Which is better likelihood ratio or Wald test?
Usually the Wald, likelihood ratio, and score tests are covered. In this post I’m going to revise the advantages and disadvantages of the Wald and likelihood ratio test. I will focus on confidence intervals rather than tests, because the deficiencies of the Wald approach are more transparently seen here.
How are the likelihood ratio, Wald and Lagrange related?
These tests are sometimes described as tests for differences among nested models, because one of the models can be said to be nested within the other. The null hypothesis for all three tests is that the smaller model is the “true” model, a large test statistics indicate that the null hypothesis is false.
How is the likelihood ratio test statistic calculated?
Now that we have both log likelihoods, calculating the test statistic is simple: So our likelihood ratio test statistic is 36.05 (distributed chi-squared), with two degrees of freedom.
What’s the difference between Wald and regression output?
The difference is that the Wald test can be used to test multiple parameters simultaneously, while the tests typically printed in regression output only test one parameter at a time. Returning to our example, we will use a statistical package to run our model and then to perform the Wald test.
What is the Wald confidence interval for log odds?
For the binomial probability , this can be achieved by calculating the Wald confidence interval on the log odds scale, and then back-transforming to the probability scale (see Chapter 2.9 of In All Likelihood for the details). For our n=10 and x=1 example, a 95% confidence interval for the log odds is (-4.263, -0.131).
How are Wald intervals calculated in logistic regression?
A further advantage is that, in the context of fitting models (e.g. logistic regression), the Wald intervals for each coefficient can be calculated using quantities which are all available from the algorithm used to find the maximum likelihood estimates of the model parameters.