FMA.concurrent.boot {cfma}

Functional mediation analysis under concurrent regression model with point-wise bootstrap confidence interval

Description

This function performs functional mediation regression under the concurrent model with given tuning parameter. Point-wise confidence bands are obtained from bootstrap.

Usage

FMA.concurrent.boot(Z, M, Y, intercept = TRUE, basis = NULL, Ld2.basis = NULL, 
    basis.type = c("fourier"), nbasis = 3, timeinv = c(0, 1), timegrids = NULL, 
    lambda.m = 0.01, lambda.y = 0.01, sims = 1000, boot = TRUE, 
    boot.ci.type = c("bca", "perc"), conf.level = 0.95, verbose = TRUE)

Arguments

Z

a data matrix. Z is the treatment trajectory in the mediation analysis. The number of rows is the number of subjects, and the number of columns is the number of measured time points.

M

a data matrix. M is the mediator trajectory in the mediation analysis. The number of rows is the number of subjects, and the number of columns is the number of measured time points.

Y

a data matrix. Y is the outcome trajectory in the mediation analysis. The number of rows is the number of subjects, and the number of columns is the number of measured time points.

intercept

a logic variable. Default is TRUE, an intercept term is included in the regression model.

basis

a data matrix. Basis function used in the functional data analysis. The number of columns is the number of basis function considered. If basis = NULL, Fourier basis functions will be generated.

Ld2.basis

a data matrix. The second derivative of the basis function. The number of columns is the number of basis function considered. If Ld2.basis = NULL, the second derivative of Fourier basis functions will be generated.

basis.type

a character of basis function type. Default is Fourier basis (basis.type = "fourier").

nbasis

an integer, the number of basis function included. If basis is provided, this argument will be ignored.

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 timegrids = NULL, it is assumed the between measurement time interval is constant.

lambda.m

a numeric value of the tuning parameter in the mediator model.

lambda.y

a numeric value of the tuning parameter in the outcome model.

sims

an integer indicating the number of simulations for inference.

boot

a logical value, indicating whether or not bootstrap should be used. Default is TRUE.

boot.ci.type

a character of confidence interval method. boot.ci.type = "bca" bias corrected confidence interval; boot.ci.type = "perc" percentile confidence interval.

conf.level

a number of significance level. Default is 0.95.

verbose

a logical value, indicating whether print out bootstrap replications.

Details

The concurrent mediation model is

M(t)=Z(t)\alpha(t)+\epsilon_{1}(t),

Y(t)=Z(t)\gamma(t)+M(t)\beta(t)+\epsilon_{2}(t),

where \alpha(t), \beta(t), \gamma(t) are coefficient curves. The model coefficient curves are estimated by minimizing the penalized L_{2}-loss.

Value

alpha

a list of output for \alpha estimate

coefficients: the result of the coefficient estimates corresponding to the basis function

curve: the point-wise estimate of the coefficient curve

gamma

: a list of output for \gamma estimate

coefficients: the result of the coefficient estimates corresponding to the basis function

curve: the point-wise estimate of the coefficient curve

beta

a list of output for \beta estimate

coefficients: the result of the coefficient estimates corresponding to the basis function

curve: the point-wise estimate of the coefficient curve

IE

a list of output for indirect effect estimate

coefficients: the result of the coefficient estimates corresponding to the basis function

curve: the point-wise estimate of the coefficient curve

DE

a list of output for direct effect estimate

coefficients: the result of the coefficient estimates corresponding to the basis function

curve: the point-wise estimate of the coefficient curve

Author(s)

Yi Zhao, Johns Hopkins University, [e-mail];

Xi Luo, Brown University [e-mail];

Martin Lindquist, Johns Hopkins University, [e-mail];

Brian Caffo, Johns Hopkins University, [e-mail]

References

Zhao et al. (2017). Functional Mediation Analysis with an Application to Functional Magnetic Resonance Imaging Data. arXiv preprint arXiv:1805.06923.

Examples

##################################################
# Concurrent functional mediation model
data(env.concurrent)
Z<-get("Z",env.concurrent)
M<-get("M",env.concurrent)
Y<-get("Y",env.concurrent)


# consider Fourier basis
fit.boot<-FMA.concurrent.boot(Z,M,Y,intercept=FALSE,timeinv=c(0,300))

##################################################