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Third-variable effect analysis with multilevel additive models

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  • Qingzhao Yu
  • Bin Li

Abstract

Third-variable effect refers to the effect transmitted by third-variables that intervene in the relationship between an exposure and a response variable. Third-variable effect analysis has been broadly studied in many fields. However, it remains a challenge for researchers to differentiate indirect effect of individual factor from multiple third-variables, especially when the involving variables are of hierarchical structure. Yu et al. (2014) defined third-variable effects that were consistent for all different types of response (categorical or continuous), exposure, or third-variables. With these definitions, multiple third-variables can be considered simultaneously, and the indirect effects carried by individual third-variables can be separated from the total effect. In this paper, we extend the definitions of third-variable effects to multilevel data structures, where multilevel additive models are adapted to model the variable relationships. And then third-variable effects can be estimated at different levels. Moreover, transformations on variables are allowed to present nonlinear relationships among variables. We compile an R package mlma, to carry out the proposed multilevel third-variable analysis. Simulations show that the proposed method can effectively differentiate and estimate third-variable effects from different levels. Further, we implement the method to explore the racial disparity in body mass index accounting for both environmental and individual level risk factors.

Suggested Citation

  • Qingzhao Yu & Bin Li, 2020. "Third-variable effect analysis with multilevel additive models," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-17, October.
    • Handle: RePEc:plo:pone00:0241072
    DOI: 10.1371/journal.pone.0241072
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    References listed on IDEAS

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    1. Qingzhao Yu & Kaelen L. Medeiros & Xiaocheng Wu & Roxanne E. Jensen, 2018. "Nonlinear Predictive Models for Multiple Mediation Analysis: With an Application to Explore Ethnic Disparities in Anxiety and Depression Among Cancer Survivors," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 991-1006, December.
    2. Stefan Lang & Nikolaus Umlauf & Peter Wechselberger & Kenneth Harttgen & Thomas Kneib, 2012. "Multilevel structured additive regression," Working Papers 2012-07, Faculty of Economics and Statistics, Universität Innsbruck.
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