如何计算负二项式回归模型的预测概率? [英] How to calculate the predicted probability of negative binomial regression model?

问题描述

我在R MASS包中使用glm.nb()函数来估计负二项式回归模型的参数.给定新数据，我该如何计算预测概率(概率质量函数)?我可以使用哪个R函数?

I use glm.nb() function in R MASS package to estimate the parameters of a negative binomial regression model. How could I calculate the predicted probability (probability mass function) given new data, which R function can I　use?

我的数据集如下. y遵循负二项式分布，x是协变量.我使用glm.nb(y ~ x, data=data)来估计模型参数.给定新的x和y，我该如何计算预测概率.

My dataset is as follows. y follows negative binomial distribution and x is covariate. And I use glm.nb(y ~ x, data=data) to estimate model parameters. Given new x and y, how can I calculate the predicted probability.

有没有一种使用Java进行计算的方法?

Is there a way to calculate it using Java?

y     x

91    1.000000                                                                                       
79    1.000000

86    1.000000

32    1.000000

41    1.000000

29    0.890609

44    1.000000

42    1.000000

31    0.734058

35    1.000000

推荐答案

假设您像这样设置数据:

Let's say you set up your data like this:

set.seed(1)
x = seq(-2, 8, .01)
y = rnbinom(length(x), mu=exp(x), size=10)
fit = glm.nb(y ~ x)

有一个新的观点:给定x=5的情况下，您想找到y=100的概率.

and you have a new point: you want to find the probability of y=100 given x=5.

您可以使用predict从x获取y的预测值(在应用了链接函数的逆函数之后，可以使用type="response"告诉它您想要它):

You can get the predicted value of y from x using predict (with type="response" to tell it you want it after the inverse of the link function has been applied):

predicted.y = predict(fit, newdata=data.frame(x=5), type="response")

然后您可以通过以下方式找出概率:

Then you could find out the probability with:

dnbinom(100, mu=predicted.y, size=fit$theta)

(这是使用fit$theta，即负二项式的大小"参数的最大似然估计).

(This is using fit$theta, the maximum likelihood estimate of the "size" parameter of the negative binomial).

所以在一个函数中:

prob = function(newx, newy, fit) {
    dnbinom(newy, mu=predict(fit, newdata=data.frame(x=newx), type="response"), size=fit$theta)
}

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