An asymptotic result of conditional logistic regression estimator

In cluster-specific studies, ordinary logistic regression and conditional for binary outcomes provide maximum likelihood estimator (MLE) (CMLE), respectively. this paper, we show that CMLE is approaching to MLE asymptotically when each individual data point replicated infinitely many times. Our theoretical derivation based on the observation a term appearing in average log-likelihood function coefficient of polynomial, hence can be transformed complex integral by Cauchy’s differentiation formula. The asymptotic analysis then performed using classical method steepest descent. result implies biased if weights are multiplied with constant, should cautious assigning studies.