Exploring the design and analysis of complex experiments: Selective randomization and peer influence

This manuscript consists of two self-contained chapters about the design and analysis of randomized experiments. The first chapter studies a two-stage rerandomization design that can actively avoid undesirable covariate imbalances in randomized survey experiment, and is based on a joint work with Tianyi Qu and Xinran Li. The second chapter studies peer effects when the stable unit treatment value assumption in classical randomized experiments fails, and is based on a joint work with Felix Elwert, Tamas Keller and Xinran Li. Chapter 1. Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this concern, by randomly selecting the experimental units from the target population of interest. However, as pointed out by Morgan and Rubin (2012), chance imbalances often exist in covariate distributions between different treatment groups even under completely randomized experiments. Not surprisingly, such covariate imbalances also occur in randomized survey experiments. Furthermore, the covariate imbalances happen not only between different treatment groups, but also between the sampled experimental units and the overall population of interest. In this chapter, we propose a two-stage rerandomization design that can actively avoid undesirable covariate imbalances at both the sampling and treatment assignment stages. We further develop asymptotic theory for rerandomized survey experiments, demonstrating that rerandomization provides better covariate balance, more precise treatment effect estimators, and shorter large-sample confidence intervals. We also propose covariate adjustment to deal with remaining covariate imbalances after rerandomization, showing that it can further improve both the sampling and estimated precision. Our work allows general relationship among covariates at the sampling, treatment assignment and analysis stages, and generalizes both rerandomization in classical randomized experiments (Morgan and Rubin 2012) and rejective sampling in survey sampling (Fuller 2009). Chapter 2. Understanding peer effects or influences among units has been an important research topic in social sciences, where the units are often connected in practice. Motivated by a randomized field experiment recently conducted at Hungarian primary schools, we propose new statistical methodology to define and analyze peer effects among deskmates in the schools, which is one of the primary objectives of this experiment. To make the inference feasible, we assume that the peer effects are mainly driven by certain baseline or pretreatment attributes of the deskmates, while allowing some mean-zero deviances that are affected by additional aspects of seat allocations. Our inference is nonparametric and randomization-based, permitting flexible and unknown individual peer effect heterogeneity across all units, as well as investigations of the effect heterogeneity across subsets of units. We consider general randomized seat allocation mechanisms that are symmetric in units with the same characteristic, including both the common random partition and the constrained randomization that restricts the numbers of desks with different pairs of units' features, where both the characteristics and features are certain pretreatment covariates of the units that can be chosen by the researchers. Finally, we conduct simulations to illustrate the advantage of the proposed methodology.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Yang, Zihao

Contributors dc:contributor

• Li, Xinran
• Shao, Xiaofeng
• Liang, Feng
• Yu, Ruoqi

• Causal Inference
• Potential Outcome
• Randomization-based Inference
• Covariate Imbalance
• Peer Effects

Statement dc:rights

• Copyright 2023 Zihao Yang

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/122253

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F122253