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Abstract:
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The density ratio model has received increasing attention in recent years. Under the density ratio model, the probability density/mass function of the outcome variable is the product of an unknown baseline density/mass function and an exponential term involving a finite dimensional regression parameters. This model includes several commonly used generalized linear models as special cases. In this paper, we propose a stratified version of the density ratio model, which allows the baseline distributions of the outcome to be different across different levels of a categorical variable. Compared to the standard density ratio model, the proposed model is more flexible in that it also accommodates heteroscedasticity. We develop efficient likelihood based estimation and inference procedures. Furthermore, we propose a goodness-of-fit test for the standard density ratio model. Extensive simulation studies demonstrate that the proposed methodology performs well. A real application is provided.
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