simulate_simple_dfrr: Simulating a Simple 'dfrr' Model
In asgari-fatemeh/dfrr: Dichotomized Functional Response Regression

Simulation from a simple dfrr model:

Y_{i}(t)=I(β_0(t)+β_1(t)*x_{i}+\varepsilon_{i}(t)+ε_{i}(t)\timesσ^2>0),

where I(.) is the indicator function, \varepsilon_{i} is a Gaussian random function, and ε_{i}(t) are iid standard normal for each i and t independent of \varepsilon_{i}. For demonstration purpose only.

simulate_simple_dfrr(
  beta0 = function(t) {     cos(pi * t + pi) },
  beta1 = function(t) {     2 * t },
  X = rnorm(50),
  time = seq(0, 1, length.out = 24),
  sigma2 = 0.2
)

`beta0, beta1`	(optional) functional intercept and slope parameters
`X`	an (optional) vector consists of scalar covariate
`time`	an (optional) vector of time points for which, each sample curve is observed at.
`sigma2`	variance of the measurement error in the `dfrr` model

N<-50;M<-24
X<-rnorm(N,mean=0)
time<-seq(0,1,length.out=M)
Y<-simulate_simple_dfrr(beta0=function(t){cos(pi*t+pi)},
                        beta1=function(t){2*t},
                        X=X,time=time)