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## NetLogo User Community Models

WHAT IS IT?

This is a simulation using the System Dynamics Modeler of some actual data collected by John Gottman (Gottman, et al. 2002). Gottman originally develop a non-linear equation to explain the data he collected on married couples participating in his so-called "Love Lab". This was an experimental set-up where he would take 15-20 minutes of video of married couples freely discussing an issue that they disagreed about. He and his colleagues would code the resulting data and use the scores to predict whether or not the couple would be divorced within three years. Gottman claims that the reason this can work is that over the course of a short discussion, couples socio-emotional scores demonstrate a trajectory through a state-space that quickly settles on a "set point" (a steady state). In other words, that the dynamics of human conversation are so predictable and powerful that they remain essentially unchanged over the course of years. Eventually, (and to oversimplify a bit) if the couple's set-point is in the positive range, they likely will remain married, if in the negative range, then eventually they will be at significantly higher risk of divorce. This model simulates those findings.

HOW IT WORKS

There are two main "agents" involved in the system model, the husband and the wife (technically, their emotional expressive scores over time). Each agent is associated with a formula that contains the following elements: 1) Each has a stock which represents the expression score (positive or negative) at any one point in time 2) Each has a flow containing the formula that calculates the score at time = +1 3) Three variables that affect the formula including I (the influence that one partner has on the other), a (a constant associated with the individual), and r (a measure of the rate at which one person can change or respond within the system).

Thus, for the husband, the formula is H(t+1) r1 + a + W (t=1) I(wh)
This should read, the value of the husband's score at time 1 times his rate, plus his personality, plus the value of the wife's score at the current time, times the influence the wife has on the husband. Each of these are usually represented as valued between 0 and 1 (except the scores, which can have any arbitrary initial value). The wife's formula is similar.

HOW TO USE IT

This model demonstrates how computer simulations can be used to create formulas that either match or fail to match actual data. Formulas should be derived from theory, therefore a match will represent a confirmation of that theory. Gottman himself proposed a theory in which husbands and wives influenced each others' feelings by means of conversational dynamics which, in spite of being dynamic and based on non-linear factors, remain remarkably stable over time. He tested his theory not only with equations, but by using training interventions to help couples improve their set-points.

THINGS TO NOTICE

Gottman derived his model equations more or less directly from similar equations in biology (Murray, 1989). Some of you may recognize them as being very similar in the way they operate to so-called "preditor-prey" models, found elsewhere in the Netlogo web site. In other words, seen strictly in system terms, the husband's negative expressions act as "preditors" eliminating the wife's positive expressions, and vice versa.

THINGS TO TRY

Try varying each of the three constants in the system, either simultaneously for wife and husband or seperately. You will find that different combinations of r and I most strongly affect the outcome. Unstable outcomes (where the values shoot upward indefinately, for example) are unrealistic. Models that settle down on a set of positive or negative scores demonstrate possible outcomes.

EXTENDING THE MODEL

It would be very intersting to extend the model to a "three-person" problem, outlining the dynamics that influence can take in such a situation.

CREDITS AND REFERENCES

Gottman, J., Murray, J., Swanson, C., Tyson, R., and Swanson, K. (2002). The Mathematics of Marriage: Dynamic Nonlinear Models. Cambridge, MA: MIT Press.
Murray, J. (1989). Mathematical Biology. Berlin: Springer-Verlag.

Victor Wooddell is an assistant professor at Oakland University in Rochester, Michigan, and can be contacted at wooddell@wayne.edu

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