In this paper, we apply the model selection approach based on Likelihood Ratio (LR) tests developed in Vuong (1985) to the problem of choosing between two normal linear regression models which are not nested in each other. First we compare our model selection procedure to other model selection criteria. Then we explicitly derive the procedure when the competing linear models are non-nested and neither one is correctly specified. Some simplifications are seen to arise when both models are contained in a larger correctly specified linear regression model, or when at least one competing linear model is correctly specified. A comparison of our model selection tests and previous non-nested hypothesis tests concludes the paper
