# R/omniRLRT_fast.R In CKLRT: Composite Kernel Machine Regression Based on Likelihood Ratio Test

#### Documented in omniRLRT_fast

```#' Composite kernel machine regression based restricted likelihood ratio test
#'
#' @param y vector of the continous outcomes.
#' @param X the additional covariates.
#' @param K1 the first kernel corresponding to the genetic main effect.
#' @param K2 the second kernel corresponding to the genetic and environment interaction effect.
#' @param N total number of randomly generated normal variables used to generate the emprical null distribution of LRT. Default value is 10,000.
#' @param length.lambda the length of lambda. Dafult value is 200. The values of lambda are all more than 0.
#' @param length.rho the length of rho. Default value is 21. The values of rho are between 0 and 1.
#'
#' @return the result is a list containing three elements. 1. p.dir is the p-value of restricted likelihood ratio test based on emprical distrition. 2. p.aud is the p-value by approximating the null distribution as a mixture of a point mass at zero with probability b and weighted chi square distribution with d degrees of freedom with probality of 1-b. 3. LR is the likelihood ratio test statistics.

#' @export
#'
#' @examples
#' set.seed(6)
#' n = 50 # the number of observations
#' X = rnorm(n) # the other covariates
#' p = 2 # two snp in a gene will be simulated
#' G = runif(n*p)< 0.5
#' G = G + runif(n*p) < 0.5
#' G = matrix(G, n,p) #genetic matrix
#' E = (runif(n) < 0.5)^2 #enviroment effect
#' y = rnorm(n) + G[,1] * 0.3 #observations
#' omniRLRT_fast(y, X =  cbind(X, E),K1 = G %*% t(G),K2 = (G*E) %*% t(G * E))
#' @importFrom MASS ginv
#' @import nlme
#' @import Rcpp
#' @import mgcv
#' @import compiler

omniRLRT_fast = function(y, X,K1, K2, N = 10000, length.rho = 200, length.lambda = 21){
method = "REML"
Lambdas = exp(seq(from = -12, to = 12, length.out = length.lambda))
all_rho = seq(from = 0,to = 1, length.out = length.rho)
n  = length(y)
if (is.null(X)){
X1 = matrix(1, nrow=n)
px = 1
}else{
X1 = cbind(1,X)
px = ncol(X1)
}
XX   = MatMult_C(t(X1),X1)
P0   = diag(n)- MatMult_C(MatMult_C(X1,ginv(XX)),t(X1))

eP   = Eigen_C(P0)
A    = eP\$vector[,eP\$values > 1e-10]
# invP = ginv(P0)
# A2   = eP\$vectors %*% diag(eP\$values)
eK1  = Eigen_C(K1)
wK1  = which(eK1\$values  > 1e-10)
# phi1 = t(t(eK1\$vectors[,wK1])*sqrt(eK1\$values[wK1]))
if (length(wK1) == 1){
phi1 = eK1\$vectors[,wK1] * sqrt(eK1\$values[wK1])
}else{
phi1 = t(t(eK1\$vectors[,wK1])*sqrt(eK1\$values[wK1])) # this actually works for all of them
}

eK2  = Eigen_C(K2)
wK2  = which(eK2\$values  > 1e-10)

if (length(wK2) == 1){
phi2 = eK2\$vectors[,wK2] * sqrt(eK2\$values[wK2])
}else{
phi2 = t(t(eK2\$vectors[,wK2])*sqrt(eK2\$values[wK2]))
}
# if wK1 and wK2 are 1, what would this happen to others?

group= rep(1,n)
fit1 = lme(y~X, random = list(group=pdIdent(~-1+phi1), group = pdIdent(~-1+phi2))) #  Default = REML
fit0 = lm(y~X)
LR = max(0, 2*(logLik(fit1, REML = T) -logLik(fit0, REML = T)))

if (LR <= 0){
p.dir =p.au1= p.aud = 1
}else{

#For the first kernel
LR0_allRho = matrix(NA, N, length.rho)
#set.seed(123)
w = matrix(rnorm(N*(n-px)), n-px,N)
LR0_fixRho = matrix(NA, N, length.lambda)

rho = 0
K = K2
k = length(wK2)
xi = eK2\$values[wK2]
AKA = MatMult_C(MatMult_C(t(A),K),A)
eV = Eigen_C(AKA)
#eV = Eigen_C(AKA)
U_1 = eV\$vectors
mu = eV\$values[eV\$values > 1e-10]

mu = mu/max(mu, xi)
xi = xi/max(mu,xi)

# original U_1 in this case
W1 = MatMult_C(A,U_1)
w.double <- w^2
w1 = w.double[1:k,]
w2 = ColSum_C((w.double)[-(1:k),])

if (length(mu) < k){mu = c(mu,rep(0, k - length(mu)))}
if (length(xi) < k){xi = c(xi,rep(0, k - length(xi)))}

LR0_fixRho <- LR0_fixRho_C(Lambdas,
mu,
w1,
w2,
n-px)
# for (i in 1:length.lambda){
#   lam = Lambdas[i]
#   Dn = (1/(1 + lam*mu))%*%w1+ w2
#   Nn = (lam*mu/(1 + lam*mu))%*%w1
#   temp = (n-px)*log(1 + Nn/Dn) - Sum_C(log(1 + lam*mu))
#   LR0_fixRho[,i] = ifelse(temp < 0, 0, temp)
# }
LR0_allRho[,1] = MatrixRowMax_C(LR0_fixRho)

LR0_allRho <- doubleloop(K1,
K2,
P0,
A,
U_1,
w,
Lambdas,
n-px,
all_rho,
LR0_allRho)
LR0 = MatrixRowMax_C(LR0_allRho)
LR0 = ifelse(LR0 > 0, LR0, 0)
p.dir = mean(LR < LR0)
p.au1 = getp_au1(null = LR0, LR = LR)\$p
p.aud= getp_aud_estimate_pi_first(null = LR0, LR = LR)\$p
}
out = list(p.dir = p.dir,p.aud = p.aud, LR = LR)
return(out)
}
```

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CKLRT documentation built on May 1, 2019, 10:20 p.m.