A solution to control for nonresponse bias consists of multiplying the design weights of respondents by the inverse of estimated response probabilities to compensate for the nonrespondents. Maximum likelihood and calibration are two approaches that can be applied to obtain estimated response probabilities. We consider a common framework in which these approaches can be compared. We develop an asymptotic study of the behavior of the resulting estimator when calibration is applied. A logistic regression model for the response probabilities is postulated. Missing at random and unclustered data are supposed. Three main contributions of this work are: 1) we show that the estimators with the response probabilities estimated via calibration are asymptotically equivalent to unbiased estimators and that a gain in efficiency is obtained when estimating the response probabilities via calibration as compared to the estimator with the true response probabilities, 2) we show that the estimators with the response probabilities estimated via calibration are doubly robust to model misspecification and explain why double robustness is not guaranteed when maximum likelihood is applied, and 3) we discuss and illustrate problems related to response probabilities estimation, namely existence of a solution to the estimating equations, problems of convergence, and extreme weights. We explain and illustrate why the first aforementioned problem is more likely with calibration than with maximum likelihood estimation. We present the results of a simulation study in order to illustrate these elements.

翻译：解决无应答偏差的一种方法是将受访者的设计权重乘以估计响应概率的倒数，以补偿未应答者。最大似然估计和校准是两种可用于获得估计响应概率的方法。我们考虑一个可比较这些方法的通用框架。我们开展了一项关于应用校准时所得估计量行为的渐近研究。假设响应概率遵循逻辑回归模型，并假定数据为随机缺失且未经聚类。本研究的三项主要贡献为：1）我们证明，通过校准估计响应概率的估计量渐近等价于无偏估计量，且与使用真实响应概率的估计量相比，通过校准估计响应概率可获得效率提升；2）我们证明，通过校准估计响应概率的估计量对模型误设具有双重稳健性，并解释了为何应用最大似然估计时无法保证双重稳健性；3）我们讨论并说明了与响应概率估计相关的问题，即估计方程解的存在性、收敛问题以及极端权重。我们解释并说明了为何上述第一个问题在校准中比在最大似然估计中更易出现。我们通过模拟研究结果来阐述这些要素。