Clash Royale CLAN TAG

R: MaxLik estimates is just equal to the initial parameters I've set (any initial parameter)

I have this log-likelihood function coded and tried to maximize it using the maxLik. However, 3 out of 4 parameters I've estimated is just the same with the any initial parameter I've used.

What I know is that my actual parameters won't be sensitive on what my initial parameters are. Thus, I believe there is something wrong with my code as it does not converge to the maximum log-likelihood estimates. Any thoughts on how to fix it?

# Flexible expo-power utility function
expoUtility <- function(x, alpha, param_beta, W){
(1-exp(-alpha*(W + x)^(1-param_beta)))/alpha
}

# Calculate the probability of a single outcome in the next round
Round.Probability.Table <- cbind(Round.Probability.Table,c(1:10))
Round.Probability.Table <- Round.Probability.Table[,1:3]
names(Round.Probability.Table) <- c("Round","CasesAtEnd","Probability")

for (i in 1:9) {
Round.Probability.Table$Probability[i] <- 1/choose(Round.Probability.Table$CasesAtEnd[i],Round.Probability.Table$CasesAtEnd[i+1])
}

LL.expoUtility <- function (parameters) {

alpha <- parameters[1]
param_beta <- parameters[2]
W <- parameters[3]
sigma <- parameters[4]

LL <- foreach(i=1:nrow(data), .combine = "c", .export = ls(envir = globalenv()), .packages = c("data.table","doParallel", "maxLik", "dplyr")) %dopar% {

sv <- expoUtility(data$Bank.Offer[i], alpha = alpha, param_beta = param_beta, W = W)

cv <- combn(Set.Cases.Remaining[[i]], Round.Probability.Table[1+match(data$Round[i], Round.Probability.Table$Round),2]) %>%
apply(2,mean) %>%
sapply(FUN = predictedBankOffer, b = data$Bank.Offer.Percent[i], r = data$Round[i]) %>%
sapply(FUN = expoUtility, alpha = alpha, param_beta = param_beta, W = W)*Round.Probability.Table$Probability[data$Round[i]]
cv <- sum(cv)

delta <- combn(Set.Cases.Remaining[[i]], Round.Probability.Table[1+match(data$Round[i], Round.Probability.Table$Round), 2]) %>%
apply(2,mean) %>%
sapply(FUN = predictedBankOffer, b = data$Bank.Offer.Percent[i], r = data$Round[i]) %>%
sapply(FUN = expoUtility, alpha = alpha, param_beta = param_beta, W = W) - cv
delta <- delta^2 %>%
sum() %>%
sqrt()

if (data$Answer[i] == 0) {
z <- (cv-sv)/(delta*sigma)
} else {
z <- (sv-cv)/(delta*sigma)
}
}
LL <- sapply(LL, FUN = pnorm, mean = 0, sd = 1, log.p = TRUE)
return(LL)
}

LL.logUtility <- function (parameters) {

sigma <- parameters[1]

LL <- foreach(i=1:nrow(data), .combine = "c", .packages = c("data.table","doParallel", "maxLik", "dplyr")) %dopar% {

sv <- log(data$Bank.Offer[i])

cv <- combn(Set.Cases.Remaining[[i]], Round.Probability.Table[1+match(data$Round[i], Round.Probability.Table$Round),2]) %>%
apply(2,mean) %>%
sapply(FUN = predictedBankOffer, b = data$Bank.Offer.Percent[i], r = data$Round[i]) %>%
sapply(FUN = log)*Round.Probability.Table$Probability[data$Round[i]]
cv <- sum(cv)

delta <- combn(Set.Cases.Remaining[[i]], Round.Probability.Table[1+match(data$Round[i], Round.Probability.Table$Round), 2]) %>%
apply(2,mean) %>%
sapply(FUN = predictedBankOffer, b = data$Bank.Offer.Percent[i], r = data$Round[i]) %>%
sapply(FUN = log) - cv
delta <- delta^2 %>%
sum() %>%
sqrt()

if (data$Answer[i] == 0) {
z <- (cv-sv)/(delta*sigma)
} else {
z <- (sv-cv)/(delta*sigma)
}
}
LL <- sapply(LL, FUN = pnorm, mean = 0, sd = 1, log.p = TRUE)
return(LL)
}

## Maximise the Log likelihood function. Reported estimates equal to the Initial parameters
ptm.1 <- proc.time()
mle.1 <- maxLik(logLik = LL.expoUtility, start = c(0.1233,0.958,82370,0.1625), method = "NM", tol = 1e-20, iterlim = 3)
proc.time() - ptm.1

summary(mle.1)


P.S. I am a Windows user and a friend suggested that my codes are MAC-specific.

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