40,552 research outputs found
Cluster-Robust Bootstrap Inference in Quantile Regression Models
In this paper I develop a wild bootstrap procedure for cluster-robust
inference in linear quantile regression models. I show that the bootstrap leads
to asymptotically valid inference on the entire quantile regression process in
a setting with a large number of small, heterogeneous clusters and provides
consistent estimates of the asymptotic covariance function of that process. The
proposed bootstrap procedure is easy to implement and performs well even when
the number of clusters is much smaller than the sample size. An application to
Project STAR data is provided.Comment: 46 pages, 4 figure
A new approach to hierarchical data analysis: Targeted maximum likelihood estimation for the causal effect of a cluster-level exposure
We often seek to estimate the impact of an exposure naturally occurring or
randomly assigned at the cluster-level. For example, the literature on
neighborhood determinants of health continues to grow. Likewise, community
randomized trials are applied to learn about real-world implementation,
sustainability, and population effects of interventions with proven
individual-level efficacy. In these settings, individual-level outcomes are
correlated due to shared cluster-level factors, including the exposure, as well
as social or biological interactions between individuals. To flexibly and
efficiently estimate the effect of a cluster-level exposure, we present two
targeted maximum likelihood estimators (TMLEs). The first TMLE is developed
under a non-parametric causal model, which allows for arbitrary interactions
between individuals within a cluster. These interactions include direct
transmission of the outcome (i.e. contagion) and influence of one individual's
covariates on another's outcome (i.e. covariate interference). The second TMLE
is developed under a causal sub-model assuming the cluster-level and
individual-specific covariates are sufficient to control for confounding.
Simulations compare the alternative estimators and illustrate the potential
gains from pairing individual-level risk factors and outcomes during
estimation, while avoiding unwarranted assumptions. Our results suggest that
estimation under the sub-model can result in bias and misleading inference in
an observational setting. Incorporating working assumptions during estimation
is more robust than assuming they hold in the underlying causal model. We
illustrate our approach with an application to HIV prevention and treatment
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