Hougaard P, Lee M L, Whitmore G A
Novo Nordisk, Bagsvaerd, Denmark.
Biometrics. 1997 Dec;53(4):1225-38.
Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.
与泊松分布相比，计数数据常常表现出过度离散。过度离散通常通过基于伽马分布的均值随机效应进行建模，从而得到计数的负二项分布。本文考虑了一个更大的混合分布族，包括逆高斯混合分布。结果表明，它对癫痫发作频率的数据集拟合效果显著更好。同样的方法可用于从泊松过程生成计数过程，其中速率或时间是随机的。随机速率对应患者之间的差异，而随机时间对应患者内部的差异。
