linmodel {dyad}R Documentation

Gottman-Murray Marriage Model with Linear Influence

Description

Fit the Gottman-Murray marriage model with a linear influence function.

Usage

linmodel(observations)

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

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 linear function.

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

Value

linmodel 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 linmodel. 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 linmodel 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 linmodel contains the following parameters.

a0 Initial state
a1 Inertia
ls Slope for influence function
ss Sum squared residuals
loglik Log likelihood assuming equal variance of residuals across regimes
nparams Number parameters, assuming unequal variance of residuals across regimes
BIC Bayesian Information Criterion
AIC Akaike's Information Criterion
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, ojivemodel, combimodel,bilinmodel, origmodel

Examples

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

[Package dyad version 1.0 Index]