##CONSTANT DEFINITIONS
NN <- 500#number of iterations
BB <- 150 #number of bootstrap iterations. only for bootstrap. consider smaller NN for bootstrap simulation.
###This defines what the distribution to be used will be
#Distributiony <- "Normal";truealpha <- -.001;Q <- function(x) x 
Distributiony <- "Lognormal";truealpha <- 1;Q <- function(x) log(x)
Distributionx <- "Normal"; sigmaAge <- 10; sigmaCD4 <- 100;
#Distributionx <- "Unif"
Independentx <- F; rho <- -.25
Linear <-F ##are the truefs and truehs linear or not.

###Effects
MEANCD4 <- 5.4 #mean of y. if lognormal it should change to mean og log(y)
sigmay <- .05##as above but the sd ofy. should change if lognormal
ES.AGE <- .4#this is how strong the effect of age on r is
ES.CD4 <- .2##this is hos strong the effect of cd4 on r is 
ES2.CD4 <- .1#*sigmay #this is how strong the effect of cd4 is on y.
ES2.AGE <- .15#*sigmay #this is how strong effect ofg age on y
##NOTE, if using linear hs and fs do not multiply ny sigmay in previous two
n <- 619 ##this is sample size
PM <- .3##average probability of missing

alphas <- truealpha#c(-5,-2,0)#truealpha ##these are the alphas to try
DFS <-c(12,8,6,4,3,2,1)#seq(8,1,-1)#these are the degrees of freedom for the h1
DFS2 <- DFS#rep(3,length(DFS))#c(6,5,4,3,2) ##this is for the h2, must be same length DFS
DFS3 <- c(30,24,18,12,6,2,1)#these are teh degrees of freedom for the fs to try
###ONE HAS TO BE FIRST in both DFS!
##DF3 will also be used for orthogonal estimator
MAXDF <- 24 ##high degree of freedom to get started
maxh <- 750 ##if h is bigger than this its too big
epsilon <- 10^-3##stopping criterion
GRIDSIZE <- 1000 ##this is the size of grid for log normal look up table
Maxcount <- 15 #maximum nuumber of iteration in gam

###here we define the functions
##below are calculations of mean and sd of truef1, truef2 etc..
##below here should not change unless model-generation.S chagnes.
if(!Linear){
  H1 <- function(x) (MIDAGE-x)*(x > MIDAGE)
  H2 <- function(x) (x-MIDCD4)^2
  F1 <- function(x) - x + 0.65*(x-MIDAGE)*(x>MIDAGE)
  F2 <- function(x) -(MIDCD4-x)^2
  
  ##functions need for trueh,etc.. to have mean0
  NNN <- 500000
  if(Distributionx=="Normal"){
    if(Independentx) {
      Age <- rnorm(NNN,0,sigmaAge)
      CD4 <- rnorm(NNN,0,sigmaCD4)
    }
    else{
      Age <- rnorm(NNN,0,sigmaAge)
      CD4 <- rnorm(NNN,rho*sigmaCD4/sigmaAge*Age,sqrt(1-rho^2)*sigmaCD4)
    }
    MIDAGE <- -1.5*sigmaAge;MIDCD4 <- 3*sigmaCD4
    trueh1 <- H1(Age)
    trueh2 <- H2(CD4)
    truef1 <- F1(Age)
    truef2 <- F2(CD4)
    
    h1mean <- mean(trueh1)
    h1SD <- sd(trueh1)
    f1mean <- mean(truef1)
    f1SD <- sd(truef1)
    
    h2mean <- mean( trueh2)
    h2SD <- sd( trueh2)
    f2mean <- mean( truef2)
    f2SD <- sd( truef2)
  }
  if(Distributionx=="Unif"){
    ##We redefine MIDAGE etc..
    MINAGE <- 18;MIDAGE <- 35;MAXAGE <- 70
    MINCD4 <- 10;  MIDCD4 <- 800; MAXCD4 <- 900
    na1 <- round(.1*n);na2 <-n-na1 # na1/n is percent "young"
    nc1 <- round(.1*n);nc2 <- n-nc1#nc1/n is pecent "healthy"
    
    Age <- c(runif(na1,MINAGE,MIDAGE),runif(na2,MIDAGE,MAXAGE))
    CD4 <- c(runif(nc1,MIDCD4,MAXCD4),runif(nc2,MINCD4,MIDCD4))
    if(Independentx){
      Age <- sample(Age)
      CD4 <- sample(CD4)
    }
    trueh1 <- H1(Age)
    trueh2 <- H2(CD4)
    truef1 <- F1(Age)
    truef2 <- F2(CD4)
  
    h1mean <- mean(trueh1)
    h1SD <- sd(trueh1)
    f1mean <- mean(truef1)
    f1SD <- sd(truef1)
    
    h2mean <- mean( trueh2)
    h2SD <- sd( trueh2)
    f2mean <- mean( truef2)
    f2SD <- sd( truef2)
  }
}