R: Error in estimating mle using MaxLik() package

Jasmine Helen

My purpose is to find the maximum likelihood estimator using Newton Raphson's algorithm and compare this solution with glm(). So I try to use maxLik() in R. The result is an error, I have not used this package before, please fix this error, thank you! !

d <- read.delim("http://dnett.github.io/S510/Disease.txt")
    
d$disease=as.factor(d$disease)
d$ses=as.factor(d$ses)
d$sector=as.factor(d$sector)
str(d)

y<-as.numeric(as.character(d$disease))
x1<-as.numeric(as.character(d$age))
x2<-as.numeric(as.character(d$sector))
x3<-as.numeric(as.character(d$ses))

oreduced <- glm(disease ~ age + sector, family=binomial(link = logit), data=d)
summary(oreduced)
    
    
nlldbin=function(param){
  eta<-param[1]+param[2]*x1+param[3]*(x2==2)
  p<-1/(1+exp(-eta))
  -sum(y*log(p)+(1-y)*log(1-p),na.rm=TRUE)
}
est_nr<-maxLik(nlldbin,start=c(0.01,0.01,0.01))
summary(est_nr)

The result is

Iteration 1 
Parameter:
[1]   9841290 377928533   4325584
Gradient (first 30 components):
     [,1] [,2] [,3]
[1,]  NaN  NaN  NaN
Error in maxNRCompute(fn = function (theta, fnOrig, gradOrig = NULL, hessOrig = NULL,  : 
  NA in gradient
user 20650

We are trying to maximize the log-likelihood, but your function is minimizing due to applying a negative number to the sum. So just remove the negation, giving:

nlldbin <- function(param){
  eta <- param[1] + param[2]*x1 + param[3]*(x2==2)
  p <- 1/(1+exp(-eta))  
  sum(y*log(p) + (1-y) * log(1-p), na.rm=TRUE)
}

This is different from other optimizers, for example optim, which usually minimize by default. That's why you negate the sum, as you did.

ps you can use the built-in function to write your function, which might be a bit more stable (and less typing):

nlldbin2 <- function(param){
  eta <- cbind(1, x1, x2 == 2) %*% param
  p <- plogis(eta)
  sum(dbinom(y, 1, p, log=TRUE))
}

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