 Sergio Nolazco - 3 years ago 217
R Question

# NaNs produced in negative binomial regression when using dnbinom()

I am using

`dnbinom()`
for writing the log-likelihood function and then estimate parameters using
`mle2()`
{bbmle} in R.

The problem is that I got 16 warnings for my negative binomial model, all of them NaNs produced like this one:

1: In dnbinom(y, mu = mu, size = k, log = TRUE) : NaNs produced

My code:

``````# data
x <- c(0.35,0.45,0.90,0.05,1.00,0.50,0.45,0.25,0.15,0.40,0.26,0.37,0.43,0.34,0.00,0.11,0.00,0.00,0.00,0.41,0.14,0.80,0.60,0.23,0.17,0.31,0.30,0.00,0.23,0.33,0.30,0.00,0.00)
y <- c(1,10,0,0,67,0,9,5,0,0,0,82,36,0,32,7,7,132,14,33,0,67,11,39,41,67,9,1,44,62,111,52,0)

# log-likelihood function
negbinglmLL = function(beta,gamma,k) {
mu= exp(beta+gamma*x)
-sum(dnbinom(y,mu=mu, size=k, log=TRUE))
}

# maximum likelihood estimator
model <- mle2(negbinglmLL, start=list(beta=mean(y), gamma= 0, k=mean(y)^2/(var(y)-mean(y))))
``````

What do these warnings mean, and if this is a serious problem how can I avoid it? Ben Bolker

You're not restricting the negative log-likelihood function from trying negative values of `k`. This probably doesn't mess up your final answer, but it's always best to avoid these kinds of warnings if you can. Two simple strategies:

• put a lower bound on `k` (switching to `method=L-BFGS-B`)
• fit the `k` parameter on the log scale, as follows:
``````negbinglmLL = function(beta,gamma,logk) {
mu= exp(beta+gamma*x)
-sum(dnbinom(y,mu=mu, size=exp(logk), log=TRUE))
}

model <- mle2(negbinglmLL,
start=list(beta=mean(y),
gamma= 0,
logk=log(mean(y)^2/(var(y)-mean(y)))))
``````

By the way, for simple problems like this you can use a formula-based shortcut as follows:

``````mle2(y~dnbinom(mu=exp(logmu),size=exp(logk)),
parameters=list(logmu~x),
start=list(logmu=0,logk=0),
data=data.frame(x,y))
``````

For this simple case `MASS::glm.nb` should also work perfectly well (but perhaps this is the simplest version of something that will get more complicated/beyond the scope of `glm.nb`).

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