Third-variable effect analysis with multilevel additive models.

Third-variable effect analysis with multilevel additive models.

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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 chocolate chip cookie purse 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 canine spectra kc 3 intranasal single dose 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.