#' @article{Vallejo/Ato/Fernandez/Livacic-Rojas:2019,
#'   author = {Vallejo, Guillermo and Ato, Manuel and Fernández, M. Paula and Livacic-Rojas, Pablo E.},
#'   year = {2019},
#'   title = {Sample size estimation for heterogeneous growth curve models with attrition},
#'   fjournal = {Behavior Research Methods},
#'   journal = {Behav Res},
#'   pages = {1216--1243},
#'   volume = {51},
#'   doi = {10.3758/s13428-018-1059},
#' }

tau11 = function(r1,rho1,k1,t)
{
  
  t11 =( 2*r1^2*rho1+(k1-1)-2*r1*sqrt(r1^1*rho1^2+rho1*(k1-1)))/(t-1)^2
  return(t11)
}

beta11 = function(k1,t,dL)
{
  return(dL*sqrt(k1)/(t-1))
}
sb1 = function(r1,rho1,k1,t)
{
  
t11 = tau11(r1,rho1,k1,t)
sb1 = sqrt(t11 + 12*(1-rho1)/(t^2-1)/t)
return(sb1)
}

sample.size = function(alpha,beta,rho1,r1,p1,k1,dL)
{
   N = (qnorm(1-alpha/2)+qnorm(1-beta))^2*(s1/b11)^2/(p1*(1-p1))
   return(N)
}
#
p1=0.5

r1=-0.5
dL = 0.4 
t=4
k1=25
rho1 = 0.1
alpha=0.05
beta = 0.2
s1 = sb1(r1,rho1,k1,t)
b11 = beta11(k1,t,dL)
b11/s1
sample.size(alpha,beta,rho1,r1,p1,k1,dL)
#
p1=0.5

r1=.5
dL = 0.6 
t=8
k1=25
rho1 = 0.5
alpha=0.05
beta = 0.2
s1 = sb1(r1,rho1,k1,t)
b11 = beta11(k1,t,dL)
b11/s1
sample.size(alpha,beta,rho1,r1,p1,k1,dL)