Diagnostics for Regression Models with Discrete Outcomes Using Surrogate Empirical Residual Distribution Functions
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Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. The commonly used residuals show a large discrepancy from the hypothesized pattern for discrete outcomes even under the true model and are not informative especially when data are highly discrete. To fill this gap, we propose a surrogate empirical residual distribution function for discrete outcomes which serves as an alternative to the empirical Cox-Snell residual distribution function. When at least one continuous covariate is available, the proposed function converges uniformly to the identity function under the correctly specified model. We demonstrate theoretically and empirically that the proposed surrogate empirical residual distribution function is close to a hypothesized pattern under the true model and significantly departs from this pattern with model misspecification, and is thus an effective diagnostic tool.
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