One p-value for glm model

Question

i'm searching for a way to get one p-value which describes the goodness of fit for a glm-model. Here is a slightly modified example from the lm manpage:

 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)

With summary(lm.D9) one gets

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 

If id do the same with glm

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

i get

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 has the F-statistics as summary for the whole model, glm has not. So again the question: How can i get one p-value from the glm model which describes the fit?

thanks

Answer 1

You can calculate the F statistics like this:

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

See ?anova.glm for details and other tests available.