Nothing
### Perform H0: alpha_1 == alpha_2 && beta_1 == beta_2 vs
### Ha: alpha_1 != alpha_2 || beta_1 != beta_2
lrt.betaab <- function(PV.gbd, CLASS.gbd, K, proc = c("1", "2")){
K.CLASS <- as.integer(max.gbd(CLASS.gbd))
if(K.CLASS > K){
stop("CLASS.gbd and K are not matched.")
}
### For constrOptim() and H0.
fn.H0 <- function(theta, x.all){
-sum(dbeta(x.all, theta[1], theta[2], log = TRUE))
}
### For constrOptim() and Ha.
fn.Ha <- function(theta, x.1, x.2){
-sum(dbeta(x.1, theta[1], theta[2], log = TRUE)) -
sum(dbeta(x.2, theta[3], theta[4], log = TRUE))
}
### For initial Beta parameters.
fn.init <- function(x.gbd){
x.bar <- mean(x.gbd)
v.bar <- var(x.gbd)
a.hat <- x.bar * (x.bar * (1 - x.bar) / v.bar - 1)
b.hat <- (1 - x.bar) * (x.bar * (1 - x.bar) / v.bar - 1)
ret <- c(a.hat, b.hat)
if(v.bar > x.bar * (1 - x.bar))
ret <- -ret
ret
}
### Run for all (K-1)*K/2 pairs.
ret <- NULL
for(i.k.1 in 2:(K - 1)){
N.class.gbd.1 <- sum(CLASS.gbd == i.k.1)
if(N.class.gbd.1 > 1){ # in case of empty cluster.
x.1.gbd <- PV.gbd[CLASS.gbd == i.k.1]
for(i.k.2 in (i.k.1 + 1):K){
N.class.gbd.2 <- sum(CLASS.gbd == i.k.2)
if(N.class.gbd.2 > 1){ # in case of empty cluster.
x.2.gbd <- PV.gbd[CLASS.gbd == i.k.2]
### logL under H0.
x.all <- c(x.1.gbd, x.2.gbd)
theta <- fn.init(x.all)
tmp <- constrOptim(theta, fn.H0, NULL, diag(2), rep(1e-16, 2),
method = "Nelder-Mead", x.all = x.all)
H0.alpha <- tmp$par[1]
H0.beta <- tmp$par[2]
logL.0 <- -tmp$value
### logL under Ha.
theta <- c(fn.init(x.1.gbd), fn.init(x.2.gbd))
tmp <- constrOptim(theta, fn.Ha, NULL, diag(4), rep(1e-16, 4),
method = "Nelder-Mead", x.1 = x.1.gbd, x.2 = x.2.gbd)
Ha.alpha.1 <- tmp$par[1]
Ha.beta.1 <- tmp$par[2]
Ha.alpha.2 <- tmp$par[3]
Ha.beta.2 <- tmp$par[4]
logL.a <- -tmp$value
### LRT.
lrt <- -2 * (logL.0 - logL.a)
if(lrt < 0){
lrt <- 0
}
### p-value.
p.value <- pchisq(lrt, 2, lower.tail = FALSE)
ret <- rbind(ret, c(i.k.1, i.k.2, logL.0, logL.a, lrt, p.value))
}
}
}
}
if(proc[1] == "1"){
ret <- cbind(ret, qvalue(ret[, ncol(ret)]))
} else if(proc[1] == "2"){
qvalue.p2 <- fdr.bh.p2(ret[, ncol(ret)], q = 0.05)$adjp
ret <- cbind(ret, qvalue.p2)
} else{
stop("proc is not found.")
}
colnames(ret) <- c("i.k.1", "i.k.2",
"logL.0", "logL.a", "lrt", "p.value", "q.value")
ret
} # End of lrt.betaab().
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