Randomized experiments have been the gold standard for drawing causal inference. The conventional model-based approach has been one of the most popular ways for analyzing treatment effects from randomized experiments, which is often carried through inference for certain model parameters. In this paper, we provide a systematic investigation of model-based analyses for treatment effects under the randomization-based inference framework. This framework does not impose any distributional assumptions on the outcomes, covariates and their dependence, and utilizes only randomization as the "reasoned basis". We first derive the asymptotic theory for Z-estimation in completely randomized experiments, and propose sandwich-type conservative covariance estimation. We then apply the developed theory to analyze both average and individual treatment effects in randomized experiments. For the average treatment effect, we consider three estimation strategies: model-based, model-imputed, and model-assisted, where the first two can be sensitive to model misspecification or require specific ways for parameter estimation. The model-assisted approach is robust to arbitrary model misspecification and always provides consistent average treatment effect estimation. We propose optimal ways to conduct model-assisted estimation using generally nonlinear least squares for parameter estimation. For the individual treatment effects, we propose to directly model the relationship between individual effects and covariates, and discuss the model's identifiability, inference and interpretation allowing model misspecification.

翻译：随机化实验已成为因果推断的黄金标准。传统的基于模型的方法一直是分析随机化实验中处理效应最常用的手段之一，通常通过对特定模型参数进行推断来实现。本文在随机化推断框架下，对处理效应的基于模型分析进行了系统性研究。该框架不对结果变量、协变量及其依赖关系施加任何分布假设，仅将随机化作为“合理依据”。我们首先推导了完全随机化实验中Z估计的渐近理论，并提出了三明治型保守协方差估计方法。随后将所发展的理论应用于分析随机化实验中的平均处理效应与个体处理效应。对于平均处理效应，我们考虑了三种估计策略：基于模型、模型插补与模型辅助方法，其中前两种可能对模型设定错误敏感或需要特定的参数估计方式。模型辅助方法对任意模型设定错误具有稳健性，且始终能提供一致的平均处理效应估计。我们提出了使用广义非线性最小二乘法进行参数估计以实现模型辅助估计的最优方法。对于个体处理效应，我们建议直接建模个体效应与协变量之间的关系，并在允许模型设定错误的条件下讨论了模型的可识别性、推断与解释问题。