A score test for non-nested hypotheses with applications to discrete data models

In this paper it is shown that a convenient score test against non-nested alternatives can be constructed from the linear combination of the likelihood functions of the competing models. This is essentially a test for the correct specification of the conditional distribution of the variable of interest. Given its characteristics, the proposed test is particularly attractive to check the distributional assumptions in models for discrete data. The usefulness of the test is illustrated with an application to models for recreational boating trips.