arXiv subjects

Ambarish Chattopadhyay

Publications and source records attributed to Ambarish Chattopadhyay.

9 recordsLinked to original sources

arXiv2026

Neymanian inference in randomized experiments

In his seminal 1923 work, Neyman studied the variance estimation problem for the difference-in-means estimator of the average treatment effect in completely randomized experiments. He proposed a variance estimator that is conservative in general and unbiased under homogeneous treatment effects. While widely used under complete randomization, there is no unique or natural way to extend this estimator to more complex designs. To this end, we show that Neyman's estimator can be alternatively derived in two ways, leading to two novel variance estimation approaches: the imputation approach and the contrast approach. While both approaches recover Neyman's estimator under complete randomization, they yield fundamentally different variance estimators for more general designs. In the imputation approach, the variance is expressed in terms of observed and missing potential outcomes and then estimated by imputing the missing potential outcomes, akin to Fisherian inference. In the contrast approach, the variance is expressed in terms of unobservable contrasts of potential outcomes and then estimated by exchanging each unobservable contrast with an observable contrast. We examine the properties of both approaches, showing that for a large class of designs, each produces non-negative, conservative variance estimators that are unbiased in finite samples or asymptotically under homogeneous treatment effects.

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arXiv2026

An Anatomy of Event Studies: Hypothetical Experiments, Exact Decomposition, and Weighting Diagnostics

In recent decades, event studies have become widely used in health and social research to estimate the dynamic effects of staggered interventions. In this paper, we develop a framework grounded in experimental design principles for observational studies that encompasses common event study estimators and makes explicit how they borrow information across units and time periods. We consider two routes to identification, unconfoundedness in treatment initiation and parallel trends with limited anticipation, and construct weighted contrasts from outcome levels under the first and within-unit differences under the second. We propose a robust weighting estimator that draws on progressively larger sets of observations as stronger assumptions on treatment assignment and potential outcomes are imposed. We derive exact finite-sample decompositions of dynamic two-way fixed effects and interaction-weighted estimators, and of doubly robust estimators, into weighted contrasts of within-unit outcome differences, revealing the hypothetical experiment each approximates. These decompositions show which unit-period observations enter each contrast and how they are weighted, clarifying and supplementing the notion of forbidden comparisons. The implied weights yield diagnostics for covariate balance, sign reversal, effective sample size, information shares across observation groups, and each observation's influence on the estimate. We illustrate these diagnostics in a study of the effects of Castle Doctrine laws on homicide rates.

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arXiv2024

Design-based inference for generalized network experiments with stochastic interventions

A growing number of researchers are conducting randomized experiments to analyze causal relationships in network settings where units influence one another. A dominant methodology for analyzing these experiments is design-based, leveraging random treatment assignments as the basis for inference. In this paper, we generalize this design-based approach to accommodate complex experiments with a variety of causal estimands and different target populations. An important special case of such generalized network experiments is a bipartite network experiment, in which treatment is randomized among one set of units, and outcomes are measured on a separate set of units. We propose a broad class of causal estimands based on stochastic interventions for generalized network experiments. Using a design-based approach, we show how to estimate these causal quantities without bias and develop conservative variance estimators. We apply our methodology to a randomized experiment in education where participation in an anti-conflict promotion program is randomized among selected students. Our analysis estimates the causal effects of treating each student or their friends among different target populations in the network. We find that the program improves the overall conflict awareness among students but does not significantly reduce the total number of such conflicts.

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arXiv2024

lmw: Linear Model Weights for Causal Inference

The linear regression model is widely used in the biomedical and social sciences as well as in policy and business research to adjust for covariates and estimate the average effects of treatments. Behind every causal inference endeavor there is a hypothetical randomized experiment. However, in routine regression analyses in observational studies, it is unclear how well the adjustments made by regression approximate key features of randomized experiments, such as covariate balance, study representativeness, sample boundedness, and unweighted sampling. In this paper, we provide software to empirically address this question. We introduce the lmw package for R to compute the implied linear model weights and perform diagnostics for their evaluation. The weights are obtained as part of the design stage of the study; that is, without using outcome information. The implementation is general and applicable, for instance, in settings with instrumental variables and multi-valued treatments; in essence, in any situation where the linear model is the vehicle for adjustment and estimation of average treatment effects with discrete-valued interventions.

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arXiv2024

Notes on Causation, Comparison, and Regression

Comparison and contrast are the basic means to unveil causation and learn which treatments work. To build good comparison groups, randomized experimentation is key, yet often infeasible. In such non-experimental settings, we illustrate and discuss diagnostics to assess how well the common linear regression approach to causal inference approximates desirable features of randomized experiments, such as covariate balance, study representativeness, interpolated estimation, and unweighted analyses. We also discuss alternative regression modeling, weighting, and matching approaches and argue they should be given strong consideration in empirical work.

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arXiv2023

Balanced and Robust Randomized Treatment Assignments: The Finite Selection Model for the Health Insurance Experiment and Beyond

The Finite Selection Model (FSM) was developed by Carl Morris in the 1970s for the design of the RAND Health Insurance Experiment (HIE) (Morris 1979, Newhouse et al. 1993), one of the largest and most comprehensive social science experiments conducted in the U.S. The idea behind the FSM is that each treatment group takes its turns selecting units in a fair and random order to optimize a common assignment criterion. At each of its turns, a treatment group selects the available unit that maximally improves the combined quality of its resulting group of units in terms of the criterion. In the HIE and beyond, we revisit, formalize, and extend the FSM as a general tool for experimental design. Leveraging the idea of D-optimality, we propose and analyze a new selection criterion in the FSM. The FSM using the D-optimal selection function has no tuning parameters, is affine invariant, and when appropriate, retrieves several classical designs such as randomized block and matched-pair designs. For multi-arm experiments, we propose algorithms to generate a fair and random selection order of treatments. We demonstrate FSM's performance in a case study based on the HIE and in ten randomized studies from the health and social sciences. On average, the FSM achieves 68% better covariate balance than complete randomization and 56% better covariate balance than rerandomization in a typical study. We recommend the FSM be considered in experimental design for its conceptual simplicity, efficiency, and robustness.

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arXiv2023

One-Step weighting to generalize and transport treatment effect estimates to a target population

The problem of generalization and transportation of treatment effect estimates from a study sample to a target population is central to empirical research and statistical methodology. In both randomized experiments and observational studies, weighting methods are often used with this objective. Traditional methods construct the weights by separately modeling the treatment assignment and study selection probabilities and then multiplying functions (e.g., inverses) of their estimates. In this work, we provide a justification and an implementation for weighting in a single step. We show a formal connection between this one-step method and inverse probability and inverse odds weighting. We demonstrate that the resulting estimator for the target average treatment effect is consistent, asymptotically Normal, multiply robust, and semiparametrically efficient. We evaluate the performance of the one-step estimator in a simulation study. We illustrate its use in a case study on the effects of physician racial diversity on preventive healthcare utilization among Black men in California. We provide R code implementing the methodology.

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arXiv2022

On the implied weights of linear regression for causal inference

A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances. Now, linear regression models are commonly used to analyze observational data and estimate causal effects. How do linear regression adjustments in observational studies emulate key features of randomized experiments, such as covariate balance, self-weighted sampling, and study representativeness? In this paper, we provide answers to this and related questions by analyzing the implied (individual-level data) weights of linear regression methods. We derive new closed-form expressions of the weights and examine their properties in both finite and asymptotic regimes. We show that the implied weights of general regression problems can be equivalently obtained by solving a convex optimization problem. Among others, we study doubly and multiply robust properties of regression estimators from the perspective of their implied weights. This equivalence allows us to bridge ideas from the regression modeling and causal inference literatures. As a result, we propose novel regression diagnostics for causal inference that are part of the design stage of an observational study. As special cases, we analyze the implied weights in common settings such as multi-valued treatments and regression adjustment after matching. We implement the weights and diagnostics in the new lmw package for R.

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arXiv2021

Randomized and Balanced Allocation of Units into Treatment Groups Using the Finite Selection Model for R

The original Finite Selection Model (FSM) was developed in the 1970s to enhance the design of the RAND Health Insurance Experiment (HIE; Newhouse et al. 1993). At the time of its development by Carl Morris (Morris 1979), there were fundamental computational limitations to make the method widely available for practitioners. Today, as randomized experiments increasingly become more common, there is a need for implementing experimental designs that are randomized, balanced, robust, and easily applicable to several treatment groups. To help address this problem, we revisit the original FSM under the potential outcome framework for causal inference and provide its first readily available software implementation. In this paper, we provide an introduction to the FSM and a step-by-step guide for its use in R.

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