  Although the log-likelihood is widely used in model selection, the
log-likelihood ratio has had few applications in this area. We develop a
log-likelihood ratio based method for selecting regression models by focusing
on the set of models deemed plausible by the likelihood ratio test. We 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, we select this smallest model. The significance level of the
test serves as a parameter for this method. We consider three levels of this
parameter in a simulation study and compare this method with the Akaike
Information Criterion and Bayesian Information Criterion to demonstrate its
excellent accuracy and adaptability to different sample sizes. We also apply
this method to select a logistic regression model for a South African heart
disease dataset.
