FMA.historical.CV.RdThis function performs functional mediation regression under the historical influence model. Tuning parameter is chosen based on cross-validation.
FMA.historical.CV(Z, M, Y, delta.grid1 = 1, delta.grid2 = 1, delta.grid3 = 1,
intercept = TRUE, basis1 = NULL, Ld2.basis1 = NULL, basis2 = NULL, Ld2.basis2 = NULL,
basis.type = c("fourier"), nbasis1 = 3, nbasis2 = 3,
timeinv = c(0, 1), timegrids = NULL, lambda1 = NULL, lambda2 = NULL, nfolds = 5)| Z | a data matrix. |
|---|---|
| M | a data matrix. |
| Y | a data matrix. |
| delta.grid1 | a number indicates the width of treatment-mediator time interval in the mediator model. |
| delta.grid2 | a number indicates the width of treatment-outcome time interval in the outcome model. |
| delta.grid3 | a number indicates the width of mediator-outcome time interval in the outcome model. |
| intercept | a logic variable. Default is |
| basis1 | a data matrix. Basis function on the \(s\) domain used in the functional data analysis. The number of columns is the number of basis function considered. If |
| Ld2.basis1 | a data matrix. The second derivative of the basis function on the \(s\) domain. The number of columns is the number of basis function considered. If |
| basis2 | a data matrix. Basis function on the \(t\) domain used in the functional data analysis. The number of columns is the number of basis function considered. If |
| Ld2.basis2 | a data matrix. The second derivative of the basis function on the \(t\) domain. The number of columns is the number of basis function considered. If |
| basis.type | a character of basis function type. Default is Fourier basis ( |
| nbasis1 | an integer, the number of basis function on the \(s\) domain included. If |
| nbasis2 | an integer, the number of basis function on the \(t\) domain included. If |
| timeinv | a numeric vector of length two, the time interval considered in the analysis. Default is (0,1). |
| timegrids | a numeric vector of time grids of measurement. If |
| lambda1 | a numeric vector of tuning parameter values on the \(s\) domain. |
| lambda2 | a numeric vector of tuning parameter values on the \(t\) domain. |
| nfolds | a number gives the number of folds in cross-validation. |
The historical influence mediation model is $$M(t)=\int_{\Omega_{t}^{1}}Z(s)\alpha(s,t)ds+\epsilon_{1}(t),$$ $$Y(t)=\int_{\Omega_{t}^{2}}Z(s)\gamma(s,t)ds+\int_{\Omega_{t}^{3}}M(s)\beta(s,t)ds+\epsilon_{2}(t),$$ where \(\alpha(s,t)\), \(\beta(s,t)\), \(\gamma(s,t)\) are coefficient curves; \(\Omega_{t}^{j}=[(t-\delta_{j})\vee 0,t]\) for \(j=1,2,3\). The model coefficient curves are estimated by minimizing the penalized \(L_{2}\)-loss. Tuning parameter \(\lambda\) controls the smoothness of the estimated curves, and is chosen by cross-validation.
the basis functions on the \(s\) domain used in the analysis.
the basis functions on the \(t\) domain used in the analysis.
a list of output for the mediator model coefficient: the estimated coefficient with respect to the basis function curve: the estimated coefficient curve fitted: the fitted value of M lambda1: the chosen \(\lambda\) value on the \(s\) domain lambda2: the chosen \(\lambda\) value on the \(t\) domain
a list of output for the outcome model coefficient: the estimated coefficient with respect to the basis function curve: the estimated coefficient curve fitted: the fitted value of Y lambda1: the chosen \(\lambda\) value on the \(s\) domain lambda2: the chosen \(\lambda\) value on the \(t\) domain
a list of output for the indirect effect comparing \(Z_{1}(t)=1\) versus \(Z_{0}(t)=0\) curve: the estimated causal curve
a list of output for the direct effect comparing \(Z_{1}(t)=1\) versus \(Z_{0}(t)=0\) curve: the estimated causal curve
Zhao et al. (2017). Functional Mediation Analysis with an Application to Functional Magnetic Resonance Imaging Data. arXiv preprint arXiv:1805.06923.
Yi Zhao, Johns Hopkins University, zhaoyi1026@gmail.com;
Xi Luo, Brown University xi.rossi.luo@gmail.com;
Martin Lindquist, Johns Hopkins University, mal2053@gmail.com;
Brian Caffo, Johns Hopkins University, bcaffo@gmail.com
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# Historical influence functional mediation model
data(env.historical)
Z<-get("Z",env.historical)
M<-get("M",env.historical)
Y<-get("Y",env.historical)
if (FALSE) {
# consider Fourier basis
fit<-FMA.historical.CV(Z,M,Y,delta.grid1=3,delta.grid2=3,delta.grid3=3,
intercept=FALSE,timeinv=c(0,300))
}
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