Multilevel regression and poststratification (MrP) has become a workhorse method for estimating population quantities from non-probability surveys, and is the primary model-based alternative to traditional survey calibration weighting methods, such as raking. For simple linear regression models, MrP methods admit ``equivalent weights'', allowing for direct comparisons between MrP and traditional calibration weighting. Such weights, however, have been unavailable for the most widely used MrP models, such as logistic regression. In this paper, we develop a natural generalization, ``MrP locally equivalent weights'' (MrPlew), which represent MrP as a weighting-style estimator that is locally equivalent to calibration weights near the observed responses. This enables a suite of standard weighting diagnostics, including frequentist sampling variability, covariate balance, and subgroup contribution. We formally justify the use of MrPlew in these cases: we prove the MrPlew-based variance estimator is asymptotically equivalent to the infinitesimal jackknife for common exponential family models, and we introduce a novel class of model checks based on invariance to data perturbations that generalize covariate balance and subgroup contribution to nonlinear models. We further show that MrPlew can be computed easily using existing MCMC samples and provide open-source software to compute MrPlew using the output of standard software. We illustrate our approach for several canonical studies that use MrP, including via a logistic regression outcome model, showing that implied covariate balance can sometimes be worse for MrP than for raking. Given the ease of computing, we recommend making MrPlew a standard part of the MrP model interrogation workflow.

翻译：多层回归与事后分层（Multilevel Regression and Poststratification, MrP）已从非概率调查中估计总体量提供了有效方法，成为传统调查校准加权方法（如层级调整）的主要基于模型的替代方案。对于简单线性回归模型，MrP方法允许构建“等价权重”，从而实现MrP与传统校准加权之间的直接比较。然而，对于最广泛使用的MrP模型（如逻辑回归），此类权重尚不可得。本文提出一种自然推广——"MrP局部等价权重"（MrPlew），将MrP表示为一种加权式估计量，在观测响应附近与校准权重局部等价。这使一系列标准加权诊断成为可能，包括频率学派抽样变异性、协变量平衡及子组贡献。我们为MrPlew在这些场景中的应用提供严格的理论依据：证明基于MrPlew的方差估计量在常见指数族模型下与无穷小刀切法渐近等价，并引入一种新型模型检验方法——基于数据扰动的不变性，将协变量平衡和子组贡献推广至非线性模型。进一步，我们展示MrPlew可通过现有MCMC样本轻松计算，并提供开源软件以利用标准软件输出计算MrPlew。通过若干使用MrP的经典研究案例（包括基于逻辑回归结果模型）验证方法有效性，结果表明MrP隐含的协变量平衡有时可能劣于层级调整。鉴于其计算简便性，我们建议将MrPlew标准化纳入MrP模型诊断流程。