arXiv subjects

Peng Ding

Publications and source records attributed to Peng Ding.

At least 109 records · Page 6Linked to original sources

arXiv2020

Is being an only child harmful to psychological health?: Evidence from an instrumental variable analysis of China's One-Child Policy

This paper evaluates the effects of being an only child in a family on psychological health, leveraging data on the One-Child Policy in China. We use an instrumental variable approach to address the potential unmeasured confounding between the fertility decision and psychological health, where the instrumental variable is an index on the intensity of the implementation of the One-Child Policy. We establish an analytical link between the local instrumental variable approach and principal stratification to accommodate the continuous instrumental variable. Within the principal stratification framework, we postulate a Bayesian hierarchical model to infer various causal estimands of policy interest while adjusting for the clustering data structure. We apply the method to the data from the China Family Panel Studies and find small but statistically significant negative effects of being an only child on self-reported psychological health for some subpopulations. Our analysis reveals treatment effect heterogeneity with respect to both observed and unobserved characteristics. In particular, urban males suffer the most from being only children, and the negative effect has larger magnitude if the families were more resistant to the One-Child Policy. We also conduct sensitivity analysis to assess the key instrumental variable assumption.

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arXiv2020

Two seemingly paradoxical results in linear models: the variance inflation factor and the analysis of covariance

A result from a standard linear model course is that the variance of the ordinary least squares (OLS) coefficient of a variable will never decrease when including additional covariates. The variance inflation factor (VIF) measures the increase of the variance. Another result from a standard linear model or experimental design course is that including additional covariates in a linear model of the outcome on the treatment indicator will never increase the variance of the OLS coefficient of the treatment at least asymptotically. This technique is called the analysis of covariance (ANCOVA), which is often used to improve the efficiency of treatment effect estimation. So we have two paradoxical results: adding covariates never decreases the variance in the first result but never increases the variance in the second result. In fact, these two results are derived under different assumptions. More precisely, the VIF result conditions on the treatment indicators but the ANCOVA result averages over them. Comparing the estimators with and without adjusting for additional covariates in a completely randomized experiment, I show that the former has smaller variance averaging over the treatment indicators, and the latter has smaller variance at the cost of a larger bias conditioning on the treatment indicators. Therefore, there is no real paradox.

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arXiv2020

Overlap in Observational Studies with High-Dimensional Covariates

Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument, suggesting that these assumptions are stronger than investigators likely realize. Our key innovation is to explore how strict overlap restricts global discrepancies between the covariate distributions in the treated and control populations. Exploiting results from information theory, we derive explicit bounds on the average imbalance in covariate means under strict overlap and show that these bounds become more restrictive as the dimension grows large. We discuss how these implications interact with assumptions and procedures commonly deployed in observational causal inference, including sparsity and trimming.

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arXiv2020

Rerandomization and Regression Adjustment

Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome-generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting analysis of covariance (ANCOVA) in the analysis stage. We can embed blocking into a wider class of experimental design called rerandomization, and extend the classical ANCOVA to more general regression adjustment. Rerandomization trumps complete randomization in the design stage, and regression adjustment trumps the simple difference-in-means estimator in the analysis stage. It is then intuitive to use both rerandomization and regression adjustment. Under the randomization-inference framework, we establish a unified theory allowing the designer and analyzer to have access to different sets of covariates. We find that asymptotically (a) for any given estimator with or without regression adjustment, rerandomization never hurts either the sampling precision or the estimated precision, and (b) for any given design with or without rerandomization, our regression-adjusted estimator never hurts the estimated precision. Therefore, combining rerandomization and regression adjustment yields better coverage properties and thus improves statistical inference. To theoretically quantify these statements, we discuss optimal regression-adjusted estimators in terms of the sampling precision and the estimated precision, and then measure the additional gains of the designer and the analyzer. We finally suggest using rerandomization in the design and regression adjustment in the analysis followed by the Huber--White robust standard error.

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arXiv2019

Conservative Wasserstein Training for Pose Estimation

This paper targets the task with discrete and periodic class labels ($e.g.,$ pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or regression loss is not well matched to this problem as they ignore the periodic nature of the labels and the class similarity, or assume labels are continuous value. We propose to incorporate inter-class correlations in a Wasserstein training framework by pre-defining ($i.e.,$ using arc length of a circle) or adaptively learning the ground metric. We extend the ground metric as a linear, convex or concave increasing function $w.r.t.$ arc length from an optimization perspective. We also propose to construct the conservative target labels which model the inlier and outlier noises using a wrapped unimodal-uniform mixture distribution. Unlike the one-hot setting, the conservative label makes the computation of Wasserstein distance more challenging. We systematically conclude the practical closed-form solution of Wasserstein distance for pose data with either one-hot or conservative target label. We evaluate our method on head, body, vehicle and 3D object pose benchmarks with exhaustive ablation studies. The Wasserstein loss obtaining superior performance over the current methods, especially using convex mapping function for ground metric, conservative label, and closed-form solution.

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arXiv2019

Sharp bounds on the relative treatment effect for ordinal outcomes

For ordinal outcomes, the average treatment effect is often ill-defined and hard to interpret. Echoing Agresti and Kateri (2017), we argue that the relative treatment effect can be a useful measure especially for ordinal outcomes, which is defined as $γ= \mathrm{pr}\{ Y_i(1) > Y_i(0) \} - \mathrm{pr}\{ Y_i(1) < Y_i(0) \}$, with $Y_i(1)$ and $Y_i(0)$ being the potential outcomes of unit $i$ under treatment and control, respectively. Given the marginal distributions of the potential outcomes, we derive the sharp bounds on $γ,$ which are identifiable parameters based on the observed data. Agresti and Kateri (2017) focused on modeling strategies under the assumption of independent potential outcomes, but we allow for arbitrary dependence.

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arXiv2019

A bracketing relationship between difference-in-differences and lagged-dependent-variable adjustment

Difference-in-differences is a widely-used evaluation strategy that draws causal inference from observational panel data. Its causal identification relies on the assumption of parallel trends, which is scale dependent and may be questionable in some applications. A common alternative is a regression model that adjusts for the lagged dependent variable, which rests on the assumption of ignorability conditional on past outcomes. In the context of linear models, \citet{APbook} show that the difference-in-differences and lagged-dependent-variable regression estimates have a bracketing relationship. Namely, for a true positive effect, if ignorability is correct, then mistakenly assuming parallel trends will overestimate the effect; in contrast, if the parallel trends assumption is correct, then mistakenly assuming ignorability will underestimate the effect. We show that the same bracketing relationship holds in general nonparametric (model-free) settings. We also extend the result to semiparametric estimation based on inverse probability weighting. We provide three examples to illustrate the theoretical results with replication files in \citet{ding2019bracketingData}.

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arXiv2019

Measurement errors in the binary instrumental variable model

Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment or outcome. We first consider non-differential measurement errors, that is, the mis-measured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, the measurement error of the treatment biases the estimate away from zero, and the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings.

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arXiv2019

Causal inference with confounders missing not at random

It is important to draw causal inference from observational studies, which, however, becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. We propose a novel framework to nonparametrically identify causal effects with confounders subject to an outcome-independent missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal effects.

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arXiv2018

Rerandomization in $2^K$ Factorial Experiments

With many pretreatment covariates and treatment factors, the classical factorial experiment often fails to balance covariates across multiple factorial effects simultaneously. Therefore, it is intuitive to restrict the randomization of the treatment factors to satisfy certain covariate balance criteria, possibly conforming to the tiers of factorial effects and covariates based on their relative importances. This is rerandomization in factorial experiments. We study the asymptotic properties of this experimental design under the randomization inference framework without imposing any distributional or modeling assumptions of the covariates and outcomes. We derive the joint asymptotic sampling distribution of the usual estimators of the factorial effects, and show that it is symmetric, unimodal, and more "concentrated" at the true factorial effects under rerandomization than under the classical factorial experiment. We quantify this advantage of rerandomization using the notions of "central convex unimodality" and "peakedness" of the joint asymptotic sampling distribution. We also construct conservative large-sample confidence sets for the factorial effects.

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arXiv2018

Randomization Inference for Peer Effects

Many previous causal inference studies require no interference, that is, the potential outcomes of a unit do not depend on the treatments of other units. However, this no-interference assumption becomes unreasonable when a unit interacts with other units in the same group or cluster. In a motivating application, a university in China admits students through two channels: the college entrance exam (also known as Gaokao) and recommendation (often based on Olympiads in various subjects). The university randomly assigns students to dorms, each of which hosts four students. Students within the same dorm live together and have extensive interactions. Therefore, it is likely that peer effects exist and the no-interference assumption does not hold. It is important to understand peer effects, because they give useful guidance for future roommate assignment to improve the performance of students. We define peer effects using potential outcomes. We then propose a randomization-based inference framework to study peer effects with arbitrary numbers of peers and peer types. Our inferential procedure does not assume any parametric model on the outcome distribution. Our analysis gives useful practical guidance for policy makers of the university in China.

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arXiv2018

Using Missing Types to Improve Partial Identification with Application to a Study of HIV Prevalence in Malawi

Frequently, empirical studies are plagued with missing data. When the data are missing not at random, the parameter of interest is not identifiable in general. Without additional assumptions, we can derive bounds of the parameters of interest, which, unfortunately, are often too wide to be informative. Therefore, it is of great importance to sharpen these worst-case bounds by exploiting additional information. Traditional missing data analysis uses only the information of the binary missing data indicator, that is, a certain data point is either missing or not. Nevertheless, real data often provide more information than a binary missing data indicator, and they often record different types of missingness. In a motivating HIV status survey, missing data may be due to the units' unwillingness to respond to the survey items or their hospitalization during the visit, and may also be due to the units' temporarily absence or relocation. It is apparent that some missing types are more likely to be missing not at random, but other missing types are more likely to be missing at random. We show that making full use of the missing types results in narrower bounds of the parameters of interest. In a real-life example, we demonstrate substantial improvement of more than 50% reduction in bound widths for estimating the prevalence of HIV in rural Malawi. As we illustrate using the HIV study, our strategy is also useful for conducting sensitivity analysis by gradually increasing or decreasing the set of types that are missing at random. In addition, we propose an easy-to-implement method to construct confidence intervals for partially identified parameters with bounds expressed as the minimums and maximums of finite parameters, which is useful for not only our problem but also many other problems involving bounds.

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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.

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arXiv2018

Using Survival Information in Truncation by Death Problems Without the Monotonicity Assumption

In some randomized clinical trials, patients may die before the measurements of their outcomes. Even though randomization generates comparable treatment and control groups, the remaining survivors often differ significantly in background variables that are prognostic to the outcomes. This is called the truncation by death problem. Under the potential outcomes framework, the only well-defined causal effect on the outcome is within the subgroup of patients who would always survive under both treatment and control. Because the definition of the subgroup depends on the potential values of the survival status that could not be observed jointly, without making strong parametric assumptions, we cannot identify the causal effect of interest and consequently can only obtain bounds of it. Unfortunately, however, many bounds are too wide to be useful. We propose to use detailed survival information before and after the measurements of the outcomes to sharpen the bounds of the subgroup causal effect. Because survival times contain useful information about the final outcome, carefully utilizing them could improve statistical inference without imposing strong parametric assumptions. Moreover, we propose to use a copula model to relax the commonly-invoked but often doubtful monotonicity assumption that the treatment extends the survival time for all patients.

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arXiv2018

Causal Inference: A Missing Data Perspective

Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes of the same units under different treatment conditions. Because for each unit at most one of the potential outcomes is observed and the rest are missing, causal inference is inherently a missing data problem. Indeed, there is a close analogy in the terminology and the inferential framework between causal inference and missing data. Despite the intrinsic connection between the two subjects, statistical analyses of causal inference and missing data also have marked differences in aims, settings and methods. This article provides a systematic review of causal inference from the missing data perspective. Focusing on ignorable treatment assignment mechanisms, we discuss a wide range of causal inference methods that have analogues in missing data analysis, such as imputation, inverse probability weighting and doubly-robust methods. Under each of the three modes of inference--Frequentist, Bayesian, and Fisherian randomization--we present the general structure of inference for both finite-sample and super-population estimands, and illustrate via specific examples. We identify open questions to motivate more research to bridge the two fields.

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arXiv2017

Asymptotic Theory of Rerandomization in Treatment-Control Experiments

Although complete randomization ensures covariate balance on average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. To supplement existing results, we develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and a truncated Gaussian random variable. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We also demonstrate that, compared to complete randomization, rerandomization reduces the asymptotic sampling variances and quantile ranges of the difference-in-means estimator. Moreover, our work allows the construction of accurate large-sample confidence intervals for the average causal effect, thereby revealing further advantages of rerandomization over complete randomization.

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arXiv2017

Decomposing Treatment Effect Variation

Understanding and characterizing treatment effect variation in randomized experiments has become essential for going beyond the "black box" of the average treatment effect. Nonetheless, traditional statistical approaches often ignore or assume away such variation. In the context of randomized experiments, this paper proposes a framework for decomposing overall treatment effect variation into a systematic component explained by observed covariates and a remaining idiosyncratic component. Our framework is fully randomization-based, with estimates of treatment effect variation that are entirely justified by the randomization itself. Our framework can also account for noncompliance, which is an important practical complication. We make several contributions. First, we show that randomization-based estimates of systematic variation are very similar in form to estimates from fully-interacted linear regression and two stage least squares. Second, we use these estimators to develop an omnibus test for systematic treatment effect variation, both with and without noncompliance. Third, we propose an $R^2$-like measure of treatment effect variation explained by covariates and, when applicable, noncompliance. Finally, we assess these methods via simulation studies and apply them to the Head Start Impact Study, a large-scale randomized experiment.

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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.

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