泊松回归可以使用分组和未分组的数据进行。这两种方法之间应该有一些区别。为了确定这一点，我尝试使用一组模拟数据来研究这些差异。我发现的结果是，两种方法的估计参数相同，但剩余偏差却大不相同。

这让我想到了在我们对数据进行分组之前是否需要满足任何假设的问题。

# Rcode for simulated data #
rm(list=ls())
set.seed(1)
##############################################################
# Creating Random Age, Gender, obs count and population      #
##############################################################
nsim = 10000
age = sample(20:70,size = nsim, replace = T)
Gender = sample(c("M","F"),size = nsim, replace = T)
obs.count = sample(c(0,0,1),size = nsim, replace = T)
population = sample(c(0.7,0.8,0.9,1), size=nsim, replace = T)
ungrouped.data = data.frame(age,Gender,obs.count,population)
grouped.data = aggregate(cbind(ungrouped.data$obs.count,ungrouped.data$population),list(ungrouped.data$age,ungrouped.data$Gender), FUN = "sum")
names(grouped.data) = c("age", "Gender", "obs.count", "population")

############################################
# GLM model for group and ungroup data set #
############################################
model.group = glm(obs.count ~ age + Gender + offset((log(population))), family = poisson, data = grouped.data)
summary(model.group)
model.ungroup = glm(obs.count ~ age + Gender + offset((log(population))), family = poisson, data = ungrouped.data)
summary(model.ungroup)