I have two categorical IVs each with three levels:
group (Control, Int1, Int2) and a longitudinal variable
wave (T1, T2, T3). After reading through the various coding schemes on the UCLA website, I've set up the following contrasts in R: Helmert contrasts for
group and Simple coding for
Control_Int Int1_Int2 [1,] -2/3 0 [2,] 1/3 -1/2 [3,] 1/3 1/2
Pre_Post Pre_FU [1,] -1/3 -1/3 [2,] 2/3 -1/3 [3,] -1/3 2/3
I'm primarily interested in the interaction between
wave; my research question relates to whether change over time differs between intervention and control, and also between the two intervention groups.
Using nlme in R, my (abridged) models are specified as follows:
model1 <- lme(outcome ~ wave + group, random = ~wave | id, method = "ML") model2 <- lme(outcome ~ wave * group, random = ~wave | id, method = "ML") anova(model2, model1) # Is interaction model a better fit?
Model 1 fixed effects:
est se t df Pr(>|t|) (Intercept) 130.648 1.727 75.651 272.950 0.000 wavePre_Post -16.607 1.893 -8.773 272.302 0.000 wavePre_FU -13.797 2.262 -6.099 272.994 0.000 groupControl_Int -12.598 3.538 -3.561 272.753 0.000 groupInt1_Int2 -2.851 4.119 -0.692 272.959 0.489
Model 2 fixed effects:
est se t df Pr(>|t|) (Intercept) 130.477 1.729 75.484 268.967 0.000 wavePre_Post -16.708 1.724 -9.690 268.142 0.000 wavePre_FU -13.681 2.192 -6.240 268.995 0.000 groupControl_Int -15.655 3.632 -4.310 268.972 0.000 groupInt1_Int2 -6.607 4.273 -1.546 268.962 0.123 wavePre_Post:groupControl_Int -14.931 3.565 -4.189 268.587 0.000 wavePre_FU:groupControl_Int -10.133 4.503 -2.250 268.995 0.025 wavePre_Post:groupInt1_Int2 -15.260 4.327 -3.526 267.916 0.000 wavePre_FU:groupInt1_Int2 -13.920 5.536 -2.515 268.995 0.012
The interaction is significant in the above example. However, if the interaction had not been significant here, would it be more appropriate to retain Model 2 and interpret its first-order effects (presumably as marginal effects), or drop Model 2 and interpret the main effects from Model 1?
I ask the above as there seems to be a lack of consensus in other posts around whether this should be a statistically driven or substantively driven decision. In my case, the interaction model is of more substantive interest to my research question, yet including the interaction in the model changes the first-order parameters (specifically, the parameter estimates for
wave are reasonably similar between the two models, but differ to a greater degree for
group) and presumably complicates their interpretation. I'm aware that with dummy coding the first-order terms in the interaction model are actually simple effects and not interpretable as main effects. What are the implications here given I have avoided dummy coding (and used two different types of coding schemes)?
Finally, looking for clarification on how I would interpret the first-order coefficients in Model 2, in light of the coding schemes I've used. For example, my understanding of the interaction terms is that they represent mean differences in slopes between groups. So if I was explaining it to a 5th-grader I might say that immediately after treatment (i.e. at Post), scores for the Int2 group had on average reduced 15.26 points more than scores for the Int1 group. How would I explain the first-order terms (for Model 2) in a similar fashion?