of the Relationship Research Institute, a nonprofit research institute dedicated to marriage, family and child developmental research, and cofounder of The Gottman Institute in Seattle. He is Professor Emeritus of Psychology at the
University of Washington. He graduated Magna Cum Laude from Fairleigh Dickinson University
in 1962 with a B.S. in Mathematics-Physics, obtained his M.S. in Mathematics-Psychology at the
Massachusetts Institute of Technology in 1964; his M.A. in Clinical Psychology-Mathematics from
the University of Wisconsin in 1967; and his Ph.D. in Clinical Psychology from the University of
Wisconsin in 1971. Dr. Gottman is the author of over 130 journal articles and has authored,
coauthored or edited over 30 books, including The Mathematics of Marriage, Dynamic Non-linear
Models (MIT press).
James D. Murray, DSc, FRS is an Emeritus Professor of the University of Oxford and the
University of Washington. He has a B.Sc. and Ph.D. from the University of St. Andrews, an M.A.
and D.Sc. from University of Oxford, and honorary degrees from the University of St. Andrews
and Strathclyde University. He is a Fellow of the Royal Society (London), Fellow of the Royal
Society of Edinburgh, Fellow of the Institute of Biology (UK) and a Foreign Member of the French
Academy (Sciences), Formerly: Director and Professor, Centre for Mathematicsl Biology,
University of Oxford, Philips Professor and Boeing Professor, University of Washington. He has
been a Visiting Professor at numerous universities around the world, such as Florence, Paris,
Heidelberg, MIT, Tsing Hua. He has worked on the application of mathematical models in biology
and medicine since c1970, has published several books (e.g. Mathematical Biology) and more
than 200 papers in scientific journals on a spectrum of topics, such as, animal coat markings,
wound healing, brain tumour growth, temperature dependent sex determination, animal
territoriality and survival, alligator teeth, marital interaction, spread of rabies, honeycomb patterns
and breathalysers.
Kristin Swanson, Ph.D. is a Research Assistant Professor at the University of Washington.
Kristin graduated Magna Cum Laude from Tulane University in New Orleans in 1996 with a BS in
Mathematics-Physics. She obtained her PhD in Mathematical Biology in 1999 from the University
of Washington in Seattle. She has been working with John Gottman's group to help develop
mathematical models for relationship interaction dynamics for over 6 years. She is presently on
faculty in the department of Pathology in the University of Washington School of Medicine where
she develops and analyzes mathematical models for a variety of topics in biology, medicine and
psychology ranging from cancer and imaging to relationship interactions.