Abstract

Although log-likelihood is widely used in model selection, the log-likelihood ratio has
had few applications in this area. In this talk, I present a log-likelihood ratio based
method for selecting regression models which focuses on the set of models deemed
plausible by the likelihood ratio test. I show that when the sample size is large and
the significance level of the test is small, there is a high probability that the smallest
model in the set is the true model; thus, the method selects this smallest model. The
significance level of the test serves as a tuning parameter that controls the balance
between the false active rate and false inactive rate of the selected model. I consider
three levels of this parameter in a simulation study and compare this method with
the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to
demonstrate its excellent accuracy and adaptability to different sample sizes.

Note
Model selection is an active area of research with a long history, a wide range of
perspectives, and a rich collection of methods. For students unfamiliar with this
area, this talk includes a review of key methods including the AIC, BIC and modern
Lp penalty methods. The new method presented in this talk offers a frequentist
perspective on the model selection problem. It is an alternative and a strong
competitor to the AIC and BIC for selecting regression models.