Wald Versus Likelihood Ratio Tests

The Wald test and the likelihood ratio tests are asymptotic tests, meaning that the distribution from which p-values are calculated for a finite number of samples draws on the distribution of the test statistic as the sample size grows to infinity. The Wald test is a simple test that is easy to compute based only on parameter estimates and their (asymptotic) standard errors. The likelihood ratio test, on the other hand, requires the likelihoods of the full model and the model reduced under . It is computationally more demanding, but also provides the asymptotically more powerful and reliable test. The likelihood ratio test is almost always preferable to the Wald test, unless computational demands make it impractical to refit the model.