The package is used to do mediation analysis with generalized multilevel models.
Qingzhao Yu qyu@lsuhsc.edu, Bin Li bli@lsu.edu
Maintainer: Qingzhao Yu qyu@lsuhsc.edu
"data.org" is used to transform the variables and organize the predictor, mediators and outcome into the format that are ready to be used for multilevel mediation analysis. "mlma" is for multilevel mediation analysis on the original data set. "boot.mlma" is a combined function that organized data set, do multilevel mediation analysis on original data sets and bootstrapping samples.
The multilevel mediation is based on the following linear multilevel additive models: $$Y_{ij} = u_{0j}^Y(X_{.j}, \mathbf{M}_{.j}, \mathbf{Z}_{.j})+{\boldsymbol{\beta}_{10}^Y}^T\mathbf{f}_{10}^Y(X_{ij}-X_{.j})+\sum_{k=1}^K{\boldsymbol{\beta}_{20k}^Y}^T\mathbf{f}_{20k}^Y(M_{ijk}-M_{.jk})+{\boldsymbol{\beta}_{30}^Y}^T(\mathbf{Z}_{ij}-\mathbf{Z}_{.j})+r_{ij}^Y,$$ where $$u_{0j}^Y(X_{.j}, \mathbf{M}_{.j}, \mathbf{Z}_{.j}) = c_{00}^Y + {\boldsymbol{\beta}_{01}^Y}^T\mathbf{f}_{01}^Y(X_{.j}) + \sum_{k=1}^K{\boldsymbol{\beta}_{02k}^Y}^T\mathbf{f}_{02k}^Y(M_{.jk}) + {\boldsymbol{\beta}_{03}^Y}^T\mathbf{Z}_{.j} + r_{0j}^Y.$$ For \(k=1,\ldots,K,\) $$M_{.jk} = u_{0jk}^M(X_{.j})+{\boldsymbol{\beta}_{10k}^M}^T\mathbf{f}_{10k}^M(X_{ij}-X_{.j})+r_{ijk}^M,$$ $$u_{0jk}^M(X_{.j}) = c_{00k}^M + {\boldsymbol{\beta}_{01k}^M}^T\mathbf{f}_{01k}^{M1}(X_{.j}) + r_{0jk}^M.$$ If for some k, \(M_k\) is level 2 variable, $$M_{.jk} = c_{00k}^M + {\boldsymbol{\beta}_{01k}^M}^T\mathbf{f}_{01k}^{M2}(X_{.j}) + r_{0jk}^M.$$
Note that in the models, \(\mathbf{f}(\cdot)=(f_1(\cdot), f_2(\cdot), \cdots, f_l(\cdot))^T\) is a set of l transformation functions on \(\cdot\), with the corresponding linear coefficients vector \(\boldsymbol{\beta}=(\beta_1, \beta_2, \cdots, \beta_l)^T\). \(\mathbf{f}\) and l are known for model fitting. l may be different with \(\mathbf{f}\) of different sub- and super-scripts.
Yu, Q. and Li, B., (2020). <doi:10.1371/journal.pone.0241072>. "Third-Variable Effect Analysis with Multilevel Additive Models," PLoS ONE 15(10): e0241072.
Yu, Q., Yu, M., Zou, J., Wu, X., Gomez, SL, Li, B. (2021). <doi:10.1177/26320843211061292>. "Multilevel Mediation Analysis on Time-to-Event Outcomes - Exploring racial/ethnic Disparities in Breast Cancer Survival in California," Research Methods in Medicine & Health Sciences.
Yu, Q. and Li, B., 2022. Statistical Methods for Mediation, Confounding and Moderation Analysis Using R and SAS. Chapman and Hall/CRC. ISBN 9780367365479.