warpMix {warpMix}

Estimate the non linear mixed effect functional model.

Description

This function returns estimates of parameters in the non linear functional mixed-effect model defined to warp data and estimate the underlying model with mixed effect.

Usage

warpMix(t, y, baseMu, baseU, baseW, sigmaEpsilonTilde = 10^-3,
  threshold = 10^-3, nIte = 100)

Arguments

t

A vector of numbers, corresponding to time points.

y

A matrix of numbers, corresponding to observations (size: T * n).

baseMu

A B-spline used to decompose the global mean.

baseU

A B-spline used to decompose the individual effects.

baseW

A B-spline used to decompose the warping functions.

sigmaEpsilonTilde

A number, defining the variance of the noise in the linear mixed- effect model fitted on the warping parameters.

threshold

A number, defining the threshold of convergence.

nIte

Maximum number of iterations

Details

Notice that the warping parameters are considered as random effects.

Value

A list, with fonct, functional quantities (indCurvAlign the individual aligned curves, warping the warping functions and theta, the warping parameters), para the estimates of parameters (alphaMu, sigmaU,theta0, sigmaTheta, sigmaEpsHat), dist the criterion computed to reach the convergence, and others other values (successAlphaMu, initTheta, initPara, CPUtime).

Examples

T = seq(0.5,0.841,length.out = 9)
n = 10
t = c(qnorm(T),1)
mu = cos(2*pi*t+pi/2)
library(fda)
baseMu = create.bspline.basis(c(0,max(t)), norder = 2, breaks = seq(0,1,0.5))
splineBasisMu = eval.basis(t,baseMu)
alphaMu = Data2fd(mu,argvals = t, baseMu)$coef
muApprox = (splineBasisMu) %*% alphaMu
baseU = create.bspline.basis(c(0,max(t)),norder = 2, breaks = seq(0,1,0.5))
mU = baseU$nbasis
sigmaU = diag(0.1,mU)
library(MASS)
alphaU = t(mvrnorm(n,rep(0,mU),sigmaU))
splineBasisU = eval.basis(t,baseU)
U = splineBasisU %*% alphaU
epsilon = t(mvrnorm(n,rep(0,length(t)),0.01 * diag(1,length(t))))
X = as.vector(muApprox) + U + epsilon
baseW = create.bspline.basis(c(0,max(t)), norder = 2, breaks = c(0,0.6,1))
mW = baseW$nbasis
splineBasisW = eval.basis(t,baseW)
theta = t(mvrnorm(n,rep(0,mW),diag(0.1,mW + 1e-3 * diag(1,mW))))
wtheta = matrix(rep(0,n*length(t)),ncol = n)
for (i in c(1:n)){
 wtheta[,i] = warpTimeFunction(splineBasisW,theta[,i],t)$warpTime
}
Y = matrix(0, nrow = length(t), ncol = n)
for (i in c(1:n)){
 y = approxfun(wtheta[,i],X[,i])
 Y[,i] = y(t)
}
warpMix(t,Y,baseMu, baseU, baseW, nIte = 2)