R语言泊松回归分析

响应变量是计数形式，响应变量（因变量y）的值遵循泊松分布。

1. 数据集载入

### 数据集载入
library(AER) 
data()  # 查看AER包里面的数据集
data(Affairs) # 载入Affairs数据集
# 查看数据集
summary(Affairs)
str(Affairs)
View(Affairs)

2. 模型拟合

poisson_fit <- glm(affairs ~ ., family = poisson,
               data = Affairs)

summary(poisson_fit)
coef(poisson_fit)
plot(poisson_fit)

## 检测是否有过度离势overdispersion
deviance(poisson_fit)/df.residual(poisson_fit)
install.packages("qcc")
library(qcc)
qcc.overdispersion.test(Affairs$affairs,type="poisson")
# p小于 0.05,表明确实存在过度离势,family选择quasipoisson
poisson_fit2 <- glm(affairs ~., family = quasipoisson(),data = Affairs)

summary(poisson_fit2)

## 根据因变量的显着性水平，找出和结果结果变量显著相关的因变量，重新建模 
poisson_fit3 <- glm(affairs ~age+yearsmarried+religiousness+rating, 
                    family = quasipoisson,data = Affairs)

summary(poisson_fit3)
anova(poisson_fit3)

poisson_fit3$fitted.values

3. 预测

## 构造数据，固定其他变量，检测rating值对预测结果的影响
new_data <-data.frame(age = mean(Affairs$age),
                      yearsmarried = mean(Affairs$yearsmarried),
                      religiousness = mean(Affairs$religiousness),
                      rating=seq(1:5))
#?predict.glm
pred_value <- predict(poisson_fit3,new_data,type='response')