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# Functions from package 'SKAT' v.0.82 (c) 2011
#
# Get Parameter for the Liu et. al
#
Get_Liu_Params<-function(c1){
## Helper function for getting the parameters for the null approximation
muQ<-c1[1]
sigmaQ<-sqrt(2 *c1[2])
s1 = c1[3] / c1[2]^(3/2)
s2 = c1[4] / c1[2]^2
beta1<-sqrt(8)*s1
beta2<-12*s2
type1<-0
if(s1^2 > s2){
a = 1/(s1 - sqrt(s1^2 - s2))
d = s1 *a^3 - a^2
l = a^2 - 2*d
} else {
type1<-1
a = 1/s1
d = 0
l = 1/s1^2
}
muX <-l+d
sigmaX<-sqrt(2) *a
re<-list(l=l,d=d,muQ=muQ,muX=muX,sigmaQ=sigmaQ,sigmaX=sigmaX)
return(re)
}
Get_Liu_Params_Mod<-function(c1){
## Helper function for getting the parameters for the null approximation
muQ<-c1[1]
sigmaQ<-sqrt(2 *c1[2])
s1 = c1[3] / c1[2]^(3/2)
s2 = c1[4] / c1[2]^2
beta1<-sqrt(8)*s1
beta2<-12*s2
type1<-0
#print(c(s1^2,s2))
if(s1^2 > s2){
a = 1/(s1 - sqrt(s1^2 - s2))
d = s1 *a^3 - a^2
l = a^2 - 2*d
} else {
type1<-1
l = 1/s2
a = sqrt(l)
d = 0
}
muX <-l+d
sigmaX<-sqrt(2) *a
re<-list(l=l,d=d,muQ=muQ,muX=muX,sigmaQ=sigmaQ,sigmaX=sigmaX)
return(re)
}
Get_Liu_Params_Mod_Lambda<-function(lambda){
## Helper function for getting the parameters for the null approximation
c1<-rep(0,4)
for(i in 1:4){
c1[i]<-sum(lambda^i)
}
muQ<-c1[1]
sigmaQ<-sqrt(2 *c1[2])
s1 = c1[3] / c1[2]^(3/2)
s2 = c1[4] / c1[2]^2
beta1<-sqrt(8)*s1
beta2<-12*s2
type1<-0
#print(c(s1^2,s2))
if(s1^2 > s2){
a = 1/(s1 - sqrt(s1^2 - s2))
d = s1 *a^3 - a^2
l = a^2 - 2*d
} else {
type1<-1
l = 1/s2
a = sqrt(l)
d = 0
}
muX <-l+d
sigmaX<-sqrt(2) *a
re<-list(l=l,d=d,muQ=muQ,muX=muX,sigmaQ=sigmaQ,sigmaX=sigmaX)
return(re)
}
Get_Liu_PVal.MOD<-function(Q, W, Q.resampling = NULL){
Q.all<-c(Q,Q.resampling)
A1<-W/2
A2<-A1 %*% A1
c1<-rep(0,4)
c1[1]<-sum(diag(A1))
c1[2]<-sum(diag(A2))
c1[3]<-sum(A1*t(A2))
c1[4]<-sum(A2*t(A2))
param<-Get_Liu_Params_Mod(c1)
Q.Norm<-(Q.all - param$muQ)/param$sigmaQ
Q.Norm1<-Q.Norm * param$sigmaX + param$muX
p.value<- pchisq(Q.Norm1, df = param$l,ncp=param$d, lower.tail=FALSE)
p.value.resampling = NULL
if(length(Q.resampling) > 0){
p.value.resampling<-p.value[-1]
}
re<-list(p.value = p.value[1], param=param, p.value.resampling = p.value.resampling )
return(re)
}
Get_Liu_PVal.MOD.Lambda<-function(Q.all, lambda){
param<-Get_Liu_Params_Mod_Lambda(lambda)
Q.Norm<-(Q.all - param$muQ)/param$sigmaQ
Q.Norm1<-Q.Norm * param$sigmaX + param$muX
p.value<- pchisq(Q.Norm1, df = param$l,ncp=param$d, lower.tail=FALSE)
return(p.value)
}
Get_Liu_PVal.MOD.Lambda.Zero<-function(Q, muQ, muX, sigmaQ, sigmaX, l, d){
Q.Norm<-(Q - muQ)/sigmaQ
Q.Norm1<-Q.Norm * sigmaX + muX
temp<-c(0.05,10^-10, 10^-20,10^-30,10^-40,10^-50, 10^-60, 10^-70, 10^-80, 10^-90, 10^-100)
#qchisq(temp, df=1000000000,lower.tail=FALSE)
out<-qchisq(temp,df = l,ncp=d, lower.tail=FALSE)
#cat(c(Q.Norm1,l,d, out))
#cat("\n")
IDX<-max(which(out < Q.Norm1))
pval.msg<-sprintf("Pvalue < %e", temp[IDX])
return(pval.msg)
}
Get_Lambda <-function(K){
out.s<-eigen(K,symmetric=TRUE, only.values = TRUE)
#print(out.s$values)
#out.s1<-eigen(K,symmetric=TRUE)
#print(out.s1$values)
lambda1<-out.s$values
IDX1<-which(lambda1 >= 0)
# eigenvalue bigger than sum(eigenvalues)/1000
IDX2<-which(lambda1 > mean(lambda1[IDX1])/100000)
if(length(IDX2) == 0){
stop("No Eigenvalue is bigger than 0!!")
}
lambda<-lambda1[IDX2]
return(lambda)
}
Get_PValue.Lambda<-function(lambda,Q){
#print(lambda)
n1<-length(Q)
p.val<-rep(0,n1)
p.val.liu<-rep(0,n1)
is_converge<-rep(0,n1)
p.val.liu<-Get_Liu_PVal.MOD.Lambda(Q, lambda)
for(i in 1:n1){
out<-davies(Q[i],lambda,acc = 0.00000001,lim = 1000000)
p.val[i]<-out$Qq
#p.val.liu[i]<-SKAT_liu(Q[i],lambda)
is_converge[i]<-1
# check convergence
if(length(lambda) == 1){
p.val[i]<-p.val.liu[i]
} else if(out$ifault != 0){
is_converge[i]<-0
}
# check p-value
if(p.val[i] > 1 || p.val[i] <= 0 ){
is_converge[i]<-0
p.val[i]<-p.val.liu[i]
}
}
p.val.msg = NULL
#cat(p.val[1])
if(p.val[1] == 0){
param<-Get_Liu_Params_Mod_Lambda(lambda)
p.val.msg<-Get_Liu_PVal.MOD.Lambda.Zero(Q[1], param$muQ, param$muX, param$sigmaQ, param$sigmaX, param$l, param$d)
}
return(list(p.value=p.val, p.val.liu=p.val.liu, is_converge=is_converge, pval.zero.msg=p.val.msg))
}
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