I are analyzing time to event using a Cox model. There is a continuous variable C, and I are conducting a likelihood ratio test comparing the following two models to see if the variable C should be added.
model_a ~ A + B
model_b ~ A + B + C
anova(model_a, model_b, test = "LRT")
In this case, can we call model_a a null model, or is the null model an intercept-only model. There is no intercept-only model in Cox model, so there is no null model?
A standard likelihood ratio test compares two nested models, i.e., one model is more complex than the other, and the simpler model is actually a submodel of the more complex model (e.g., by having one or more parameters equal to zero). In such a test the null hypothesis (null model) is always the simpler one of the two models. If the test rejects, the likelihood of the more complex model looks so much better than that of the simpler model that this would be very unlikely to happen if the simpler model actually were true.
In your case the simpler model and therefore the null model is indeed model_a.
