Significant interaction no significant comparision

#1
Dear community,

I did a linear mixed model full factorial with 2x2. I use the linear mixed model like an ANOVA and I have one significant main effect and a significant interaction effect.To solve the interaction I split my data by one variable and analyze the main effect by the other variable (just like pairwise comparisons) but both my to analyze don't show a significant effect. So why is there a significant interaction then? In the Graph I see that it is nearly a crossed interaction but as no comparison becomes significant I would not expect a significant interaction. Any help would be very much appreciated. Unknown.jpg
 
#2
Can you clarify what "I split my data by one variable and analyze the main effect by the other variable." means? I look at multiple comparisons using Tukey adjusted p-values in SAS. When there is significant interaction don't analyze the main effect.
 
#3
Can you clarify what "I split my data by one variable and analyze the main effect by the other variable." means? I look at multiple comparisons using Tukey adjusted p-values in SAS. When there is significant interaction don't analyze the main effect.
I mean that I created to subsets of my data one with all data points with kong=0 and one with kong=1 and did a linear model for each with the main effect for emopart2 as a substitute for TuKeys comparisions as I should not use that. But I mean the main effect for Kong is interpretable regardless of that pseudo interaction isn't it?
 
#4
I've always been taught to not interpret the main effect if there is a significant interaction. Perhaps there are other opinions.
 

hlsmith

Not a robit
#5
In the saturated model y = bo + b1(X1) + b2(X2) + b3(X1*X2), you would keep in the model the base terms (X1 and X2), but you would not interpret their coefficients since results on conditional on each other. If you ran simple models based on stratified data you could interpret them.

Was the above imagine generated using the data stratified into two sets or the full model? Also, by linear mixed model you don't mean multilevel, correct?

Well you can see you have potentially disordinal interaction - lines are not parallel and cross. I would what the graph would look like if you generated it using the saturated model, if the above is not. I say this because the graph is telling but not conclusive. I feel like in the difference-in-differences area, I have seen the formula for using the saturated models coefficients to construct the graph. What software are you using, if it is SAS -> it has the effectplots and an interaction plot similar to the above that may be able to help shed light on your problem.