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DTSTAMP:20260506T144019
DTSTART;TZID=America/Detroit:20260507T150000
DTEND;TZID=America/Detroit:20260507T170000
SUMMARY:Lecture / Discussion:Methods for Causal Inference in Settings with Clustered Data Subject to Missingness and Measurement Error
DESCRIPTION:Educational programs\, healthcare policies\, and economic shocks frequently act upon intact clusters rather than isolated individuals. Evaluations of such interventions can adjust for baseline differences between clusters with matching\, then address persisting imbalances through regression adjustment. The Peters-Belson (PB)/Oaxaca-Blinder (OB) estimator fits a regression to predict outcomes individuals would have had if they were in the control condition\, and adjusts for imbalances in predicted outcomes by comparing individuals’ differences between observed and predicted outcomes.\n\nThis dissertation begins by showing that in studies that enroll or match only a small number of clusters\, the regression fit contributes non-negligibly to variability of the PB/OB estimator both across studies and across treatment allocations within studies. It makes two proposals in response: first\, incorporating auxiliary clusters—those that are not retained in the initial cluster match—into the regression fit\, and second\, defining the regression coefficients and the PB/OB estimator as M-estimators of regression. The first proposal exhibits promising gains in precision in simulations and an empirical application\, while the second exhibits improved estimation of sampling variability over variance estimators that ignore variation from the coefficient estimates\, particularly when paired with a novel jackknife-type bias correction.\n\nThe CR2 adjustment is a widely used bias correction for cluster-robust variance estimates\, but it may be computationally infeasible in studies with large clusters given existing routines’ reliance on obtaining spectral decompositions of estimated cluster-specific covariance matrices. Chapter 4 provides exact representations of CR2 that obviate this step of the computations\, reducing walltime of CR2 estimates from over a day to just over a minute in settings previously deemed too computationally burdensome.\n\nThe concluding chapter focuses on the initial cluster-level match\, proposing two propensity score (PS) estimators that balance latent confounders when only noisy measurements are available\, if they are available at all. These PS estimators improve matching feasibility and reduce the MSE of treatment effect estimators compared to propensity scores generated from a logistic regression fit to the noisy measurements.
UID:148137-21903034@events.umich.edu
URL:https://events.umich.edu/event/148137
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation
LOCATION:West Hall - 438
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20260504T114020
DTSTART;TZID=America/Detroit:20260521T130000
DTEND;TZID=America/Detroit:20260521T150000
SUMMARY:Lecture / Discussion:Distributional Learning via Flexible Expectile Regression: Methods for Dependent\, Multivariate and Incomplete Data
DESCRIPTION:We develop a unified framework for flexible distributional learning based on expectile regression with adaptive basis functions\, allowing one to capture heterogeneous covariate effects across different regions of the outcome distribution. Building on this foundation\, we introduce a series of methodological contributions that extend expectile regression to increasingly complex data settings.\n\nFirst\, we propose a flexible nonparametric framework for expectile regression using reproducing kernel Hilbert spaces (RKHS)\, motivated by longitudinal studies in human biology in which aspects of the distribution of offspring anthropometry covary with parental characteristics. We develop a computationally efficient algorithm based on over-relaxed alternating direction method of multipliers (ADMM) to estimate expectiles across multiple distributional levels\, and establish valid joint inference procedures for a collection of expectiles using both cross-fitting and robust analytic approaches.\n\nSecond\, we extend expectile regression to event time data subject to right censoring and left truncation\, motivated by biomedical and public health studies where outcomes are incompletely observed and covariate effects may vary across the lifespan. Our motivating application is to understand how lifespans in different demographic groups correspond to neighborhood deprivation\, allowing for different effects on early and late mortality. To capture such patterns\, we estimate conditional expectiles of patient lifespans using weighting to account for censoring and truncation.  We then derive asymptotic linear expansions of the estimators and construct robust sandwich variance estimators\, enabling valid inference for distributional contrasts\, including comparisons across demographic groups and difference-in-difference analyses across expectile levels.\n\nThird\, we develop a unified framework for multivariate generalized expectile regression to analyze multi-output longitudinal data\, motivated by applications in which multiple related outcomes are measured repeatedly over time and exhibit complex dependence. Examples include biomedical studies where multiple health indicators are tracked for each patient\, or demographic data where event counts in geographic strata evolve jointly over time. Such data may exhibit heterogeneous covariate effects that predict different features of the response distribution. We begin by extending expectile regression to have a link function for each response\, enabling the specification of models with additive and multiplicative structures. We formulate the problem as a stacked estimating equation system capturing dependence across outcomes\, across time\, and across distributional levels without requiring specification of a working correlation structure. We develop cluster-robust sandwich covariance estimators that support valid inference for joint hypotheses\, enabling simultaneous assessment of distributional effects across outcomes and expectile levels.\n\nFinally\, we introduce a new class of interpretable distributional summaries based on expectile L-moments (EL-moments)\, motivated by the need for robust and informative measures of distributional shape that can be modeled in relation to covariates. Classical measures such as skewness and kurtosis are often sensitive to extreme observations and are not readily adapted to regression settings\, while quantile-based summaries lack smoothness and can be difficult to integrate into unified modeling frameworks. By projecting the expectile function onto a shifted Legendre polynomial basis\, we obtain EL-moments that provide interpretable summaries of location\, scale\, asymmetry\, and tail behavior. We further extend these summaries to conditional settings via expectile regression\, enabling covariate-dependent characterization of distributional features. We develop an influence-function-based framework for inference\, yielding consistent covariance estimators for both the EL-moment coefficients and their derived ratios.
UID:148074-21902920@events.umich.edu
URL:https://events.umich.edu/event/148074
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation
LOCATION:West Hall - 438
CONTACT:
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