用于稀疏逻辑回归的定向Hosmer-Lemeshow拟合优度检验
A modified Hosmer-Lemeshow goodness-of-fit test for asymmetric links: second-order power and robustness
- Alexandria University（亚历山大大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究二元逻辑回归模型在协变量连续时拟合优度评估难题，提出用单一定向校正项修改Hosmer-Lemeshow统计量的划分检验，模拟显示其在不对称链接不匹配时表现出色，实际数据应用展示了用途。
AI中文摘要：
当协变量为连续变量时，二元逻辑回归模型的拟合优度评估较为困难：数据有效稀疏，经典的Pearson检验和偏差检验失效，从业者依赖基于划分的检验，如Hosmer-Lemeshow检验，该检验在比较观察计数和预期计数之前对观察值进行分组。我们研究了一种划分检验，它用一个由(1 - 2π̅g)加权的单一定向校正项修改Hosmer-Lemeshow统计量，并参考χ²G - 2分布。校正项是Osius-Rojek/Farrington标准化的分组形式；分组使其在稀疏情况下定义良好，并且针对错误指定的链接所导致的不对称过度预测和预测不足。一个单一的对齐函数捕捉其效果，预测检验在何处获得功效（不对称链接错误指定）以及在何处不获得功效（对称偏差以及概率分组检验无法看到的协变量空间结构）。在模拟中，该检验保持其大小；没有经过良好校准的划分检验对不对称链接不匹配更敏感，并且在那里明显超过Hosmer-Lemeshow检验，对于互补对数-对数链接最为明显——随着n的增长，这种适度的增益会逐渐消失；在遗漏交互项时它与Hosmer-Lemeshow检验相当，在遗漏二次项时功效较低（在n = 1,000时约低10个百分点）。一个实际数据应用说明了它的用途，并且该检验在R包this http URL中实现。
英文摘要：
The Hosmer-Lemeshow test is the routine check of fit for logistic regression, yet it is weak against a wrong link, and the directed tests that are stronger lose their level when a single covariate is recorded in error. We apply Farrington's correction to its risk groups, which removes the single-record terms of the statistic and keeps the within-group products of residuals. The result is the score test for records of similar fitted risk sharing a miscalibration: locally most powerful against a smooth misfit in either direction, and as robust to gross errors as the Hosmer-Lemeshow test. One alignment functional, mapped in advance for asymmetric links, decides when it is more powerful than the Hosmer-Lemeshow test, at second order with ten groups and at first order with many. For the many groups of large samples, normal limits for both statistics correct the chi-squared reference of the widely used grouping rule of Paul and colleagues, under which the Hosmer-Lemeshow test reached a size of 12% or lost all its power, and they explain why that rule hid a clear misfit in 8873 SUPPORT patients that groups of 25 records detected. In pre-registered simulations, one gross covariate error in a thousand records raised the false-alarm rates of Stukel's, the cubic calibration and the GiViTI tests to 25-39%, while the risk-grouped tests stayed near 5%; among these, the corrected test was the most powerful in all 34 settings with negative alignment and a visible difference. The test is in the R package ebrahim.gof.
