linmodel {dyad} | R Documentation |
Fit the Gottman-Murray marriage model with a linear influence function.
linmodel(observations)
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 |
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).
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 |
Tara Madhyastha and Ellen Hamaker
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.
noinfmodel
, ojivemodel
, combimodel
,bilinmodel
, origmodel
require(dyad) data(couple) ## fit a linear model fit <- linmodel(couple); ## plot influence function for husband on wife plot(fit$wife)