使用dnbinom()在负二项式回归中产生的NaN [英] NaNs produced in negative binomial regression when using dnbinom()

问题描述

我正在使用dnbinom()编写对数似然函数，然后使用R中的mle2() {bbmle}估计参数.

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

问题是我的负二项式模型收到了16条警告，所有的NaN都是这样产生的:

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

1:在dnbinom中(y，mu = mu，大小= k，log = TRUE):产生了NaNs

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

我的代码:

# 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))))

这些警告是什么意思，如果这是一个严重的问题，我该如何避免呢?

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

推荐答案

您没有在限制负对数可能性函数尝试使用k的负值.这个可能不会弄乱您的最终答案，但是如果可以的话，最好避免出现此类警告.两种简单的策略:

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:

• 在k上设置一个下限(切换到method=L-BFGS-B)
• 使k参数适合对数刻度，如下所示:

• 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)))))

顺便说一句，对于像这样的简单问题，您可以使用基于公式的快捷方式，如下所示:

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))

对于这种简单的情况，MASS::glm.nb也应该可以很好地工作(但是，这可能是最简单的版本，它将变得更加复杂/超出了glm.nb的范围).

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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