In outcome‐dependent sampling, the continuous or binary outcome variable in a regression model is available in advance to guide selection of a sample on which explanatory variables are then measured. Selection probabilities may either be a smooth function of the outcome variable or be based on a stratification of the outcome. In many cases, only data from the final sample is accessible to the analyst. A maximum likelihood approach for this data configuration is developed here for the first time. The likelihood for fully general outcome‐dependent designs is stated, then the special case of Poisson sampling is examined in more detail. The maximum likelihood estimator differs from the well‐known maximum sample likelihood estimator, and an information bound result shows that the former is asymptotically more efficient. A simulation study suggests that the efficiency difference is generally small. Maximum sample likelihood estimation is therefore recommended in practice when only sample data is available. Some new smooth sample designs show considerable promise.

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结果依赖样本的最大似然估计

在依赖结果的抽样中，可以提前使用回归模型中的连续或二进制结果变量来指导选择样本，然后在该样本上测量解释变量。选择概率可以是结果变量的平滑函数，也可以基于结果的分层。在许多情况下，分析人员只能访问最终样本中的数据。此处首次开发了针对此数据配置的最大似然方法。陈述了完全基于结果的设计的可能性，然后对泊松采样的特殊情况进行了更详细的研究。最大似然估计器与众所周知的最大样本似然估计器不同，并且信息绑定结果表明，前者在渐近上更有效。仿真研究表明，效率差异通常很小。因此，在实际操作中，当只有样本数据可用时，建议使用最大样本似然估计。一些新的平滑样本设计显示出可观的前景。