are neither strictly non-nested nor partially non-nested. The zero-inflated Poisson model and its non-zero-inflated counterpart are an example of such a pair of non-nested models. Consequently, Vuong's test is not a valid test for discriminating between them. Example of strictly and partially non-nested models Vuong (1989) gives two examples of strictly non-nested models: A pair of standard linear regression models with different distributional assumptions on the distribution of error terms (e.g., normally distributed and logistically distributed). A pair of standard linear regression models with the same distributional assumptions on the distribution of error terms but different functional forms such as and , where and is a non-degenerate real random vector. Vuong (1989) also gives an intuitive example of partially non-nested (aka overlapping) models: A pair of standard linear regression models with some common explanatory variables and neither model nested in the other. References Statistical tests