fdapace (version 0.6.0)

Dyn_test: Bootstrap test of Dynamic Correlation

Description

Perform one sample (H0: Dynamic correlation = 0) or two sample (H0:Dynamic_correlation_1 = Dynamic_correlation_2) bootstrap test of H_0: Dynamical Correlation=0.

Usage

Dyn_test(x1, y1, t1, x2, y2, t2, B = 1000)

Value

a list of the following

stats

Test statistics.

pval

p-value of the test.

Arguments

x1

a n by m matrix where rows representing subjects and columns representing measurements, missings are allowed.

y1

a n by m matrix where rows representing subjects and columns representing measurements, missings are allowed.

t1

a vector of time points where x1,y1 are observed.

x2

(optional if missing will be one sample test) a n by m matrix where rows representing subjects and columns representing measurements, missings are allowed.

y2

(optional if missing will be one sample test) a n by m matrix where rows representing subjects and columns representing measurements, missings are allowed.

t2

(optional if missing will be one sample test) a vector of time points where x2,y2 are observed.

B

number of bootstrap samples.

References

Dubin J A, Müller H G. (2005) Dynamical correlation for multivariate longitudinal data. Journal of the American Statistical Association 100(471): 872-881.

Liu S, Zhou Y, Palumbo R, Wang, J.L. (2016). Dynamical correlation: A new method for quantifying synchrony with multivariate intensive longitudinal data. Psychological Methods 21(3): 291.

Examples

n=20             # sample size
t=seq(0,1,length.out=100)       # length of data
mu_quad_x=8*t^2-4*t+5
mu_quad_y=8*t^2-12*t+6
fun=rbind(rep(1,length(t)),-t,t^2)
z1=matrix(0,n,3)
z1[,1]=rnorm(n,0,2)
z1[,2]=rnorm(n,0,16/3)
z1[,3]=rnorm(n,0,4)   # covariance matrix of random effects
x1_quad_error=y1_quad_error=matrix(0,nrow=n,ncol=length(t))
for (i in 1:n){
  x1_quad_error[i,]=mu_quad_x+z1[i,]%*%fun+rnorm(length(t),0,0.01)
  y1_quad_error[i,]=mu_quad_y+2*z1[i,]%*%fun +rnorm(length(t),0,0.01)
}
bt_DC=Dyn_test(x1_quad_error,y1_quad_error,t,B=500) # using B=500 for speed consideration