[R] How to read the summary

mathallan mathanmath at gmail.com
Tue Apr 28 15:09:44 CEST 2009


How can I from the summary function, decide which glm (fit1, fit2 or fit3)
fits to data best? I don't know what to look after, so I would please
explain the important output.

> fit1 <- glm(Y~X, family=gaussian(link="identity"))
> fit2 <- glm(Y~X, family=gaussian(link="log"))
> fit3 <- glm(Y~X, family=Gamma(link="log"))
> summary(fit1)

Call:
glm(formula = Y ~ X, family = gaussian(link = "identity"))

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.6619  -1.9693  -0.4119   2.0787   3.9664  

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.4285     1.6213  -0.264 0.798258    
X             4.3952     0.7089   6.200 0.000259 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

(Dispersion parameter for gaussian family taken to be 6.784605)

    Null deviance: 315.081  on 9  degrees of freedom
Residual deviance:  54.277  on 8  degrees of freedom
AIC: 51.294

Number of Fisher Scoring iterations: 2

> summary(fit2)

Call:
glm(formula = Y ~ X, family = gaussian(link = "log"))

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.5489  -0.2960   0.4776   0.6353   1.2773  

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.50537    0.16562   3.051   0.0158 *  
X            0.66352    0.05083  13.055 1.13e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

(Dispersion parameter for gaussian family taken to be 1.083989)

    Null deviance: 315.0810  on 9  degrees of freedom
Residual deviance:   8.6718  on 8  degrees of freedom
AIC: 32.954

Number of Fisher Scoring iterations: 6

> summary(fit3)

Call:
glm(formula = Y ~ X, family = Gamma(link = "log"))

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.35269  -0.09272   0.02550   0.13625   0.18018  

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.85959    0.11244   7.645 6.04e-05 ***
X            0.53134    0.04916  10.808 4.74e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

(Dispersion parameter for Gamma family taken to be 0.03262828)

    Null deviance: 4.31315  on 9  degrees of freedom
Residual deviance: 0.28385  on 8  degrees of freedom
AIC: 36.65

Number of Fisher Scoring iterations: 5
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