2020/05/13 by Zhulin He, He, Zhulin, Yuyuan Ouyang +1
Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2005.06158
openalex publication_date 2020/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.