library(nlme)
library(dyadr)
riggsp <- read.csv("riggsp.csv") Possible Patterns
Actor-Only Model: actor effect non-zero and partner effect of zero
Couple Model: actor and partner effects non-zero and equal
Contrast Model: actor and partner effects non-zero and equal of opposite sign
Test for a Pattern
An Actor-Only Model is simple to test. It implies a significant actor effect and a nonsignificant partner effect.
A Couple Model implies that the actor and partner effects are equal. One tests the sum and difference of the two effects and hopes to find a significant sum effect and no difference effect. Such a result is consistent with a couple model: equal actor and partner effects. Note that the test of the difference effect takes as the null hypothesis that the actor and partner effects are equal.
A Contrast Model implies that the actor and partner effects are equal but opposite sign. One tests the sum and difference of the two effects and hopes to find a non-significant sum effect and a significant difference effect. Such a result is consistent with a contrast model. Note that the test of the sum effect takes as the null hypothesis that the actor and partner effects are equal but opposite in sign.
If both the Sum and the Difference are needed, then we know that actor and partner effects are different in magnitude. For instance, the actor effect may be large and the partner effect moderate in size.
If neither the Sum nor the Difference is needed, then likely neither the actor and partner effects are needed they explain little or no variance. It makes no sense to think about patterns as there are no effects.
If members are distinguishable, one can test these two models hold for both members. For example, we can tests the sum and difference for both husband and wife. There is a choice in determining the two coefficients are from say the husband’s X or to the husband’s Y. Note that patterns may be different. For instance in a parent child study, the parent might be using a Couple Model and the child an Actor-Only Model.
The run examining the effect of own Attachment Anxiety (Anxiety_A) or actor and the effect of partner’s Attachment Anxiety (Anxiety_A) on satisfaction (Sat_A), allowing for nonindependence by correlating the errors of the two members and treating dyad members as indistinguishable:
apimi = gls(Sat_A ~ Anxiety_A + Anxiety_P ,
na.action=na.omit,
correlation=corCompSymm (form=~1|Dyad),
data=riggsp)"Coefficient, standard error, p-value"## [1] "Coefficient, standard error, p-value"lincomb(apimi, 2, 3,"D")## [1] -0.51204519 0.29670262 0.08438594lincomb(apimi, 2, 3,"S")## [1] -3.066071e+00 5.085911e-01 1.654284e-09The test of the difference between coefficients is not significant, but the test of the sum is significant is. We can then conclude that the data are consistent with a couple model: One’s relationship satisfaction depends on the average level of the couple’s Attachment Anxiety.
Note that lincomb (i.e., linear combinations) can be used to test various hypotheses. It contains four arguments: 1) name of gls object; 2) the number of the first coefficient (note if there is an intercept it is the first coefficient); 3) number of the second coefficient; 4) test: “S”" for sum, “A” for average, and “D” for difference.
Kenny and Ledermann (2010) propose the following index: p/a or the ratio of the partner or p to actor or a effect. (The index is called k in honor of Larry Kurdek a pioneer in the area of dyadic analysis.) Note that when k equals 1 implies a Couple Model, when k equals 0 implies an Actor Only model, and when k equals -1 implies a Contrast Model. For the Riggs example, the estimate of k is 0.714. To obtain estimates of k and its confidence interval, Kenny & Lederman propose using Structural Equation Modeling (SEM) and using bootstrapping to obtain the confidence interval (to be discussed Thursday).
For multilevel modeling, one can also use the Monte Carlo method, also called the parametric bootstrap, to obtain a confidence interval for k (to be discussed Wednesday). One needs an estimate of the correlations of the estimates of p and a as well as each of their standard errors. Using a modified version of the Selig and Preacher program, we obtain a 95% confidence interval from 0.434 to 1.041. Because one is in the confidence interval, the data are consistent with a Couple Model. Treating dyads as distinguishable, for women the k is 0.686 (CI: 0.207 to 1.670) and for men k is .728 (0.178 to 1.904).