combimodel {dyad}R Documentation

Gottman-Murray Marriage Model with Combination of Bilinear and Ojive Influence

Description

Fit the Gottman-Murray marriage model using a combination of ojive and bilinear influence, optimizing the threshold.

Usage

combimodel(observations, mpr = NA, nregime = 2)

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
nregime Number of regimes (either 2 or 3). If 2 regimes are specified, there is a negative and positive regime. If 3 regimes are specified, there is a negative, neutral, and positive regime. Default is 2.
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, where the wife should be interpreted as partner 1 and the husband as partner 2.

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 influence functions IHW (influence of husband on wife) or IWH (influence of wife on husband).

The influence function here is a combination of an ojive influence function (see ojivemodel and a bilinear influence function bilinmodel. Therefore, the model allows for large changes between regimes, as with the ojive model, and gradual variation in influence within a regime, as in the bilinear influence model.

Value

combimodel returns a list consisting of the results (the parameters fit by the model) for the wife (person 1) and the husband (person 2). Each set of results is an object of class combimodel. 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 combimodel objects graphs the partner score against the influence 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 combimodel contains the following parameters, depending on the number of regimes specified.

a0 Initial state
a1 Inertia
l1 Difference in constant between regime 1 and regime 2
l2 Difference in constant between regime 2 and regime 3 (3 regime only)
s1 Slope in regime 1
s2 Slope in regime 2
s3 Slope in regime 3 (3 regime only)
th Threshold between regime 1 and regime 2 (2 regime only)
nth Threshold between regime 1 and regime 2 (3 regime only)
pth Threshold between regime 1 and regime 2 (3 regime only)
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
nregime Number of regimes (2 or 3)
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

bilinmodel, ojivemodel, origmodel

Examples

require(dyad)
data(couple)
## fit a combination model with 3 regimes
fit <- combimodel(couple, nregime=3);
## plot influence function for wife on husband
plot(fit$husband)


[Package dyad version 1.0 Index]