Description Usage Arguments Details Value Author(s) References Examples
This function performs functional mediation regression under the historical influence model with given tuning parameter.
1 2 3 4 5  FMA.historical(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.m = 0.01, lambda2.m = 0.01, lambda1.y = 0.01, lambda2.y = 0.01)

Z 
a data matrix. 
M 
a data matrix. 
Y 
a data matrix. 
delta.grid1 
a number indicates the width of treatmentmediator time interval in the mediator model. 
delta.grid2 
a number indicates the width of treatmentoutcome time interval in the outcome model. 
delta.grid3 
a number indicates the width of mediatoroutcome 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.m 
a numeric vector of tuning parameter values on the s domain in the mediator model. 
lambda2.m 
a numeric vector of tuning parameter values on the t domain in the mediator model. 
lambda1.y 
a numeric vector of tuning parameter values on the s domain in the outcome model. 
lambda2.y 
a numeric vector of tuning parameter values on the t domain in the outcome model. 
The historical influence mediation model is
M(t)=\int_{Ω_{t}^{1}}Z(s)α(s,t)ds+ε_{1}(t),
Y(t)=\int_{Ω_{t}^{2}}Z(s)γ(s,t)ds+\int_{Ω_{t}^{3}}M(s)β(s,t)ds+ε_{2}(t),
where α(s,t), β(s,t), γ(s,t) are coefficient curves; Ω_{t}^{j}=[(tδ_{j})\vee 0,t] for j=1,2,3. The model coefficient curves are estimated by minimizing the penalized L_{2}loss.
basis1 
the basis functions on the s domain used in the analysis. 
basis2 
the basis functions on the t domain used in the analysis. 
M 
a list of output for the mediator model

Y 
a list of output for the outcome model

IE 
a list of output for the indirect effect comparing Z_{1}(t)=1 versus Z_{0}(t)=0

DE 
a list of output for the direct effect comparing Z_{1}(t)=1 versus Z_{0}(t)=0

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
Zhao et al. (2017). Functional Mediation Analysis with an Application to Functional Magnetic Resonance Imaging Data. arXiv preprint arXiv:1805.06923.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  ##################################################
# Historical influence functional mediation model
data(env.historical)
Z<get("Z",env.historical)
M<get("M",env.historical)
Y<get("Y",env.historical)
# consider Fourier basis
fit<FMA.historical(Z,M,Y,delta.grid1=3,delta.grid2=3,delta.grid3=3,
intercept=FALSE,timeinv=c(0,300))
# estimate of causal curves
plot(fit$IE$curve,type="l",lwd=5)
plot(fit$DE$curve,type="l",lwd=5)
##################################################

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