glm模型的一個p值

Question

我正在尋找一種方法來獲得一個描述適用於glm模型的p值的方法。下面是從lm手冊頁稍微修改例如：

ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14) 
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69) 
conf<- c(rnorm(mean=-1, sd=1, n=10), rnorm(mean=1, sd=1, n=10)) 

group <- gl(2,10,20, labels=c("Ctl","Trt")) 
weight <- c(ctl, trt) 
lm.D9 <- lm(weight ~ group + conf) 

隨着summary(lm.D9)一個得到

Call: 
lm(formula = weight ~ group + conf) 

Residuals: 
    Min  1Q Median  3Q  Max 
-1.17619 -0.40373 -0.05262 0.24987 1.40777 

Coefficients: 
      Estimate Std. Error t value Pr(>|t|)  
(Intercept) 4.97416 0.25153 19.775 3.6e-13 *** 
groupTrt -0.23724 0.41117 -0.577 0.572  
conf  -0.07044 0.13725 -0.513 0.614  
--- 
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0.7111 on 17 degrees of freedom 
Multiple R-squared: 0.08722, Adjusted R-squared: -0.02017 
F-statistic: 0.8122 on 2 and 17 DF, p-value: 0.4604 

如果ID做同樣的GLM

glm.D9 <- glm(weight ~ group + conf) 
summary(glm.D9) 

我得到

Call: 
glm(formula = weight ~ group + conf) 

Deviance Residuals: 
    Min  1Q Median  3Q  Max 
-1.17619 -0.40373 -0.05262 0.24987 1.40777 

Coefficients: 
      Estimate Std. Error t value Pr(>|t|)  
(Intercept) 4.97416 0.25153 19.775 3.6e-13 *** 
groupTrt -0.23724 0.41117 -0.577 0.572  
conf  -0.07044 0.13725 -0.513 0.614  
--- 
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

(Dispersion parameter for gaussian family taken to be 0.5056514) 

    Null deviance: 9.4175 on 19 degrees of freedom 
Residual deviance: 8.5961 on 17 degrees of freedom 
AIC: 47.869 

Number of Fisher Scoring iterations: 2 

lm已將F統計作爲整個模型的摘要，glm還沒有。 所以再次提出這個問題：我如何從glm模型中得到一個p值來描述適合度？

感謝

Answer 1

可以計算這樣的F統計量：

glm.D9 <- glm(weight ~ group + conf) 

glm.0 <- glm(weight ~ 1) 

anova(glm.D9, glm.0, test="F") 

# Analysis of Deviance Table 
# 
# Model 1: weight ~ group + conf 
# Model 2: weight ~ 1 
# Resid. Df Resid. Dev Df Deviance  F Pr(>F) 
# 1  17  8.5868       
# 2  19  9.4175 -2 -0.8307 0.8223 0.4562 

見?anova.glm可用的詳細信息和其他測試。