当使用dnbinom()时，负二项回归产生r语言 - NaNs

Question

我使用dnbinom()来编写对数似然函数，然后使用r中的mle2() {bbmle}来估计参数

问题是我的负二项模型得到了16个警告，所有这些警告都是这样产生的:

1:在dnbinom(y, mu = mu, size = k, log = TRUE): NaNs产生

我代码:

# 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，我该如何避免它?

Answer 1

您没有限制负对数似然函数尝试k的负值。这个可能不会弄乱你的最终答案，但如果可以的话，最好避免这些警告。两个简单的策略:

• 设置k的下限(切换到method=L-BFGS-B)
• 在对数尺度上拟合k参数，如下:

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)))))

顺便说一下，对于这样的简单问题，您可以使用基于公式的快捷方式，如下所示:

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

对于这个简单的例子，MASS::glm.nb应该也可以很好地工作(但也许这是最简单的版本，将变得更复杂/超出glm.nb的范围)。