Likelihood ratio test model selection

1. Is likelihood ratio test only for nested models?
2. What does a likelihood ratio test tell you?
3. How would you carry out a likelihood ratio test between Model 1 and Model 2?
4. Can we use likelihood ratio test for comparing non nested models?

Is likelihood ratio test only for nested models?

The LRT is only valid if used to compare hierarchically nested models. That is, the more complex model must differ from the simple model only by the addition of one or more parameters. Adding additional parameters will always result in a higher likelihood score.

What does a likelihood ratio test tell you?

In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after imposing some constraint.

How would you carry out a likelihood ratio test between Model 1 and Model 2?

To perform a likelihood ratio test on these two models, we will use the lrtest() function from the lmtest package. Let's try now reduced fit model, we can remove hp and wt from this model. We now have both models and are ready to run the likelihood ratio test to see if there are any differences between them.

Can we use likelihood ratio test for comparing non nested models?

The LRT is a standard statistical test for comparing nested models. By use of simulation the LRT can also be used in an analogous fashion to compare non-nested models, thereby providing a unified approach for model comparison within the null hypothesis testing paradigm.