Likelihood Ratio Test

This is typically performed to determine if a simpler model can be used to adequately model the data. The test is based on a comparison of full and reduced models where both models are fitted to the data and their log-likelihoods are calculated.

Let the full model (F) have p parameters and the reduced model (R) have q parameters such that q < p.

Full Model

Reduced Model

Let L(F) denote the maximized log-likelihood of the full model and L(R) represent the maximized log-likelihood of the reduced model. The null and alternative hypotheses with respect to this test are shown below.

The test statistic is given by:

This LR statistic is asymptotically distributed as with p-q degrees of freedom.