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BCDAG: An R package for Bayesian structure and Causal learning of Gaussian DAGs

BCDAG:高斯有向无环图的贝叶斯结构与因果学习R包

Directed Acyclic Graphs (DAGs) provide a powerful framework to model causal relationships among variables in multivariate settings; in addition, through the do-calculus theory, they allow for the identification and estimation of causal effects between variables also from pure observational data. In this setting, the process of inferring the DAG structure from the data is referred to as causal structure learning or causal discovery. We introduce BCDAG, an R package for…

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Estimating Heterogeneous Treatment Effects for General Responses

一般响应变量的异质性处理效应估计

Heterogeneous treatment effect models allow us to compare treatments at subgroup and individual levels, and are of increasing popularity in applications like personalized medicine, advertising, and education. In this talk, we first survey different causal estimands used in practice, which focus on estimating the difference in conditional means. We then propose DINA, the difference in natural parameters, to quantify heterogeneous treatment effect in exponential families and…

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Bootstrap inference for fixed-effect models

固定效应模型的Bootstrap推断

The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to correct the maximum-likelihood estimator for its bias as a means to salvage standard inferential procedures. Instead, we show that the parametric bootstrap replicates the distribution of the (uncorrected) maximum-likelihood estimator in large…

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Distributed Learning of Generalized Linear Causal Networks

广义线性因果网络的分布式学习

We consider the task of learning causal structures from data stored on multiple machines, and propose a novel structure learning method called distributed annealing on regularized likelihood score (DARLS) to solve this problem. We model causal structures by a directed acyclic graph that is parameterized with generalized linear models, so that our method is applicable to various types of data. To obtain a high-scoring causal graph, DARLS simulates an annealing process to…

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High-dimensional model-assisted inference for treatment effects with multi-valued treatments

多值处理效应的高维模型辅助推断

Consider estimation of average treatment effects with multi-valued treatments using augmented inverse probability weighted (IPW) estimators, depending on outcome regression and propensity score models in high-dimensional settings. These regression models are often fitted by regularized likelihood-based estimation, while ignoring how the fitted functions are used in the subsequent inference about the treatment parameters. Such separate estimation can be associated with known…

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Treatment effect estimation with Multilevel Regression and Poststratification

利用多层回归与后分层估计处理效应

Multilevel regression and poststratification (MRP) is a flexible modeling technique that has been used in a broad range of small-area estimation problems. Traditionally, MRP studies have been focused on non-causal settings, where estimating a single population value using a nonrepresentative sample was of primary interest. In this manuscript, MRP-style estimators will be evaluated in an experimental causal inference setting. We simulate a large-scale randomized control trial…

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Estimation of Conditional Random Coefficient Models using Machine Learning Techniques

利用机器学习估计条件随机系数模型

Nonparametric random coefficient (RC)-density estimation has mostly been considered in the marginal density case under strict independence of RCs and covariates. This paper deals with the estimation of RC-densities conditional on a (large-dimensional) set of control variables using machine learning techniques. The conditional RC-density allows to disentangle observable from unobservable heterogeneity in partial effects of continuous treatments adding to a growing literature…

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Automated causal inference in application to randomized controlled clinical trials

应用于随机对照临床试验的自动因果推断

Randomized controlled trials (RCTs) are considered as the gold standard for testing causal hypotheses in the clinical domain. However, the investigation of prognostic variables of patient outcome in a hypothesized cause-effect route is not feasible using standard statistical methods. Here, we propose a new automated causal inference method (AutoCI) built upon the invariant causal prediction (ICP) framework for the causal re-interpretation of clinical trial data. Compared to…

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Iterative Causal Discovery in the Possible Presence of Latent Confounders and Selection Bias

存在潜在混杂与选择偏差时的迭代因果发现

We present a sound and complete algorithm, called iterative causal discovery (ICD), for recovering causal graphs in the presence of latent confounders and selection bias. ICD relies on the causal Markov and faithfulness assumptions and recovers the equivalence class of the underlying causal graph. It starts with a complete graph, and consists of a single iterative stage that gradually refines this graph by identifying conditional independence (CI) between connected nodes.…

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Nonparametric Identification of Random Coefficients in Endogenous and Heterogeneous Aggregate Demand Models

内生且异质的总量需求模型中随机系数的非参数识别

This paper studies nonparametric identification in market level demand models for differentiated products with heterogeneous consumers. We consider a general class of models that allows for the individual specific coefficients to vary continuously across the population and give conditions under which the density of these coefficients, and hence also functionals such as welfare measures, is identified. A key finding is that two leading models, the BLP-model (Berry, Levinsohn,…

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Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions

通过改进精确搜索与较弱假设实现可靠因果发现

Many of the causal discovery methods rely on the faithfulness assumption to guarantee asymptotic correctness. However, the assumption can be approximately violated in many ways, leading to sub-optimal solutions. Although there is a line of research in Bayesian network structure learning that focuses on weakening the assumption, such as exact search methods with well-defined score functions, they do not scale well to large graphs. In this work, we introduce several strategies…

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Panel Data with Unknown Clusters

未知聚类结构下的面板数据

Clustered standard errors and approximate randomization tests are popular inference methods that allow for dependence within observations. However, they require researchers to know the cluster structure ex ante. We propose a procedure to help researchers discover clusters in panel data. Our method is based on thresholding an estimated long-run variance-covariance matrix and requires the panel to be large in the time dimension, but imposes no lower bound on the number of…

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Average Direct and Indirect Causal Effects under Interference

存在干扰时的平均直接与间接因果效应

We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct effect, and can be expressed without needing to compare outcomes across multiple randomized experiments. We show that the proposed indirect effect satisfies a decomposition theorem whereby, in a Bernoulli trial, the sum of the average…

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Do We Exploit all Information for Counterfactual Analysis? Benefits of Factor Models and Idiosyncratic Correction

反事实分析是否充分利用信息?因子模型与特异成分修正的作用

Optimal pricing, i.e., determining the price level that maximizes profit or revenue of a given product, is a vital task for the retail industry. To select such a quantity, one needs first to estimate the price elasticity from the product demand. Regression methods usually fail to recover such elasticities due to confounding effects and price endogeneity. Therefore, randomized experiments are typically required. However, elasticities can be highly heterogeneous depending on…

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The How and Why of Bayesian Nonparametric Causal Inference

贝叶斯非参数因果推断:方法与理由

Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this paper, we present a comprehensive overview of Bayesian nonparametric applications to causal inference. Our aims are to (i) introduce the fundamental Bayesian nonparametric toolkit; (ii) discuss how to determine which tool is most appropriate for a given problem; and (iii) show…

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A note on efficient minimum cost adjustment sets in causal graphical models

因果图模型中的高效最低成本调整集

We study the selection of adjustment sets for estimating the interventional mean under an individualized treatment rule. We assume a non-parametric causal graphical model with, possibly, hidden variables and at least one adjustment set comprised of observable variables. Moreover, we assume that observable variables have positive costs associated with them. We define the cost of an observable adjustment set as the sum of the costs of the variables that comprise it. We show…

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Matching Theory and Evidence on Covid-19 using a Stochastic Network SIR Model

用随机网络 SIR 模型连接新冠疫情理论与证据

This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic models. These moment conditions are used to investigate the identification and estimation of the transmission rates. The paper then proposes a method that jointly estimates the transmission rate and the magnitude of under-reporting of…

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Estimating Causal Effects of Multi-Aspect Online Reviews with Multi-Modal Proxies

利用多模态代理变量估计在线评论多维属性的因果效应

Online reviews enable consumers to engage with companies and provide important feedback. Due to the complexity of the high-dimensional text, these reviews are often simplified as a single numerical score, e.g., ratings or sentiment scores. This work empirically examines the causal effects of user-generated online reviews on a granular level: we consider multiple aspects, e.g., the Food and Service of a restaurant. Understanding consumers' opinions toward different aspects…

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Limited-Information Maximum Likelihood based Model Selection Procedures for Binary Outcomes

二元结果的有限信息最大似然模型选择程序

Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a limited-information maximum likelihood (LIML) estimator can obtain an unbiased estimate for causal effects despite there being nonlinear outcomes such as binary outcomes; however, it requires that we specify not only a correct outcome model but also a…

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Causal mediation with instrumental variables

工具变量下的因果中介分析

Mediation analysis is a strategy for understanding the mechanisms by which treatments or interventions affect later outcomes. Mediation analysis is frequently applied in randomized trial settings, but typically assumes: a) that randomized assignment is the exposure of interest as opposed to actual take-up of the intervention, and b) no unobserved confounding of the mediator-outcome relationship. In contrast to the rich literature on instrumental variable (IV) methods to…

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Sharp nonparametric bounds for decomposition effects with two binary mediators

两个二元中介变量下分解效应的锐利非参数界

In randomized trials, once the total effect of the intervention has been estimated, it is often of interest to explore mechanistic effects through mediators along the causal pathway between the randomized treatment and the outcome. In the setting with two sequential mediators, there are a variety of decompositions of the total risk difference into mediation effects. We derive sharp and valid bounds for a number of mediation effects in the setting of two sequential mediators…

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Estimation based on nearest neighbor matching: from density ratio to average treatment effect

基于最近邻匹配的估计:从密度比到平均处理效应

Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN matching under, however, a crucial assumption that the number of NNs, $M$, is fixed. This manuscript reveals something new out of their study and shows that, once allowing $M$ to diverge with the sample size, an intrinsic statistic in their…

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Density Regression with Bayesian Additive Regression Trees

基于贝叶斯加性回归树的密度回归

Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete mixture models, we consider a continuous latent variable model in general covariate spaces, which we call DR-BART. The prior mapping the latent variable to the observed data is constructed via a novel application of Bayesian Additive…

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Bayesian Approaches to Shrinkage and Sparse Estimation

收缩与稀疏估计的贝叶斯方法

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference is the norm in several fields of applied econometric work. The purpose of this paper is to introduce the reader to the world of Bayesian model determination, by surveying modern shrinkage and variable selection algorithms and methodologies.…

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