emtrends in a model with two interacting categorical predictors and one (or more) numeric

[samyogita-hardikar]

Hello! I was wondering how to get appropriate emtrends in a model that has 2 interacting categorical predictors and a numeric predictor.

Reproduced below using the obk.long dataset

library(lmerTest)
library(emmeans)

data("OBrienKaiser", package = "carData")
set.seed(1)
OBrienKaiser2 <- within(OBrienKaiser, {
  id <- factor(1:nrow(OBrienKaiser))
  age <- scale(sample(18:35, nrow(OBrienKaiser), replace = TRUE), scale = FALSE)})
attributes(OBrienKaiser2$age) <- NULL # needed or resahpe2::melt throws an error.
OBrienKaiser2$age <- as.numeric(OBrienKaiser2$age)
obk.long <- reshape2::melt(OBrienKaiser2, id.vars = c("id", "treatment", "gender", "age"))
obk.long[,c("phase", "hour")] <- lapply(as.data.frame(do.call(rbind,
                                                              strsplit(as.character(obk.long$variable), "\\."),)), factor)
obk.long <- obk.long[,c("id", "treatment", "gender", "age", "phase", "hour", "value")]
obk.long <- obk.long[order(obk.long$id),]
rownames(obk.long) <- NULL 

My data and model are comparable to the following where "phase" is a within subject variable, and "age" and "gender" are between.

model<-lmer(value~ (1|id) + phase +
                 phase:age + gender  , data = obk.long)

I am interested in the effect of age at every level of phase but also for both genders. The first part is achieved by doing

emtrend_age_phase<-emtrends(model, ~phase,  var="age", adjust = 'bonferroni', infer = TRUE)

emtrend_age_phase

phase age.trend SE df lower.CL upper.CL t.ratio p.value fup 0.1592 0.0845 15.9 -0.0666 0.385 1.885 0.2333 post 0.1810 0.0845 15.9 -0.0449 0.407 2.143 0.1437 pre 0.0254 0.0845 15.9 -0.2005 0.251 0.300 1.0000

Results are averaged over the levels of: gender Degrees-of-freedom method: satterthwaite Confidence level used: 0.95 Conf-level adjustment: bonferroni method for 3 estimates P value adjustment: bonferroni method for 3 tests

but after adding gender as an interaction to emtrends ...

emtrend_age_phase_gender<-emtrends(model, ~phase*gender,  var="age", adjust = 'bonferroni', infer = TRUE)

emtrend_age_phase_gender

phase gender age.trend SE df lower.CL upper.CL t.ratio p.value fup F 0.1592 0.0845 15.9 -0.0950 0.413 1.885 0.4667 post F 0.1810 0.0845 15.9 -0.0732 0.435 2.143 0.2873 pre F 0.0254 0.0845 15.9 -0.2288 0.280 0.300 1.0000 fup M 0.1592 0.0845 15.9 -0.0950 0.413 1.885 0.4667 post M 0.1810 0.0845 15.9 -0.0732 0.435 2.143 0.2873 pre M 0.0254 0.0845 15.9 -0.2288 0.280 0.300 1.0000

Degrees-of-freedom method: satterthwaite Confidence level used: 0.95 Conf-level adjustment: bonferroni method for 6 estimates P value adjustment: bonferroni method for 6 tests

even though 6 "age.trend" rows are generated, only the pvalues are adjusted to reflect 6 tests instead of 3. But the actual age.trend is still only given for each level of phase, while averaging over two levels of gender.

What would be the solution here?

[rvlenth]

What you see is a consequence of the model you fitted. In that model, gender does not interact with the other factors; in so doing, you have specified that the effects of phase, age, and phase:age are the same for both genders.

[samyogita-hardikar]

Aah, I see. Thanks for the quick help!