Moderation in the APIM
Load the Data
Read in the pairwise dataset and load the packages
library(dyadr)
library(dplyr)
library(nlme)
library(ggplot2)
riggsp <- read.csv("riggsp.csv")Riggs Example
Outcome: [Sat_A] Satisfaction
Predictor Variables: [Avoid_A, Avoid_P] Adult avoidant attachment (Actor and Partner), a mixed variable.
Moderators: [Anxiety_A, Anxiety_P] Adult anxious attachment (Actor and Partner), a mixed variable.
Data Preparation
We first grand-mean center the moderator and predictor variables.
riggsp <- riggsp %>%
mutate(CAvoid_A = Avoid_A - mean(Avoid_A),
CAvoid_P = Avoid_P - mean(Avoid_P),
CAnxiety_A = Anxiety_A - mean(Anxiety_A),
CAnxiety_P = Anxiety_P - mean(Anxiety_P)) Saturated Two-Intercept Model
We then estimate the two-intercept model with the string gender variable and all of the anxiety by avoidance interactions:
apim_sat_two <- gls(Sat_A ~ Genderstring + CAvoid_A:Genderstring
+ CAvoid_P:Genderstring + CAnxiety_A:Genderstring
+ CAnxiety_P:Genderstring
+ CAnxiety_A:CAvoid_A:Genderstring
+ CAnxiety_A:CAvoid_P:Genderstring
+ CAnxiety_P:CAvoid_A:Genderstring
+ CAnxiety_P:CAvoid_P:Genderstring - 1,
data = riggsp,
correlation = corCompSymm(form=~1|Dyad),
weights = varIdent(form=~1|Genderstring),
na.action = na.omit)
smallsummary(apim_sat_two)## Correlation structure of class corCompSymm representing
## Rho
## 0.6222822
##
## Variance function structure of class varIdent representing
## Man Woman
## 1.000000 1.077605
## Residual standard error: 6.141725
##
## Value Std.Error t-value p-value
## GenderstringMan 45.3642 0.5767 78.6632 0.0000
## GenderstringWoman 45.4681 0.6214 73.1654 0.0000
## GenderstringMan:CAvoid_A -1.2850 0.5031 -2.5542 0.0112
## GenderstringWoman:CAvoid_A -1.3207 0.5668 -2.3303 0.0205
## GenderstringMan:CAvoid_P 0.0209 0.5259 0.0397 0.9683
## GenderstringWoman:CAvoid_P -0.4061 0.5421 -0.7490 0.4545
## GenderstringMan:CAnxiety_A -1.2284 0.4338 -2.8317 0.0050
## GenderstringWoman:CAnxiety_A -1.6208 0.4904 -3.3052 0.0011
## GenderstringMan:CAnxiety_P -1.1014 0.4551 -2.4204 0.0161
## GenderstringWoman:CAnxiety_P -0.9123 0.4675 -1.9516 0.0519
## GenderstringMan:CAvoid_A:CAnxiety_A 1.4250 0.3989 3.5722 0.0004
## GenderstringWoman:CAvoid_A:CAnxiety_A -0.9834 0.4809 -2.0450 0.0418
## GenderstringMan:CAvoid_P:CAnxiety_A -1.1489 0.4214 -2.7262 0.0068
## GenderstringWoman:CAvoid_P:CAnxiety_A -0.3160 0.4496 -0.7028 0.4827
## GenderstringMan:CAvoid_A:CAnxiety_P -0.0243 0.4173 -0.0582 0.9536
## GenderstringWoman:CAvoid_A:CAnxiety_P -0.2839 0.4541 -0.6252 0.5323
## GenderstringMan:CAvoid_P:CAnxiety_P -0.9613 0.4462 -2.1542 0.0320
## GenderstringWoman:CAvoid_P:CAnxiety_P 0.3808 0.4299 0.8859 0.3764## 2.5 % 97.5 %
## GenderstringMan 44.2339 46.4945
## GenderstringWoman 44.2501 46.6861
## GenderstringMan:CAvoid_A -2.2710 -0.2989
## GenderstringWoman:CAvoid_A -2.4316 -0.2099
## GenderstringMan:CAvoid_P -1.0099 1.0517
## GenderstringWoman:CAvoid_P -1.4686 0.6565
## GenderstringMan:CAnxiety_A -2.0786 -0.3782
## GenderstringWoman:CAnxiety_A -2.5819 -0.6597
## GenderstringMan:CAnxiety_P -1.9933 -0.2095
## GenderstringWoman:CAnxiety_P -1.8285 0.0039
## GenderstringMan:CAvoid_A:CAnxiety_A 0.6431 2.2068
## GenderstringWoman:CAvoid_A:CAnxiety_A -1.9258 -0.0409
## GenderstringMan:CAvoid_P:CAnxiety_A -1.9748 -0.3229
## GenderstringWoman:CAvoid_P:CAnxiety_A -1.1973 0.5653
## GenderstringMan:CAvoid_A:CAnxiety_P -0.8421 0.7935
## GenderstringWoman:CAvoid_A:CAnxiety_P -1.1740 0.6061
## GenderstringMan:CAvoid_P:CAnxiety_P -1.8359 -0.0867
## GenderstringWoman:CAvoid_P:CAnxiety_P -0.4617 1.2233We see that 4 of the 8 moderation effects are statistically significant. Six of the eight coefficients are negative. Note that all significant actor and partner effects for anxiety and avoidance are negative—so in general, a negative interaction effect indicates a more-is-worse effect whereas a positive interaction effect indicates an alleviation effect.
Interpretation
To more easily interpret the moderation effects, it may be beneficial to switch the predictor and the moderator. In this case, we will keep the predictor as Avoidance and the moderator as Anxiety. Interpretation of the eight interactions:
Avoid_A with Anxiety_A (Man): We would predict the negative effect of men’s own avoidance on their satisfaction to be alleviated as their anxiety goes up.
Avoid_A with Anxiety_A (Woman): We would predict the negative effect of women’s own avoidance on their satisfaction to be stronger (more negative) as their anxiety goes up.
Avoid_P with Anxiety_A (Man): We would predict the lack of an effect of the woman’s avoidance on the man’s satisfaction is made negative by his own anxiety.
Avoid_P with Anxiety_A (Woman): (not significant) We would predict that the negative effect of the man’s avoidance on the woman’s satisfaction is made worse by her own anxiety.
Avoid_A with Anxiety_P (Man): (not significant) We would predict the negative effect of men’s own avoidance on their satisfaction to be stronger as the woman’s anxiety goes up.
Avoid_A with Anxiety_P (Woman): (not significant) We would predict the negative effect of women’s own avoidance on their satisfaction to be stronger as the man’s anxiety goes up.
Avoid_P with Anxiety_P (Man): We would predict the lack of an effect of the woman’s avoidance on the man’s satisfaction is made negative by the woman’s anxiety.
Avoid_P with Anxiety_P (Woman): (not significant) We would predict that the negative effect of the man’s avoidance on the woman’s satisfaction is alleviated by the man’s anxiety.
Testing for Gender Differences in Moderation Effects
We can test if these interactions are significantly different across gender by using the test function.
gen_tests <- data.frame(act_act = lincomb(apim_sat_two, 11, 12),
prt_act = lincomb(apim_sat_two, 13, 14),
act_prt = lincomb(apim_sat_two, 15, 16),
prt_prt = lincomb(apim_sat_two, 17, 18),
row.names = c("Mean diff", "SE", "p-value"))
gen_tests## act_act prt_act act_prt prt_prt
## Mean diff 2.4083279513 -0.8328326 0.2596097 -1.34206712
## SE 0.6498318363 0.6453611 0.6457962 0.64485056
## p-value 0.0002104929 0.1968803 0.6876845 0.03741502Gender Interaction Approach
Alternatively, we can test if these moderation effects are significantly different across gender by running the model with gender interactions.
apim_sat_int <- gls(Sat_A ~ CAnxiety_A*CAvoid_A*Gender_A
+ CAnxiety_A*CAvoid_P*Gender_A
+ CAnxiety_P*CAvoid_A*Gender_A
+ CAnxiety_P*CAvoid_P*Gender_A,
data = riggsp,
correlation = corCompSymm(form=~1|Dyad),
weights = varIdent(form=~1|Gender_A),
na.action = na.omit)
coef(summary(apim_sat_int))## Value Std.Error t-value
## (Intercept) 45.41612150 0.5396262 84.16219461
## CAnxiety_A -1.42457619 0.3208972 -4.43935351
## CAvoid_A -1.30286245 0.3739701 -3.48386766
## Gender_A 0.05195146 0.2611202 0.19895615
## CAvoid_P -0.19258574 0.3727011 -0.51672976
## CAnxiety_P -1.00685306 0.3197087 -3.14928235
## CAnxiety_A:CAvoid_A 0.22081234 0.2993412 0.73766113
## CAnxiety_A:Gender_A -0.19617772 0.3336852 -0.58791253
## CAvoid_A:Gender_A -0.01787352 0.3838075 -0.04656897
## CAnxiety_A:CAvoid_P -0.73243407 0.2928428 -2.50111695
## Gender_A:CAvoid_P -0.21348458 0.3825710 -0.55802598
## CAvoid_A:CAnxiety_P -0.15410981 0.2930825 -0.52582402
## Gender_A:CAnxiety_P 0.09454260 0.3325424 0.28430237
## CAvoid_P:CAnxiety_P -0.29024257 0.2966359 -0.97844730
## CAnxiety_A:CAvoid_A:Gender_A -1.20416398 0.3249159 -3.70607874
## CAnxiety_A:Gender_A:CAvoid_P 0.41641630 0.3226806 1.29049081
## CAvoid_A:Gender_A:CAnxiety_P -0.12980483 0.3228981 -0.40199934
## Gender_A:CAvoid_P:CAnxiety_P 0.67103356 0.3224253 2.08120639
## p-value
## (Intercept) 8.469629e-207
## CAnxiety_A 1.280854e-05
## CAvoid_A 5.699687e-04
## Gender_A 8.424355e-01
## CAvoid_P 6.057360e-01
## CAnxiety_P 1.806324e-03
## CAnxiety_A:CAvoid_A 4.613128e-01
## CAnxiety_A:Gender_A 5.570454e-01
## CAvoid_A:Gender_A 9.628886e-01
## CAnxiety_A:CAvoid_P 1.292790e-02
## Gender_A:CAvoid_P 5.772542e-01
## CAvoid_A:CAnxiety_P 5.994096e-01
## Gender_A:CAnxiety_P 7.763802e-01
## CAvoid_P:CAnxiety_P 3.286631e-01
## CAnxiety_A:CAvoid_A:Gender_A 2.517722e-04
## CAnxiety_A:Gender_A:CAvoid_P 1.979012e-01
## CAvoid_A:Gender_A:CAnxiety_P 6.879786e-01
## Gender_A:CAvoid_P:CAnxiety_P 3.828620e-02Looking at these three-way interactions with gender we find significant gender differences in the actor-actor moderation effect and the partner-partner moderation effect:
coef(summary(apim_sat_int))[15:18,]## Value Std.Error t-value p-value
## CAnxiety_A:CAvoid_A:Gender_A -1.2041640 0.3249159 -3.7060787 0.0002517722
## CAnxiety_A:Gender_A:CAvoid_P 0.4164163 0.3226806 1.2904908 0.1979012063
## CAvoid_A:Gender_A:CAnxiety_P -0.1298048 0.3228981 -0.4019993 0.6879786018
## Gender_A:CAvoid_P:CAnxiety_P 0.6710336 0.3224253 2.0812064 0.0382861983These are the same p-values we found with lincomb().
cbind(t(gen_tests[3,]), coef(summary(apim_sat_int))[15:18,4])## p-value
## act_act 0.0002104929 0.0002517722
## prt_act 0.1968802989 0.1979012063
## act_prt 0.6876845149 0.6879786018
## prt_prt 0.0374150187 0.0382861983You could also perform an omnibus test to see if there is distinguishability in the moderation effects.
apim_sat_int <- gls(Sat_A ~ CAnxiety_A*CAvoid_A*Gender_A
+ CAnxiety_A*CAvoid_P*Gender_A
+ CAnxiety_P*CAvoid_A*Gender_A
+ CAnxiety_P*CAvoid_P*Gender_A,
method = "ML", #using ML
data = riggsp,
correlation = corCompSymm(form=~1|Dyad),
weights = varIdent(form=~1|Gender_A),
na.action = na.omit)
apim_sat_noMod <- gls(Sat_A ~ CAnxiety_A*CAvoid_A*Gender_A
+ CAnxiety_A*CAvoid_P*Gender_A
+ CAnxiety_P*CAvoid_A*Gender_A
+ CAnxiety_P*CAvoid_P*Gender_A
- CAnxiety_A:CAvoid_A:Gender_A
- CAnxiety_A:CAvoid_P:Gender_A
- CAnxiety_P:CAvoid_A:Gender_A
- CAnxiety_P:CAvoid_P:Gender_A,
method = "ML", #using ML
data = riggsp,
correlation = corCompSymm(form=~1|Dyad),
weights = varIdent(form=~1|Gender_A),
na.action = na.omit)
anova(apim_sat_int, apim_sat_noMod)## Model df AIC BIC logLik Test L.Ratio
## apim_sat_int 1 21 1975.818 2054.286 -966.9091
## apim_sat_noMod 2 17 1984.438 2047.960 -975.2192 1 vs 2 16.62009
## p-value
## apim_sat_int
## apim_sat_noMod 0.0023There is distinguishability in the moderation effects \(\chi^2(4) = 16.62\), \(p = .002\).
Testing Simple Slopes
To interpret an interaction and test for simple slopes (e.g., at 1 SD above and below the mean for anxiety), we can use the method of re-centering. Zooming in on the partner-partner moderation effect for men only, to estimate the simple slopes of partner avoidance at high and low partner anxiety, for example, we re-estimate the model for those who are 1 standard deviation (sd) above and then 1 sd below the mean on partner anxiety. We then look at the “main effect” of partner avoidance as it will now refer to effect of CAvoid_P when CAnxiety_P is one standard deviation above the mean (high) or one standard deviation below the mean (low).
Note that to have CAnxiety_P be zero when it is one sd above the mean, we subtract 1 sd from the centered score and add 1 sd for one sd below the mean:
riggsp <- riggsp %>%
mutate(High_CAnxiety_P = CAnxiety_P - sd(CAnxiety_P),
Low_CAnxiety_P = CAnxiety_P + sd(CAnxiety_P))This might feel counterintuitive, but you can convince yourself! We then re-run the model 2 times using these 2 re-centered variables:
apim_pxp_high <- gls(Sat_A ~ Genderstring + CAvoid_A:Genderstring
+ CAvoid_P:Genderstring + CAnxiety_A:Genderstring
+ High_CAnxiety_P:Genderstring
+ CAnxiety_A:CAvoid_A:Genderstring
+ CAnxiety_A:CAvoid_P:Genderstring
+ High_CAnxiety_P:CAvoid_A:Genderstring
+ High_CAnxiety_P:CAvoid_P:Genderstring - 1,
data = riggsp,
correlation = corCompSymm(form=~1|Dyad),
weights = varIdent(form=~1|Genderstring),
na.action = na.omit)
coef(summary(apim_pxp_high))[c(1,3,5,7,9,11,13,15,17),]## Value Std.Error t-value
## GenderstringMan 43.99478660 0.7233222 60.82322491
## GenderstringMan:CAvoid_A -1.31520772 0.6570690 -2.00162791
## GenderstringMan:CAvoid_P -1.17427167 0.6387965 -1.83825627
## GenderstringMan:CAnxiety_A -1.22839846 0.4338011 -2.83170915
## GenderstringMan:High_CAnxiety_P -1.10139566 0.4550514 -2.42037628
## GenderstringMan:CAvoid_A:CAnxiety_A 1.42497632 0.3989027 3.57224043
## GenderstringMan:CAvoid_P:CAnxiety_A -1.14885037 0.4214101 -2.72620543
## GenderstringMan:CAvoid_A:High_CAnxiety_P -0.02430499 0.4172554 -0.05824966
## GenderstringMan:CAvoid_P:High_CAnxiety_P -0.96127613 0.4462317 -2.15420856
## p-value
## GenderstringMan 7.342412e-168
## GenderstringMan:CAvoid_A 4.624971e-02
## GenderstringMan:CAvoid_P 6.704028e-02
## GenderstringMan:CAnxiety_A 4.951822e-03
## GenderstringMan:High_CAnxiety_P 1.611462e-02
## GenderstringMan:CAvoid_A:CAnxiety_A 4.138415e-04
## GenderstringMan:CAvoid_P:CAnxiety_A 6.793933e-03
## GenderstringMan:CAvoid_A:High_CAnxiety_P 9.535896e-01
## GenderstringMan:CAvoid_P:High_CAnxiety_P 3.204181e-02For men, when the woman’s anxiety is high there is a marginally significant negative effect of the woman’s avoidance on his satisfaction.
apim_pxp_low <- gls(Sat_A ~ Genderstring + CAvoid_A:Genderstring
+ CAvoid_P:Genderstring + CAnxiety_A:Genderstring
+ Low_CAnxiety_P:Genderstring
+ CAnxiety_A:CAvoid_A:Genderstring
+ CAnxiety_A:CAvoid_P:Genderstring
+ Low_CAnxiety_P:CAvoid_A:Genderstring
+ Low_CAnxiety_P:CAvoid_P:Genderstring - 1,
data = riggsp,
correlation = corCompSymm(form=~1|Dyad),
weights = varIdent(form=~1|Genderstring),
na.action = na.omit)
coef(summary(apim_pxp_low))[c(1,3,5,7,9,11,13,15,17),]## Value Std.Error t-value
## GenderstringMan 46.73355349 0.8843883 52.84280189
## GenderstringMan:CAvoid_A -1.25477014 0.7827789 -1.60296871
## GenderstringMan:CAvoid_P 1.21606936 0.8722350 1.39419926
## GenderstringMan:CAnxiety_A -1.22839846 0.4338011 -2.83170915
## GenderstringMan:Low_CAnxiety_P -1.10139566 0.4550514 -2.42037628
## GenderstringMan:CAvoid_A:CAnxiety_A 1.42497632 0.3989027 3.57224043
## GenderstringMan:CAvoid_P:CAnxiety_A -1.14885037 0.4214101 -2.72620543
## GenderstringMan:CAvoid_A:Low_CAnxiety_P -0.02430499 0.4172554 -0.05824966
## GenderstringMan:CAvoid_P:Low_CAnxiety_P -0.96127613 0.4462317 -2.15420856
## p-value
## GenderstringMan 1.652271e-151
## GenderstringMan:CAvoid_A 1.100227e-01
## GenderstringMan:CAvoid_P 1.643174e-01
## GenderstringMan:CAnxiety_A 4.951822e-03
## GenderstringMan:Low_CAnxiety_P 1.611462e-02
## GenderstringMan:CAvoid_A:CAnxiety_A 4.138415e-04
## GenderstringMan:CAvoid_P:CAnxiety_A 6.793933e-03
## GenderstringMan:CAvoid_A:Low_CAnxiety_P 9.535896e-01
## GenderstringMan:CAvoid_P:Low_CAnxiety_P 3.204181e-02Now we see that when partner (woman) anxiety is low there is no statistically significant negative effect of partner avoidance on satisfaction, in fact, the coefficient for partner avoidance is now positive. But this coefficient is not significantly different from zero.
Making Interaction Figures
It would be nice to have a figure for the moderation of partner avoidance effect by actor anxiety.
To graph this interaction we need to note the position of the y-intercept and slope for CAvoid_P when CAnxiety_A is high and the y-intercept and slope for CAvoid_P when CAnxiety_A low. In this case the positions are 1 and 4 respectively. Then, we can use the graphMod() function in dyadr to make the figure. Recall that you can run the command ?graphMod to see what the graphMod() function needs.
?graphModplot <- graphMod(riggsp,
x = riggsp$CAvoid_P,
y = riggsp$Sat_A,
mod = riggsp$CAnxiety_P,
apim_pxp_high,
apim_pxp_low,
1, 5)
plot
We can then add labels and change the colors, etc.
plot +
theme_classic() +
ylab("Man's Satisfaction") +
xlab("Woman's Avoidance") +
scale_color_manual(values = c("cadetblue", "salmon")) +
scale_color_discrete(name = "Woman's Anxiety")