bilinmodel {dyad}R Documentation

Gottman-Murray Marriage Model with Bilinear Influence

Description

Fit the Gottman-Murray marriage model with the bilinear influence function, optimizing the threshold.

Usage

bilinmodel(observations, mpr = NA)

Arguments

observations A data frame with two columns, one for the wife (person 1) and one for the husband (person 2) scores for each unit of time
mpr Minimum number of observations per regime. If not specified, set to 10% of observations.

Details

This function fits the following Gottman-Murray model of marriage, where input is a series of discrete observations of the wife (W) and the husband (H). The same model can apply to single-sex couples, in which case the wife should be interpreted as partner 1 and the husband as partner 2.

The Gottman-Murray equations of marriage are written as follows.

W(t+1) = a0 + a1*W(t) + IHW(H(t))

H(t+1) = b0 + b1*H(t) + IWH(H(t))

In these equations, one partner exerts influence on the other as a function of the previous timestep, denoted by the function IHW (influence of the husband on the wife) or IWH (influence of the wife on the husband).

The influence function here is a bilinear function. This function consists of two linear pieces, which we refer to as the negative and positive regime, while the influence is zero at the threshold between regimes. If we plot H(t) against IHW, we adjust the threshold of H(t) to obtain the best least squares fit to both lines.

Parameters are estimated simultaneously using the method described by Hamaker, E., Zhang, Z., and Van der Maas, H.L. (See References).

Value

bilinmodel returns a list consisting of the results (the parameters fit by the model) for the wife (person 1) and the husband (person 2), corresponding to the solution to first and the second Gottman-Murray equations of marriage above. Each set of results is an object of class bilinmodel. Although variable names (e.g., a0 and a1) are the same for each object, their values correspond to the model fit to the husband or wife (and are generally different for each spouse). Therefore, a0 and a1 for the husband's results should be interpreted as b0 and b1 in the equation for the husband above.
The plot method for bilinmodel objects graphs the partner score against the influenced component and the interpolated influence function. For example, for the wife results, this would plot the husband score against the influence of the husband on the wife.
An object of class bilinmodel contains the following parameters.

a0 Initial state
a1 Inertia
ls Slope for influence function left of the threshold
rs Slope for influence function right of the threshold
th Threshold
ss Sum squared residuals
loglik Log likelihood assuming equal variance of residuals across regimes
nparams Number parameters, assuming unequal variance of residuals across regimes
BICeq Bayesian Information Criterion calculated assuming equal variance of residuals across regimes
BICneq Bayesian Information Criterion calculated assuming unequal variance of residuals across regimes
AICeq Akaike's Information Criterion calculated assuming equal variance of residuals across regimes
AICneq Akaike's Information Criterion calculated assuming unequal variance of residuals across regimes
nt Number of observations
score Vector of partner data (from 1 to nt-1)
influence Vector of influence, calculated using a0 and a1 above

Author(s)

Tara Madhyastha and Ellen Hamaker

References

For a general description of the marriage model and influence functions, see Gottman, J. M., Murray, J. D., Swanson, C., Tyson, R., & Swanson, K. R. (2003). The Mathematics of Marriage: Dynamic Nonlinear Models. The MIT Press.

The method of parameter estimation used here is described in Hamaker, E., Zhang, Z., Van der Maas, H.L. Using threshold autoregressive models to study dyadic interactions. Psychometrika, in press.

See Also

noinfmodel, linmodel, ojivemodel, combimodel, origmodel

Examples

require(dyad)
data(couple)
## fit a bilinear model
fit <- bilinmodel(couple);
## plot influence function for husband on wife
plot(fit$wife)


[Package dyad version 1.0 Index]