Our hypothesis is that there is a 3-way interaction between A, B, and C.
I have defined a model as follows:
I aim to use the likelihood ratio test (LRT) to determine if the three-way interaction effect is statistically significant. To do this, I constructed a nested model without the three-way interaction term:
Then, I plan to employ the LRT to test the significance of the 3-way interaction.
However, one of my co-authors disagrees with my approach. He suggests that the nested model should be simplified to:
From this, we would use the LRT to test the significance of all interaction effects, including the three-way interaction.
I'm currently uncertain about which approach is appropriate. Could someone provide clarity on this matter?