I would like to compare two nested linear mixed models: one without interaction (referred to as model 1) and one with interaction (referred to as model 2).
Interaction term: time (6 classes) x gender (2 classes).
My mentor instructed me to compare these models using the Likelihood Ratio Test. I have reviewed many instructions but still feel confused about a few aspects.
1. For the difference in DF, adding the gender*time interaction would increase the parameters by (6-1) * (2-1)=5. Am I understand it correctly?
2. I conducted tests for both models. Model 1: -2LL=3267, and for Model 2, -2LL=3272. This indicates that adding the interaction increased the deviance and decreased the model fit. In this case, should I proceed with the Likelihood Ratio Test? Because all the instructional materials I have reviewed so far assume that adding variables decreases the deviance. So they calculate the -2LL (reduced model) - -2LL( full model), and if the p is significant, the full model works better. In my case, it is reverse.
If I can proceed with the test, the deviance difference would be 3272-3267=5. Assuming a DF difference of 5, test statistic would be 11.07, and a p-value of 0.041. Does this imply that Model 1 (without the interaction term) improve the results? It sounds a little bit strange..
Thanks for any answers on these questions.
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