Q. How do you know your model works? A. You donít.
We have no special insights that allow us to know how nature works. All we have is observation and theory. We decide about the relevance of theory by testing it against observation. As modellers we can only know whether one model is more consistent or less consistent with observation than another model.
Likelihood ratio tests are an objective method for evaluating competing hypotheses against data. The advantage of LR is its ease of application lack of strong statistical assumptions. An LR test tells you whether increased complexity of one model, a s measured by the number of free parameters, is justified by expressing how much better the compex model agrees with observation.
For further reading about likelihood ratio tests, refer to:
Kendall, M and A, Stuart. 1979. The advanced theory of statistics. Volume 2. Inference and relationship. Chapter 24.