Zero adjusted regression models are used to fit variables that are discrete at zero and continuous at some interval of the positive real numbers. Diagnostic analysis in these models is usually performed using the randomized quantile residual, which is useful for checking the overall adequacy of a zero adjusted regression model. However, it may fail to identify some outliers. In this work, we introduce a residual for outlier identification in zero adjusted regression models. Monte Carlo simulation studies and an application suggest that the residual introduced here has good properties and detects outliers that are not identified by the randomized quantile residual.
Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard normally distributed. Diagnostic analysis in this class of models are usually performed using the standardized Pearson residual or the standardized deviance residual. The former has skewed distribution and the latter has negative mean, specially when the variance of the response variable is high. In this work, we introduce the adjusted quantile residual for generalized linear models. Using Monte Carlo simulation techniques and two applications, we compare this residual with the standardized Pearson residual, the standardized deviance residual and two other residuals. Overall, the results suggest that the adjusted quantile residual is a better tool for diagnostic analysis in generalized linear models.
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