ojivemodel {dyad}R Documentation

Gottman-Murray Marriage Model with Ojive Influence

Description

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

Usage

ojivemodel(observations, nregime = 3, 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.
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 3.
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 an ojive function. This is based on the assumption that the influence of one partner on the other is constant until his/her behavior passes some critical value or threshold. The region to each side of the threshold is referred to as a regime. The ojive function used here is proposed by Hamaker, E., Zhang, Z., and Van der Maas, H.L. (See References).

For values in each regime, a horizontal line is fit to the influence. By varying the threshold values (one threshold if 2 regimes are used, and two thresholds if 3 regimes are used) we can determine the fit with the minimum sum of squares residuals. We can write the ojive influence functions as IHW(H(t))

l1 if H_t <= nth

0 if nth < H_t

l1 if pth < H_t

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

Value

ojivemodel 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 ojivemodel. 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 ojivemodel 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 ojivemodel contains the following parameters, depending on the number of regimes specified.

a0 Initial state
a1 Inertia
l1 Difference in constant between neutral regime and negative regime
l2 Difference in constant between positive regime and neutral regime (3 regime only)
th Threshold (2 regime only)
nth Threshold between negative and neutral regime (3 regime only)
pth Threshold between positive and neutral regime (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, combimodel, origmodel

Examples

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


[Package dyad version 1.0 Index]