Luke Keele

A General Approach to Causal Mediation Analysis

Traditionally in the social sciences, causal mediation analysis has been formulated, understood, and implemented within the framework of linear structural equation models. We argue and demonstrate that this is problematic for 3 reasons: the lack of a general definition of causal mediation effects independent of a particular statistical model, the inability to specify the key identification assumption, and the difficulty of extending the framework to nonlinear models. In this article, we propose an alternative approach that overcomes these limitations. Our approach is general because it offers the definition, identification, estimation, and sensitivity analysis of causal mediation effects without reference to any specific statistical model. Further, our approach explicitly links these 4 elements closely together within a single framework. As a result, the proposed framework can accommodate linear and nonlinear relationships, parametric and nonparametric models, continuous and discrete mediators, and various types of outcome variables. The general definition and identification result also allow us to develop sensitivity analysis in the context of commonly used models, which enables applied researchers to formally assess the robustness of their empirical conclusions to violations of the key assumption. We illustrate our approach by applying it to the Job Search Intervention Study. We also offer easy-to-use software that implements all our proposed methods.

Identification, Inference and Sensitivity Analysis for Causal Mediation Effects

Causal mediation analysis is routinely conducted by applied researchers in a variety of disciplines. The goal of such an analysis is to investigate alternative causal mechanisms by examining the roles of intermediate variables that lie in the causal paths between the treat- ment and outcome variables. In this paper we first prove that under a particular version of sequential ignorability assumption, the aver- age causal mediation effect (ACME) is nonparametrically identified. We compare our identification assumption with those proposed in the literature. Some practical implications of our identification result are also discussed. In particular, the popular estimator based on the linear structural equation model (LSEM) can be interpreted as an ACME estimator once additional parametric assumptions are made. We show that these assumptions can easily be relaxed within and outside of the LSEM framework and propose simple nonparametric estimation strate- gies. Second, and perhaps most importantly, we propose a new sensi- tivity analysis that can be easily implemented by applied researchers within the LSEM framework. Like the existing identifying assumptions, the proposed sequential ignorability assumption may be too strong in many applied settings. Thus, sensitivity analysis is essential in order to examine the robustness of empirical findings to the possible existence of an unmeasured confounder. Finally, we apply the proposed methods to a randomized experiment from political psychology. We also make easy-to-use software available to implement the proposed methods.

Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies

Identifying causal mechanisms is a fundamental goal of social science. Researchers seek to study not only whether one variable affects another but also how such a causal relationship arises. Yet commonly used statistical methods for identifying causal mechanisms rely upon untestable assumptions and are often inappropriate even under those assumptions. Randomizing treatment and intermediate variables is also insufficient. Despite these difficulties, the study of causal mechanisms is too important to abandon. We make three contributions to improve research on causal mechanisms. First, we present a minimum set of assumptions required under standard designs of experimental and observational studies and develop a general algorithm for estimating causal mediation effects. Second, we provide a method for assessing the sensitivity of conclusions to potential violations of a key assumption. Third, we offer alternative research designs for identifying causal mechanisms under weaker assumptions. The proposed approach is illustrated using media framing experiments and incumbency advantage studies.

A Bayesian Multilevel Modeling Approach to Time-Series Cross-Sectional Data

The analysis of time-series cross-sectional (TSCS) data has become increasingly popular in political science. Meanwhile, political scientists are also becoming more interested in the use of multilevel models (MLM). However, little work exists to understand the benefits of multilevel modeling when applied to TSCS data. We employ Monte Carlo simulations to benchmark the performance of a Bayesian multilevel model for TSCS data. We find that the MLM performs as well or better than other common estimators for such data. Most importantly, the MLM is more general and offers researchers additional advantages.

Causal Mediation Analysis Using R

Causal mediation analysis is widely used across many disciplines to investigate possible causal mechanisms. Such an analysis allows researchers to explore various causal pathways, going beyond the estimation of simple causal effects. Recently, Imai et al. (2008) [3] and Imai et al. (2009) [2] developed general algorithms to estimate causal mediation effects with the variety of data types that are often encountered in practice. The new algorithms can estimate causal mediation effects for linear and nonlinear relationships, with parametric and nonparametric models, with continuous and discrete mediators, and various types of outcome variables. In this paper, we show how to implement these algorithms in the statistical computing language R. Our easy-to-use software, mediation, takes advantage of the object-oriented programming nature of the R language and allows researchers to estimate causal mediation effects in a straightforward manner. Finally, mediation also implements sensitivity analyses which can be used to formally assess the robustness of findings to the potential violations of the key identifying assumption. After describing the basic structure of the software, we illustrate its use with several empirical examples.

The Measure and Mismeasure of Emotion

Emotion, after a modest hiatus during the “cognitive revolution,” has reemerged of late to become a subject of significant attention in political science.1 The other contributions in this volume give ample evidence of the added understanding we gain by including emotion into the theoretical and empirical mix. Our entry in this volume turns to a question relevant to most if not all the other research found here: how do we best measure emotional response? We examine two central considerations—identifying which emotions define political responses and determining which kinds of questions are most suitable to assess these emotional reactions. Evaluating the measurement of emotion is important both because of the inherent challenges in securing reliable and valid measures of emotional reactions, as well as the sensitivity of our understanding of emotional reactions to our choice of measures.2

Value Conflict and Volatility in Party Identification

Are some people more prone to instabilities in partisanship due to the ways they rank and organize their core values? We investigate the mechanisms of partisan volatility, considering whether instabilities reflect value conflict and ambivalence. Our expectation is that when the basic values of the American ethos come into conflict in elite discourse, citizens have difficulty reconciling their own value arrangement with that of elites, resulting in greater partisan volatility. To this end, we use several heteroscedastic regression and ordered probit models to explore whether the conflict of competing values explains the response variance and instability of individual-level partisanship and ideology over time. To construct measures of value conflict, we rely on data from the 1992, 1994 and 1996 American National Election Studies. We find that, while instabilities in partisan identification reflect low information for some, the competition of core values generates volatility in partisan affiliations for others. In deliberating the value tradeoffs of politics, people may be of two minds even about central beliefs such as party identification.

Interpreting Regression Discontinuity Designs with Multiple Cutoffs

We consider a regression discontinuity (RD) design where the treatment is received if a score is above a cutoff, but the cutoff may vary for each unit in the sample instead of being equal for all units. This multi-cutoff regression discontinuity design is very common in empirical work, and researchers often normalize the score variable and use the zero cutoff on the normalized score for all observations to estimate a pooled RD treatment effect. We formally derive the form that this pooled parameter takes and discuss its interpretation under different assumptions. We show that this normalizing-and-pooling strategy so commonly employed in practice may not fully exploit all the information available in a multi-cutoff RD setup. We illustrate our methodological results with three empirical examples based on vote shares, population, and test scores.

Comment on Pearl: Practical implications of theoretical results for causal mediation analysis.

Mediation analysis has been extensively applied in psychological and other social science research. A number of methodologists have recently developed a formal theoretical framework for mediation analysis from a modern causal inference perspective. In Imai, Keele, and Tingley (2010), we have offered such an approach to causal mediation analysis that formalizes identification, estimation, and sensitivity analysis in a single framework. This approach has been used by a number of substantive researchers, and in subsequent work we have also further extended it to more complex settings and developed new research designs. In an insightful article, Pearl (2014) proposed an alternative approach that is based on a set of assumptions weaker than ours. In this comment, we demonstrate that the theoretical differences between our identification assumptions and his alternative conditions are likely to be of little practical relevance in the substantive research settings faced by most psychologists and other social scientists. We also show that our proposed estimation algorithms can be easily applied in the situations discussed in Pearl (2014). The methods discussed in this comment and many more are implemented via mediation, an open-source software (Tingley, Yamamoto, Hirose, Keele, & Imai, 2013).

Causal Mediation Analysis: Warning! Assumptions Ahead.

In policy evaluations, interest may focus on why a particular treatment works. One tool for understanding why treatments work is causal mediation analysis. In this essay, I focus on the assumptions needed to estimate mediation effects. I show that there is no “gold standard” method for the identification of causal mediation effects. In particular, mediation effects will always have the character of estimates from observational data since they are generally subject to a specific form of confounding. Additionally, I demonstrate how randomization of the mediator and instrumental variables methods lead to fundamentally different quantities than causal mediation analyses. I also review recent work that discusses how the assumptions of mediation analyses differ when there is treatment noncompliance or when there are multiple mediators. Throughout, I motivate concepts using path diagrams and an example of a classroom intervention designed to increase test scores.