On the implied weights of linear regression for causal inference

Chattopadhyay, Ambarish; Zubizarreta, José R.

doi:10.48550/arxiv.2104.06581

Cited by 3 publications

(8 citation statements)

References 43 publications

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“…Following Chattopadhyay and Zubizarreta (2022), we focus on two common regression modeling approaches. In the first approach, the outcome is regressed on the covariates and the treatment indicator without any treatment-covariate interactions, and the average treatment effect is estimated by the coefficient of the treatment indicator.…”

Section: Methodsmentioning

confidence: 99%

“…Recently, Chattopadhyay and Zubizarreta (2022) offered a connection between weighting and linear regression methods for causal inference. In particular, they obtained new closed form expressions for the implicit weights in different methods involving the linear regression model.…”

Section: Introductionmentioning

confidence: 99%

“…See Abadie et al (2015), Imbens (2015), Gelman andImbens (2018), andBen-Michael et al (2021) for related analyses. Chattopadhyay and Zubizarreta (2022) examined properties of the implied weights of linear regression in both finite-and large-sample regimes.…”

Section: Introductionmentioning

confidence: 99%

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lmw: Linear Model Weights for Causal Inference

Chattopadhyay¹,

Greifer²,

Zubizarreta³

2023

Preprint

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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 at least a notion of a randomized experiment. However, in routine regression analyses in observational studies, it is unclear how well the adjustments made by regression approximate key features of randomization experiments, such as covariate balance, study representativeness, sample boundedness, and unweighted sampling. In this paper, we provide software to empirically address this question. In the new lmw package for R, we compute the implied linear model weights for average treatment effects and provide diagnostics for them. 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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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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lmw: Linear Model Weights for Causal Inference

Chattopadhyay¹,

Greifer²,

Zubizarreta³

2023

Preprint

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“…Many existing approaches can be written as examples of Equation 12 with various choices of ζ and χ, including the stable balancing weights approach (Zubizarreta, 2015); the lasso minimum distance estimator of the inverse propensity score ; the regularized calibrated propensity score estimator ; and entropy balancing (Hainmueller, 2012). In fact, even imputing µ 1 by averaging the predictions of a least squares regression of Y on X fit on the treated units can be written in this form: it is a weighted average of observations Y i with weights solving the problem above (11) for σ 2 = 0 (Chattopadhyay & Zubizarreta, 2021). Similarly, ridge regression corresponds to σ 2 > 0 (Ben-Michael, Feller, & Rothstein, 2021).…”

Section: Balancing Approach To Weightingmentioning

confidence: 99%

The Balancing Act in Causal Inference

Ben‐Michael¹,

Feller²,

Hirshberg³

et al. 2021

Preprint

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The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss two broad approaches to estimating these weights: the more traditional one, which fits a propensity score model and then uses the reciprocal of the estimated propensity score to construct weights, and the balancing approach, which estimates the inverse propensity weights essentially by the method of moments, finding weights that achieve balance in the sample. We review ideas from the causal inference, sample surveys, and semiparametric estimation literatures, with particular attention to the role of balance as a sufficient condition for robust inference. We focus on the inverse propensity weighting and augmented inverse propensity weighting estimators for the average treatment effect given strong ignorability and consider generalizations for a broader class of problems including policy evaluation and the estimation of individualized treatment effects.

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“…In the case of personalization, our estimand is equivalent to a conditional average treatment effect (see, e.g., Chapter 12 of Imbens and Rubin 13 2015). In what follows, we characterize the target population by a covariate profile x*; 39 that is, a vector of q ≥ p summary statistics of its observed covariate distribution. Usually, x* amounts to the means of the covariates in the target population, but the profile will ideally include higher order summary statistics to more completely characterize the distribution of covariates in the target population.…”

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confidence: 99%

Profile Matching for the Generalization and Personalization of Causal Inferences

Cohn

Zubizarreta

2022

Epidemiology

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We introduce profile matching, a multivariate matching method for randomized experiments and observational studies that finds the largest possible unweighted samples across multiple treatment groups that are balanced relative to a covariate profile. This covariate profile can represent a specific population or a target individual, facilitating the generalization and personalization of causal inferences. For generalization, because the profile often amounts to summary statistics for a target population, profile matching does not always require accessing individual-level data, which may be unavailable for confidentiality reasons. For personalization, the profile comprises the characteristics of a single individual. Profile matching achieves covariate balance by construction, but unlike existing approaches to matching, it does not require specifying a matching ratio, as this is implicitly optimized for the data. The method can also be used for the selection of units for study follow-up, and it readily applies to multivalued treatments with many treatment categories. We evaluate the performance of profile matching in a simulation study of the generalization of a randomized trial to a target population. We further illustrate this method in an exploratory observational study of the relationship between opioid use and mental health outcomes. We analyze these relationships for three covariate profiles representing: (i) sexual minorities, (ii) the Appalachian United States, and (iii) the characteristics of a hypothetical vulnerable patient. The method can be implemented via the new function profmatch in the designmatch package for R, for which we provide a step-by-step tutorial.

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On the implied weights of linear regression for causal inference

Cited by 3 publications

References 43 publications

lmw: Linear Model Weights for Causal Inference

lmw: Linear Model Weights for Causal Inference

The Balancing Act in Causal Inference

Profile Matching for the Generalization and Personalization of Causal Inferences

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