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Register a new userIdentification of Causal Diffusion Effects Under Structural Stationarity
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Naoki Egami
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
Authors
Naoki Egami
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Although social and biomedical scientists have long been interested in the process through which ideas and behaviors diffuse, the identification of causal diffusion effects, also known as peer and contagion effects, remains challenging. Many scholars consider the commonly used assumption of no omitted confounders to be untenable due to contextual confounding and homophily bias. To address this long-standing problem, we examine the causal identification under a new assumption of structural stationarity, which formalizes the underlying diffusion process with a class of dynamic causal directed acyclic graphs. First, we develop a statistical test that can detect a wide range of biases, including the two types mentioned above. We then propose a difference-in-differences style estimator that can directly correct biases under an additional parametric assumption. Leveraging the proposed methods, we study the spatial diffusion of hate crimes against refugees in Germany. After correcting large upward bias in existing studies, we find hate crimes diffuse only to areas that have a high proportion of school dropouts.
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Causal inference concerns not only the average effect of the treatment on the outcome but also the underlying mechanism through an intermediate variable of interest. Principal stratification characterizes such mechanism by targeting subgroup causal effects within principal strata, which are defined by the joint potential values of an intermediate variable. Due to the fundamental problem of causal inference, principal strata are inherently latent, rendering it challenging to identify and estimate subgroup effects within them. A line of research leverages the principal ignorability assumption that the latent principal strata are mean independent of the potential outcomes conditioning on the observed covariates. Under principal ignorability, we derive various nonparametric identification formulas for causal effects within principal strata in observational studies, which motivate estimators relying on the correct specifications of different parts of the observed-data distribution. Appropriately combining these estimators further yields new triply robust estimators for the causal effects within principal strata. These new estimators are consistent if two of the treatment, intermediate variable, and outcome models are correctly specified, and they are locally efficient if all three models are correctly specified. We show that these estimators arise naturally from either the efficient influence functions in the semiparametric theory or the model-assisted estimators in the survey sampling theory. We evaluate different estimators based on their finite-sample performance through simulation, apply them to two observational studies, and implement them in an open-source software package.
In causal inference, principal stratification is a framework for dealing with a posttreatment intermediate variable between a treatment and an outcome, in which the principal strata are defined by the joint potential values of the intermediate variable. Because the principal strata are not fully observable, the causal effects within them, also known as the principal causal effects, are not identifiable without additional assumptions. Several previous empirical studies leveraged auxiliary variables to improve the inference of principal causal effects. We establish a general theory for identification and estimation of the principal causal effects with auxiliary variables, which provides a solid foundation for statistical inference and more insights for model building in empirical research. In particular, we consider two commonly-used strategies for principal stratification problems: principal ignorability, and the conditional independence between the auxiliary variable and the outcome given principal strata and covariates. For these two strategies, we give non-parametric and semi-parametric identification results without modeling assumptions on the outcome. When the assumptions for neither strategies are plausible, we propose a large class of flexible parametric and semi-parametric models for identifying principal causal effects. Our theory not only establishes formal identification results of several models that have been used in previous empirical studies but also generalizes them to allow for different types of outcomes and intermediate variables.
In randomized experiments, interactions between units might generate a treatment diffusion process. This is common when the treatment of interest is an actual object or product that can be shared among peers (e.g., flyers, booklets, videos). For instance, if the intervention of interest is an information campaign realized through the distribution of a video to targeted individuals, some of these treated individuals might share the video they received with their friends. Such a phenomenon is usually unobserved, causing a misallocation of individuals in the two treatment arms: some of the initially untreated units might have actually received the treatment by diffusion. Treatment misclassification can, in turn, introduce a bias in the estimation of the causal effect. Inspired by a recent field experiment on the effect of different types of school incentives aimed at encouraging students to attend cultural events, we present a novel approach to deal with a hidden diffusion process on observed or partially observed networks.Specifically, we develop a simulation-based sensitivity analysis that assesses the robustness of the estimates against the possible presence of a treatment diffusion. We simulate several diffusion scenarios within a plausible range of sensitivity parameters and we compare the treatment effect which is estimated in each scenario with the one that is obtained while ignoring the diffusion process. Results suggest that even a treatment diffusion parameter of small size may lead to a significant bias in the estimation of the treatment effect.
Assessing the magnitude of cause-and-effect relations is one of the central challenges found throughout the empirical sciences. The problem of identification of causal effects is concerned with determining whether a causal effect can be computed from a combination of observational data and substantive knowledge about the domain under investigation, which is formally expressed in the form of a causal graph. In many practical settings, however, the knowledge available for the researcher is not strong enough so as to specify a unique causal graph. Another line of investigation attempts to use observational data to learn a qualitative description of the domain called a Markov equivalence class, which is the collection of causal graphs that share the same set of observed features. In this paper, we marry both approaches and study the problem of causal identification from an equivalence class, represented by a partial ancestral graph (PAG). We start by deriving a set of graphical properties of PAGs that are carried over to its induced subgraphs. We then develop an algorithm to compute the effect of an arbitrary set of variables on an arbitrary outcome set. We show that the algorithm is strictly more powerful than the current state of the art found in the literature.
Scientists have been interested in estimating causal peer effects to understand how peoples behaviors are affected by their network peers. However, it is well known that identification and estimation of causal peer effects are challenging in observational studies for two reasons. The first is the identification challenge due to unmeasured network confounding, for example, homophily bias and contextual confounding. The second issue is network dependence of observations, which one must take into account for valid statistical inference. Negative control variables, also known as placebo variables, have been widely used in observational studies including peer effect analysis over networks, although they have been used primarily for bias detection. In this article, we establish a formal framework which leverages a pair of negative control outcome and exposure variables (double negative controls) to nonparametrically identify causal peer effects in the presence of unmeasured network confounding. We then propose a generalized method of moments estimator for causal peer effects, and establish its consistency and asymptotic normality under an assumption about $psi$-network dependence. Finally, we provide a network heteroskedasticity and autocorrelation consistent variance estimator. Our methods are illustrated with an application to peer effects in education.
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