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Tirthankar Dasgupta

Publications and source records attributed to Tirthankar Dasgupta.

28 records · Page 2Linked to original sources
arXiv2018

Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes, and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes, and are directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.

stat.ME↗
arXiv2017

A randomization-based perspective of analysis of variance: a test statistic robust to treatment effect heterogeneity

Fisher randomization tests for Neyman's null hypothesis of no average treatment effects are considered in a finite population setting associated with completely randomized experiments with more than two treatments. The consequences of using the $F$ statistic to conduct such a test are examined both theoretically and computationally, and it is argued that under treatment effect heterogeneity, use of the $F$ statistic in the Fisher randomization test can severely inflate the type I error under Neyman's null hypothesis. An alternative test statistic is proposed, its asymptotic distributions under Fisher's and Neyman's null hypotheses are derived, and its advantages demonstrated.

math.ST↗
arXiv2017

A conditional randomization test to account for covariate imbalance in randomized experiments

We consider the conditional randomization test as a way to account for covariate imbalance in randomized experiments. The test accounts for covariate imbalance by comparing the observed test statistic to the null distribution of the test statistic conditional on the observed covariate imbalance. We prove that the conditional randomization test has the correct significance level and introduce original notation to describe covariate balance more formally. Through simulation, we verify that conditional randomization tests behave like more traditional forms of covariate adjustmet but have the added benefit of having the correct conditional significance level. Finally, we apply the approach to a randomized product marketing experiment where covariate information was collected after randomization.

stat.ME↗
arXiv2016

Causal Inference in Rebuilding and Extending the Recondite Bridge between Finite Population Sampling and Experimental Design

This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization restrictions and unequal replications. Novel conditions that are "milder" than strict additivity of treatment effects, yet permit unbiased estimation of the finite population sampling variance of any treatment contrast estimator, are derived. The consequences of departures from such conditions are also studied under the criterion of minimax bias, and a new justification for using the Neymanian conservative sampling variance estimator in experiments is provided. The proposed approach can readily be extended to the case of treatments with a general factorial structure.

stat.ME↗
arXiv2016

Randomization-Based Causal Inference from Unbalanced 2^2 Split-Plot Designs

Given two 2-level factors of interest, a 2^2 split-plot design} (a) takes each of the $2^2=4$ possible factorial combinations as a treatment, (b) identifies one factor as `whole-plot,' (c) divides the experimental units into blocks, and (d) assigns the treatments in such a way that all units within the same block receive the same level of the whole-plot factor. Assuming the potential outcomes framework, we propose in this paper a randomization-based estimation procedure for causal inference from 2^2 designs that are not necessarily balanced. Sampling variances of the point estimates are derived in closed form as linear combinations of the between- and within-block covariances of the potential outcomes. Results are compared to those under complete randomization as measures of design efficiency. Interval estimates are constructed based on conservative estimates of the sampling variances, and the frequency coverage properties evaluated via simulation. Asymptotic connections of the proposed approach to the model-based super-population inference are also established. Superiority over existing model-based alternatives is reported under a variety of settings for both binary and continuous outcomes.

stat.ME↗
arXiv2015

Improving Covariate Balance in 2^K Factorial Designs via Rerandomization

Factorial designs are widely used in agriculture, engineering, and the social sciences to study the causal effects of several factors simultaneously on a response. The objective of such a design is to estimate all factorial effects of interest, which typically include main effects and interactions among factors. To estimate factorial effects with high precision when a large number of pre-treatment covariates are present, balance among covariates across treatment groups should be ensured. We propose utilizing rerandomization to ensure covariate balance in factorial designs. Although both factorial designs and rerandomization have been discussed before, the combination has not. Here, theoretical properties of rerandomization for factorial designs are established, and empirical results are explored using an application from the New York Department of Education.

stat.ME↗
arXiv2015

A Potential Tale of Two by Two Tables from Completely Randomized Experiments

Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian and Bayesian perspectives, using the potential outcomes framework. A randomization-based justification of Fisher's exact test is provided. Arguing that the crucial assumption of constant causal effect is often unrealistic, and holds only for extreme cases, some new asymptotic and Bayesian inferential procedures are proposed. The proposed procedures exploit the intrinsic non-additivity of unit-level causal effects, can be applied to linear and non-linear estimands, and dominate the existing methods, as verified theoretically and also through simulation studies.

math.ST↗
arXiv2014

Inference for deformation and interference in 3D printing

Additive manufacturing, or 3D printing, is a promising manufacturing technique marred by product deformation due to material solidification in the printing process. Control of printed product deformation can be achieved by a compensation plan. However, little attention has been paid to interference in compensation, which is thought to result from the inevitable discretization of a compensation plan. We investigate interference with an experiment involving the application of discretized compensation plans to cylinders. Our treatment illustrates a principled framework for detecting and modeling interference, and ultimately provides a new step toward better understanding quality control for 3D printing.

stat.AP↗
arXiv2012

Causal inference from $2^k$ factorial designs using the potential outcomes model

A framework for causal inference from two-level factorial designs is proposed. The framework utilizes the concept of potential outcomes that lies at the center stage of causal inference and extends Neyman's repeated sampling approach for estimation of causal effects and randomization tests based on Fisher's sharp null hypothesis to the case of 2-level factorial experiments. The framework allows for statistical inference from a finite population, permits definition and estimation of estimands other than "average factorial effects" and leads to more flexible inference procedures than those based on ordinary least squares estimation from a linear model.

stat.ME↗