arXiv subjects

Leonard Wainstein

Publications and source records attributed to Leonard Wainstein.

3 recordsLinked to original sources

arXiv2025

Sensitivity of weighted least squares estimators to omitted variables

We introduce tools for assessing the sensitivity, to unobserved confounding, of a common estimator of causal effects that employs weights: the weighted linear regression of the outcome on the treatment and observed covariates. This estimator's bias is a function of two intuitive weighted partial $R^2$ values: (i) the proportion of weighted variance in the treatment that unobserved confounding explains given the covariates and (ii) the proportion of weighted variance in the outcome that unobserved confounding explains given the covariates and the treatment. Following previous work, we define sensitivity statistics for routine reporting, derive formal bounds on the strength of unobserved confounding with (multiples of) the strength of certain covariates, and propose adjusted inference procedures. A key choice we make is to examine only how the outcome model is influenced by unobserved confounding, instead of how the weights have been affected. One benefit of this choice is that our tools apply with any (non-negative) weights (e.g., inverse propensity score, matching, or covariate balancing). Another benefit is that we can rely on omitted variable bias approaches that impose no distributional assumptions on the data or unobserved confounding, and can address misspecification bias. The tools are available in the sensewls package for R.

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arXiv2024

Comparing multilevel and fixed effect approaches in the generalized linear model setting

We extend prior work comparing linear multilevel models (MLM) and fixed effect (FE) models to the generalized linear model (GLM) setting, where the coefficient on a treatment variable is of primary interest. This leads to three insights. (i) First, as in the linear setting, MLM can be thought of as a regularized form of FE (RegFE). This explains why group-level confounding can greatly bias MLM's treatment coefficient estimates. However, unlike the linear setting, there is not an exact equivalence between MLM and RegFE in GLMs. (ii) Second, we study a generalization of "bias-corrected MLM" (bcMLM) to the GLM setting, and a corresponding "bias-corrected RegFE" (bcRegFE). None of FE, bcMLM, or bcRegFE entirely solve MLM's bias problem in GLMs, but bcMLM and bcRegFE tend to show less bias than does FE. (iii) Third, as in the linear setting, MLM's default standard errors can misspecify the true intragroup dependence structure in the GLM setting, which can yield downwardly biased standard errors. A cluster bootstrap is a more agnostic alternative. We also consider a cluster-robust standard error for (bc)RegFE. Ultimately, for non-linear GLMs, we recommend bcMLM for estimating the treatment coefficient, and a cluster bootstrap for standard errors and confidence intervals. If a bootstrap is not computationally feasible, then we recommend bcRegFE with cluster-robust standard errors, or FE with cluster-robust standard errors when group sizes are larger.

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arXiv2022

Targeted Function Balancing

This paper introduces Targeted Function Balancing (TFB), a covariate balancing weights framework for estimating the average treatment effect of a binary intervention. TFB first regresses an outcome on covariates, and then selects weights that balance functions (of the covariates) that are probabilistically near the resulting regression function. This yields balance in the regression function's predicted values and the covariates, with the regression function's estimated variance determining how much balance in the covariates is sufficient. Notably, TFB demonstrates that intentionally leaving imbalance in some covariates can increase efficiency without introducing bias, challenging traditions that warn against imbalance in any variable. Additionally, TFB is entirely defined by a regression function and its estimated variance, turning the problem of how best to balance the covariates into how best to model the outcome. Kernel regularized least squares (KRLS), the LASSO, and Bayesian Additive Regression Trees (BART) are considered as regression estimators. With KRLS, TFB contributes to the literature of kernel-based weights. As for the LASSO, TFB uses the regression function's estimated variance to prioritize balance in certain dimensions of the covariates, a feature that can be greatly exploited by choosing a sparse regression estimator. With BART, we demonstrate that TFB can apply regression estimators that do not have linear representations. The R Package tfb implements TFB.

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