I plan on using likelihood ratio tests for longitudinal multilevel modelling and using a mixture of static predictors and time-varying predictors.

I know that likelihood ratio tests are used for 'nested' models for static predictors when a new static variable is added to the model and the LRT test is used to determine whether it is significant.

What I would like to know is, what is meant by 'two nested models' in the context of likelihood ratio tests? Can time-varying predictors be considered in the 'nesting' strategy for conventional LRTs?

This then leads onto my second question- can a likelihood ratio test be done on a time-varying predictor? Say I was to do a series of likelihood ratio tests starting with a unconditional means model, then unconditional growth model, then a series of conditional growth models by adding static predictors. Could I also use a likelihood ratio test on a time-varying predictor like I would with a static predictor?

If this is not the case, can you explain why? As I am finding it difficult to find the answer to the question. Is there a specific reading material that breaks it down in simple terms?

My other question is- could you explain an alternative strategy to likelihood ratio testing that is able to judge both static and dynamic predictors?

Thanks for your help.