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Functional Causal Mediation Analysis With an Application to Brain Connectivity

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  • Martin A. Lindquist

Abstract

Mediation analysis is often used in the behavioral sciences to investigate the role of intermediate variables that lie on the causal path between a randomized treatment and an outcome variable. Typically, mediation is assessed using structural equation models (SEMs), with model coefficients interpreted as causal effects. In this article, we present an extension of SEMs to the functional data analysis (FDA) setting that allows the mediating variable to be a continuous function rather than a single scalar measure, thus providing the opportunity to study the functional effects of the mediator on the outcome. We provide sufficient conditions for identifying the average causal effects of the functional mediators using the extended SEM, as well as weaker conditions under which an instrumental variable estimand may be interpreted as an effect. The method is applied to data from a functional magnetic resonance imaging (fMRI) study of thermal pain that sought to determine whether activation in certain brain regions mediated the effect of applied temperature on self-reported pain. Our approach provides valuable information about the timing of the mediating effect that is not readily available when using the standard nonfunctional approach. To the best of our knowledge, this work provides the first application of causal inference to the FDA framework.

Suggested Citation

  • Martin A. Lindquist, 2012. "Functional Causal Mediation Analysis With an Application to Brain Connectivity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1297-1309, December.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1297-1309
    DOI: 10.1080/01621459.2012.695640
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    Cited by:

    1. repec:spr:stabio:v:9:y:2017:i:2:d:10.1007_s12561-017-9195-y is not listed on IDEAS
    2. Hye Won Suk & Heungsun Hwang, 2016. "Functional Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 940-968, December.
    3. repec:eee:csdana:v:122:y:2018:i:c:p:101-114 is not listed on IDEAS
    4. repec:bla:istatr:v:85:y:2017:i:2:p:228-249 is not listed on IDEAS
    5. Andrada Ivanescu & Ana-Maria Staicu & Fabian Scheipl & Sonja Greven, 2015. "Penalized function-on-function regression," Computational Statistics, Springer, vol. 30(2), pages 539-568, June.

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