Semicontinuous outcomes commonly arise in a wide variety of fields, such as insurance claims, healthcare expenditures, rainfall amounts, and alcohol consumption. Regression models, including Tobit, Tweedie, and two-part models, are widely employed to understand the relationship between semicontinuous outcomes and covariates. Given the potential detrimental consequences of model misspecification, after fitting a regression model, it is of prime importance to check the adequacy of the model. However, due to the point mass at zero, standard diagnostic tools for regression models (e.g., deviance and Pearson residuals) are not informative for semicontinuous data. To bridge this gap, we propose a new type of residuals for semicontinuous outcomes that are applicable to general regression models. Under the correctly specified model, the proposed residuals converge to being uniformly distributed, and when the model is misspecified, they significantly depart from this pattern. In addition to in-sample validation, the proposed methodology can also be employed to evaluate predictive distributions. We demonstrate the effectiveness of the proposed tool using health expenditure data from the US Medical Expenditure Panel Survey.

翻译：半连续结果广泛出现在各类领域，例如保险索赔、医疗支出、降水量和酒精消费。Tobit回归、Tweedie回归和两阶段模型等回归模型被广泛用于理解半连续结果与协变量之间的关系。考虑到模型误设可能带来的严重后果，拟合回归模型后，检验模型的适当性至关重要。然而，由于零点的质量集中，回归模型的标准诊断工具（如偏差残差和皮尔逊残差）对半连续数据缺乏信息量。为弥补这一不足，我们针对半连续结果提出一种新型残差，适用于一般回归模型。在正确设定的模型下，所提残差收敛于均匀分布；而当模型误设时，其分布会显著偏离该模式。除样本内验证外，该方法还可用于评估预测分布。我们利用美国医疗支出面板调查的医疗支出数据，验证了所提工具的有效性。