UNDERSTANDING A LIKELIHOOD FLAT PROBLEM: INFERENCES ON THE RATIO OF REGRESSION COEFFICIENTS IN LINEAR MODELS

Abstract

In this paper, we analyze a flat likelihood function shape that arises when performing inferences on the ratio of two regression coefficients in a linear regression model, parameter of interest in various applications. Due to this shape, infinite length likelihood-confidence intervals can be obtained. In the cases discussed here these likelihood-confidence intervals are related to the nested models problem, which is analyzed in detail through three illustrative simulated cases. It is essential to understand the shapes of the likelihood function in order to legitimately criticize likelihood inferences. This is of particular importance since the likelihood function is a key ingredient used in many inference methods