scholarly journals Asymptotic theory of rerandomization in treatment–control experiments

2018 ◽  
Vol 115 (37) ◽  
pp. 9157-9162 ◽  
Author(s):  
Xinran Li ◽  
Peng Ding ◽  
Donald B. Rubin
Keyword(s):  
Asymptotic Theory ◽  
Causal Effect ◽  
Random Variable ◽  
Causal Effects ◽  
Equal Treatment ◽  
Finite Sample ◽  
Previous Theory ◽  
Covariate Balance ◽  
Average Causal Effect ◽  
The Difference

Although complete randomization ensures covariate balance on average, the chance of 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. 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 truncated Gaussian random variables. 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 demonstrate that, compared with complete randomization, rerandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the average causal effect.

scholarly journals Data-Adaptive Causal Effects and Superefficiency

2016 ◽  
Vol 4 (2) ◽  
Author(s):  
Peter M. Aronow
Keyword(s):  
Causal Inference ◽  
Empirical Distribution ◽  
Causal Effect ◽  
Short Note ◽  
Causal Effects ◽  
Asymptotically Normal ◽  
Average Causal Effect ◽  
Population Average ◽  
Data Adaptive ◽  
Local Average

AbstractRecent approaches in causal inference have proposed estimating average causal effects that are local to some subpopulation, often for reasons of efficiency. These inferential targets are sometimes data-adaptive, in that they are dependent on the empirical distribution of the data. In this short note, we show that if researchers are willing to adapt the inferential target on the basis of efficiency, then extraordinary gains in precision can potentially be obtained. Specifically, when causal effects are heterogeneous, any asymptotically normal and root-$n$ consistent estimator of the population average causal effect is superefficient for a data-adaptive local average causal effect.

scholarly journals Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

2018 ◽  
Vol 43 (5) ◽  
pp. 540-567 ◽  
Author(s):  
Jiannan Lu ◽  
Peng Ding ◽  
Tirthankar Dasgupta
Keyword(s):  
Causal Effect ◽  
Real Life ◽  
Causal Effects ◽  
Potential Outcomes ◽  
Randomized Experiments ◽  
Sharp Bounds ◽  
Average Causal Effect ◽  
Behavioral Studies ◽  
And Control ◽  
Potential Outcomes Framework

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 is 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.

Estimating Causal Effects From Multilevel Group-Allocation Data

2005 ◽  
Vol 30 (4) ◽  
pp. 397-412 ◽  
Author(s):  
Alix I. Gitelman
Keyword(s):  
Group Membership ◽  
Causal Effect ◽  
Hierarchical Linear Model ◽  
Dynamic Effect ◽  
Educational Interventions ◽  
Causal Effects ◽  
Group Dynamic ◽  
Average Causal Effect ◽  
Effect Of Treatment ◽  
Group Allocation

In group-allocation studies for comparing behavioral, social, or educational interventions, subjects in the same group necessarily receive the same treatment, whereby a group and/or group-dynamic effect can confound the treatment effect. General counterfactual outcomes that depend on group characteristics, group membership, and treatment are developed to provide a structure for specifying causal effects of treatment in the multilevel setting. An average causal effect of treatment cannot be specified, however, without a simplifying assumption of group-membership invariance (i.e., no group-dynamic effect). Under group-membership invariance and ignorability assumptions, the average causal effect is then connected to estimable quantities of the hierarchical linear model (HLM). Furthermore, it is shown that the typical specification of the HLM involves conditional independence assumptions that actually preclude the group-dynamic effect.

scholarly journals Testing for the Unconfoundedness Assumption Using an Instrumental Assumption

2014 ◽  
Vol 2 (2) ◽  
pp. 187-199 ◽  
Author(s):  
Xavier de Luna ◽  
Per Johansson
Keyword(s):  
Simulation Study ◽  
Instrumental Variable ◽  
Observational Studies ◽  
Causal Effect ◽  
Causal Effects ◽  
Nonparametric Identification ◽  
Average Causal Effect

AbstractThe identification of average causal effects of a treatment in observational studies is typically based either on the unconfoundedness assumption (exogeneity of the treatment) or on the availability of an instrument. When available, instruments may also be used to test for the unconfoundedness assumption. In this paper, we present a set of assumptions on an instrumental variable which allows us to test for the unconfoundedness assumption, although they do not necessarily yield nonparametric identification of an average causal effect. We propose a test for the unconfoundedness assumption based on the instrumental assumptions introduced and give conditions under which the test has power. We perform a simulation study and apply the results to a case study where the interest lies in evaluating the effect of job practice on employment.

scholarly journals Large Sample Bounds on the Survivor Average Causal Effect in the Presence of a Binary Covariate with Conditionally Ignorable Treatment Assignment

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Michael H. Freiman ◽  
Dylan S. Small
Keyword(s):  
Quality Of Life ◽  
Observational Study ◽  
Causal Effect ◽  
Average Causal Effect ◽  
The Subject ◽  
The Mean ◽  
The Difference ◽  
Censoring By Death ◽  
And Control

AbstractA common problem when conducting an experiment or observational study for the purpose of causal inference is “censoring by death,” in which an event occurring during the experiment causes the desired outcome value – such as quality of life (QOL) – not to be defined for some subjects. One approach to this is to estimate the Survivor Average Causal Effect (SACE), which is the difference in the mean QOL between the treated and control arms, considering only those individuals who would have had well-defined QOL regardless of whether they received the treatment of interest, where the treatment is imposed by the researcher in an experiment or by the subject in the case of an observational study. Zhang and Rubin [

INFERENCE FOR THE JUMP PART OF QUADRATIC VARIATION OF ITÔ SEMIMARTINGALES

2009 ◽  
Vol 26 (2) ◽  
pp. 331-368 ◽  
Author(s):  
Almut E.D. Veraart
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Variance ◽  
Quadratic Variation ◽  
Estimation Bias ◽  
Finite Sample ◽  
Realized Variance ◽  
Modeling Framework ◽  
Limit Theory ◽  
Monte Carlo Studies ◽  
The Difference

Recent research has focused on modeling asset prices by Itô semimartingales. In such a modeling framework, the quadratic variation consists of a continuous and a jump component. This paper is about inference on the jump part of the quadratic variation, which can be estimated by the difference of realized variance and realized multipower variation. The main contribution of this paper is twofold. First, it provides a bivariate asymptotic limit theory for realized variance and realized multipower variation in the presence of jumps. Second, this paper presents new, consistent estimators for the jump part of the asymptotic variance of the estimation bias. Eventually, this leads to a feasible asymptotic theory that is applicable in practice. Finally, Monte Carlo studies reveal a good finite sample performance of the proposed feasible limit theory.

Identification and Extrapolation of Causal Effects with Instrumental Variables

2018 ◽  
Vol 10 (1) ◽  
pp. 577-613 ◽  
Author(s):  
Magne Mogstad ◽  
Alexander Torgovitsky
Keyword(s):  
Instrumental Variables ◽  
Policy Evaluation ◽  
General Framework ◽  
Unobserved Heterogeneity ◽  
Causal Effect ◽  
Partial Identification ◽  
Causal Effects ◽  
Average Causal Effect ◽  
Special Cases ◽  
Selection On Unobservables

Instrumental variables (IV) are widely used in economics to address selection on unobservables. Standard IV methods produce estimates of causal effects that are specific to individuals whose behavior can be manipulated by the instrument at hand. In many cases, these individuals are not the same as those who would be induced to treatment by an intervention or policy of interest to the researcher. The average causal effect for the two groups can differ significantly if the effect of the treatment varies systematically with unobserved factors that are correlated with treatment choice. We review the implications of this type of unobserved heterogeneity for the interpretation of standard IV methods and for their relevance to policy evaluation. We argue that making inferences about policy-relevant parameters typically requires extrapolating from the individuals affected by the instrument to the individuals who would be induced to treatment by the policy under consideration. We discuss a variety of alternatives to standard IV methods that can be used to rigorously perform this extrapolation. We show that many of these approaches can be nested as special cases of a general framework that embraces the possibility of partial identification.

Estimating the Magnitude of the Relation Between Bullying, E-Bullying, and Suicidal Behaviors Among United States Youth, 2015

Crisis ◽  
2019 ◽  
Vol 40 (3) ◽  
pp. 157-165 ◽  
Author(s):  
Kevin S. Kuehn ◽  
Annelise Wagner ◽  
Jennifer Velloza
Keyword(s):  
Adolescent Suicide ◽  
Suicide Attempts ◽  
Causal Effect ◽  
Strong Association ◽  
Cross Sectional ◽  
Average Causal Effect ◽  
Effects Of Bullying ◽  
Pc Algorithm ◽  
Nationally Representative ◽  
Significant Covariates

Abstract. Background: Suicide is the second leading cause of death among US adolescents aged 12–19 years. Researchers would benefit from a better understanding of the direct effects of bullying and e-bullying on adolescent suicide to inform intervention work. Aims: To explore the direct and indirect effects of bullying and e-bullying on adolescent suicide attempts (SAs) and to estimate the magnitude of these effects controlling for significant covariates. Method: This study uses data from the 2015 Youth Risk Behavior Surveillance Survey (YRBS), a nationally representative sample of US high school youth. We quantified the association between bullying and the likelihood of SA, after adjusting for covariates (i.e., sexual orientation, obesity, sleep, etc.) identified with the PC algorithm. Results: Bullying and e-bullying were significantly associated with SA in logistic regression analyses. Bullying had an estimated average causal effect (ACE) of 2.46%, while e-bullying had an ACE of 4.16%. Limitations: Data are cross-sectional and temporal precedence is not known. Conclusion: These findings highlight the strong association between bullying, e-bullying, and SA.

scholarly journals Understanding the nature of association between anxiety phenotypes and anorexia nervosa: a triangulation approach

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
E. Caitlin Lloyd ◽  
Hannah M. Sallis ◽  
Bas Verplanken ◽  
Anne M. Haase ◽  
Marcus R. Munafò
Keyword(s):  
Anorexia Nervosa ◽  
Longitudinal Study ◽  
Anxiety Disorder ◽  
Anxiety Disorders ◽  
Causal Effect ◽  
Causal Effects ◽  
Observational Research ◽  
Genome Wide Association Studies ◽  
Genetic Liability ◽  
Depressed Affect

Abstract Background Evidence from observational studies suggests an association between anxiety disorders and anorexia nervosa (AN), but causal inference is complicated by the potential for confounding in these studies. We triangulate evidence across a longitudinal study and a Mendelian randomization (MR) study, to evaluate whether there is support for anxiety disorder phenotypes exerting a causal effect on AN risk. Methods Study One assessed longitudinal associations of childhood worry and anxiety disorders with lifetime AN in the Avon Longitudinal Study of Parents and Children cohort. Study Two used two-sample MR to evaluate: causal effects of worry, and genetic liability to anxiety disorders, on AN risk; causal effects of genetic liability to AN on anxiety outcomes; and the causal influence of worry on anxiety disorder development. The independence of effects of worry, relative to depressed affect, on AN and anxiety disorder outcomes, was explored using multivariable MR. Analyses were completed using summary statistics from recent genome-wide association studies. Results Study One did not support an association between worry and subsequent AN, but there was strong evidence for anxiety disorders predicting increased risk of AN. Study Two outcomes supported worry causally increasing AN risk, but did not support a causal effect of anxiety disorders on AN development, or of AN on anxiety disorders/worry. Findings also indicated that worry causally influences anxiety disorder development. Multivariable analysis estimates suggested the influence of worry on both AN and anxiety disorders was independent of depressed affect. Conclusions Overall our results provide mixed evidence regarding the causal role of anxiety exposures in AN aetiology. The inconsistency between outcomes of Studies One and Two may be explained by limitations surrounding worry assessment in Study One, confounding of the anxiety disorder and AN association in observational research, and low power in MR analyses probing causal effects of genetic liability to anxiety disorders. The evidence for worry acting as a causal risk factor for anxiety disorders and AN supports targeting worry for prevention of both outcomes. Further research should clarify how a tendency to worry translates into AN risk, and whether anxiety disorder pathology exerts any causal effect on AN.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

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