I have two categorical variables, A and B. Each categorical variable has three
levels(0,1,2). There is a certain dependent variable P against which I make a plot and see that there is an interaction between A and B. In my next step, I make a model when I regress upon P with A*B (
model_interaction). When I look at the summary of this model I see that certain interactions terms are significant. Here is my question, is this enough evidence to say that there are significant interactions?
Why am I asking this?
Along with the interaction model, I also made a linear model with A and B regressed on P (
model_linear). When I compared
model_linear I found no statistical difference between the two and I also found that the AIC score for
model_linear was lower. So, after I've seen all of this do I still say that I have found significant interactions?
Just to summarize:
model_linear: P ~ A + B
model_interaction: P ~ A * B
Evidence for interaction:
1) Plots showing clear interaction.
2) Model with the interaction terms have significant p-values
Evidence against it:
1) Interaction model not significantly different from linear model
2) Linear model has lower AIC score compared to the interaction model.
Do I say there are interactions or not?