Design-based Hájek estimation for clustered and stratified experiments
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913858606596096 |
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| author | Wang, Xinhe Hansen, Ben B. |
| author_facet | Wang, Xinhe Hansen, Ben B. |
| contents | Random allocation is essential for causal inference, but practical constraints often require assigning participants in clusters. They may be stratified pre-assignment, either of necessity or to reduce differences between treatment and control groups; but combining clustered assignment with blocking into pairs, triples, or other fine strata makes otherwise equivalent estimators perform quite differently. The two-way ANOVA with block effects can be inconsistent, as can another popular, seemingly innocuous estimator. In contrast, Hájek estimation remains broadly consistent for sample average treatment effects, but lacks a design-based standard error applicable with clusters and fine strata. To fill this gap, we offer a new variance estimator and establish its consistency. Analytic and simulation results recommend a hybrid of it and Neyman's estimator for designs with both small and large strata. We extend the Hájek estimator to accommodate covariates and adapt variance estimators to inherit Neyman-style conservativeness, at least for hypothesis testing. Further simulations suggest that with heterogeneous treatment effects, our combination of novelties is necessary and sufficient to maintain coverage in small-$n$ designs; the relevant $n$ being that of clusters, many large-scale studies are small-$n$. We consider two: a paired, aggregate-data nutritional study and an education study with student covariates and varying block sizes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10473 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Design-based Hájek estimation for clustered and stratified experiments Wang, Xinhe Hansen, Ben B. Methodology Random allocation is essential for causal inference, but practical constraints often require assigning participants in clusters. They may be stratified pre-assignment, either of necessity or to reduce differences between treatment and control groups; but combining clustered assignment with blocking into pairs, triples, or other fine strata makes otherwise equivalent estimators perform quite differently. The two-way ANOVA with block effects can be inconsistent, as can another popular, seemingly innocuous estimator. In contrast, Hájek estimation remains broadly consistent for sample average treatment effects, but lacks a design-based standard error applicable with clusters and fine strata. To fill this gap, we offer a new variance estimator and establish its consistency. Analytic and simulation results recommend a hybrid of it and Neyman's estimator for designs with both small and large strata. We extend the Hájek estimator to accommodate covariates and adapt variance estimators to inherit Neyman-style conservativeness, at least for hypothesis testing. Further simulations suggest that with heterogeneous treatment effects, our combination of novelties is necessary and sufficient to maintain coverage in small-$n$ designs; the relevant $n$ being that of clusters, many large-scale studies are small-$n$. We consider two: a paired, aggregate-data nutritional study and an education study with student covariates and varying block sizes. |
| title | Design-based Hájek estimation for clustered and stratified experiments |
| topic | Methodology |
| url | https://arxiv.org/abs/2406.10473 |