R语言回归与分类(三)-负二项回归_mass负二项回归结果

负二项分布

负二项回归由来及其密度推导

 

 

 

负二项回归与泊松回归比较

 

模型系数解读

 

下面通过 R 语言生成随机数来了解下用 R 语言建立负二项回归模型

 

set.seed(1010)
N <- 100
x1 <- rnorm(N)
x2 <- runif(N)
err <- rnorm(N)
lambda <- exp(1+2*x1+3*x2+err)
y <- rpois(N,lambda)
sim.data <- data.frame(x1,x2,y)

调用”MASS”包里的glm.nb()进行拟合负二项回归(可以估计负二项参数ψ和回归参数βj)

library(MASS)
model <- glm.nb(y~.,data=sim.data)
summary(model)

 

除回归系数外，也可以单独输出负二项回归的参数ψ如下： 

为了对比我们可以拟合一般的泊松回归模型与准泊松回归模型，比较其系数如下：

model1 <- glm(y~.,data=sim.data,family = "poisson")
model2 <- glm(y~.,data=sim.data,family = "quasipoisson")
coef.matrix <- rbind(coef(model),coef(model1),coef(model2))
rownames(coef.matrix) <- c("NB","Poisson","Quasi-poisson")
coef.matrix

 

se.mat <- rbind(coef(summary(model))[,"Std. Error"],coef(summary(model1))[,"Std. Error"],coef(summary(model2))[,"Std. Error"])
rownames(se.mat) <- c("NB","Poisson","Quasi-poisson")
se.mat