论文标题
条件逻辑回归估计器的渐近结果
An Asymptotic Result of Conditional Logistic Regression Estimator
论文作者
论文摘要
在特定于集群的研究中，二元结果的普通逻辑回归和条件逻辑回归分别提供了最大似然估计量（MLE）和条件最大似然估计器（CMLE）。在本文中，我们表明，当每个单个数据点被无限地复制时，CMLE正在渐近地接近MLE。我们的理论推导基于这样的观察结果，即出现在条件平均对数可能性函数中的术语是多项式的系数，因此可以通过Cauchy的分化公式将其转化为复杂的积分。然后，可以使用最陡峭下降的经典方法对复合物积分进行渐近分析。我们的结果意味着，如果单个权重乘以常数，则可能会对CMLE有偏见，并且在为群集特异性研究分配权重时我们应该谨慎。
In cluster-specific studies, ordinary logistic regression and conditional logistic regression for binary outcomes provide maximum likelihood estimator (MLE) and conditional maximum likelihood estimator (CMLE), respectively. In this paper, we show that CMLE is approaching to MLE asymptotically when each individual data point is replicated infinitely many times. Our theoretical derivation is based on the observation that a term appearing in the conditional average log-likelihood function is the coefficient of a polynomial, and hence can be transformed to a complex integral by Cauchy's differentiation formula. The asymptotic analysis of the complex integral can then be performed using the classical method of steepest descent. Our result implies that CMLE can be biased if individual weights are multiplied with a constant, and that we should be cautious when assigning weights to cluster-specific studies.
