Bull Shelley B, Lewinger Juan Pablo, Lee Sophia S F
Samuel Lunenfeld Research Institute, Prosserman Centre for Health Research, Mount Sinai Hospital, Toronto, Ont., Canada M5G 1X5.
Stat Med. 2007 Feb 20;26(4):903-18. doi: 10.1002/sim.2518.
Logistic regression is one of the most widely used regression models in practice, but alternatives to conventional maximum likelihood estimation methods may be more appropriate for small or sparse samples. Modification of the logistic regression score function to remove first-order bias is equivalent to penalizing the likelihood by the Jeffreys prior, and yields penalized maximum likelihood estimates (PLEs) that always exist, even in samples in which maximum likelihood estimates (MLEs) are infinite. PLEs are an attractive alternative in small-to-moderate-sized samples, and are preferred to exact conditional MLEs when there are continuous covariates. We present methods to construct confidence intervals (CI) in the penalized multinomial logistic regression model, and compare CI coverage and length for the PLE-based methods to that of conventional MLE-based methods in trinomial logistic regressions with both binary and continuous covariates. Based on simulation studies in sparse data sets, we recommend profile CIs over asymptotic Wald-type intervals for the PLEs in all cases. Furthermore, when finite sample bias and data separation are likely to occur, we prefer PLE profile CIs over MLE methods.
逻辑回归是实践中使用最广泛的回归模型之一，但对于小样本或稀疏样本，传统最大似然估计方法的替代方法可能更合适。对逻辑回归得分函数进行修改以消除一阶偏差，等同于用杰弗里斯先验对似然进行惩罚，并产生总是存在的惩罚最大似然估计（PLE），即使在最大似然估计（MLE）为无穷大的样本中也是如此。在中小规模样本中，PLE是一种有吸引力的替代方法，并且在存在连续协变量时，比精确条件MLE更受青睐。我们提出了在惩罚多项逻辑回归模型中构建置信区间（CI）的方法，并在具有二元和连续协变量的三项逻辑回归中，将基于PLE的方法的CI覆盖率和长度与基于传统MLE的方法进行比较。基于稀疏数据集的模拟研究，我们在所有情况下都推荐使用轮廓CI而不是渐近Wald型区间来估计PLE。此外，当可能出现有限样本偏差和数据分离时，我们更喜欢基于PLE的轮廓CI而不是MLE方法。
