模型的偏差定义为： $D = -2(loglikelihood(model) - loglikelihood(saturated.model))$

所以我尝试将这个公式的结果与不同模型的 deviance() 函数的输出进行比较：

线性回归模型：

> ?cats
> m1=lm(Hwt~Bwt+Sex,data=cats)
> m1.saturated=lm(Hwt~factor(1:nrow(cats)),data=cats)
> deviance(m1)
[1] 299
> sum(residuals(m1)^2)
[1] 299
> deviance(m1.saturated)
[1] 0
> as.numeric(-2*(logLik(m1)-logLik(m1.saturated)))
[1] Inf

299 Inf 有问题$\neq$

GLM：泊松回归

> x = rnorm(10)
> y = rpois(10,lam=exp(1 + 2*x))
> m2 = glm(formula = y ~ x, family = poisson)
> m2.saturated <- glm(y ~ factor(1:10),family=poisson)
> deviance(m2) 
[1] 14
> deviance(m2.saturated) 
[1] 4.5e-10
> as.numeric(-2*(logLik(m2)-logLik(m2.saturated))) 
[1] 14

14 = 14
好的，它有效！

GLM：伽玛回归

 > cement <- read.table("cement.dat", col.names = c("time","resistance"), dec = ",") 
 > attach(cement)
 > m3 <- glm(resistance ~ I(1/time), family = Gamma)
 > m3.saturated <- glm(resistance ~ factor(1:nrow(cement)), family = Gamma)
 > deviance(m3)
 [1] 0.16
 > deviance(m3.saturated)
 [1] 9.3e-17
 > as.numeric(-2*(logLik(m3)-logLik(m3.saturated)))
 [1] 758

0.16 758 一定有什么地方出错了$\neq$

结果不应该一样吗？