Stats 4590
                    GLM's, quasilikelihood and overdispersion


 We have looked at estimating the overdispersion parameter using the
residual deviance. Another approach is to use quasilikelihood. We will
not discuss the details of this, but it can be used with GLM's when we
are not able to specify the distribution we wish to use (binomial,
poisson, etc.). All it requires (informally) is to specify the mean and
variance of the response, and the relationship between the two. 
 
 With a response variable that appears to be binomial or poisson, we can
implement quasilikelihood using the glm() command, and changing the
"family" option to "family = quasibinomial" and "family = quasipoisson"
respectively.

 Note that this approach does not give the same estimate of the
overdispersion parameter as our previous method, but they are similar.



> ships.quasi <- glm(formula = damage ~ type + cons + op + ags,
+ family=quasipoisson, data=ships.dat)

> summary(ships.quasi)

Call:
glm(formula = damage ~ type + cons + op + ags, family = quasipoisson, 
    data = ships.dat)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.5484  -1.3867  -0.4307   0.5222   3.1152  

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.786e-01  4.587e-01   0.389 0.700447    
typeB        6.701e-01  3.595e-01   1.864 0.074653 .  
typeC       -1.192e+00  5.422e-01  -2.198 0.037863 *  
typeD       -8.294e-01  4.763e-01  -1.741 0.094420 .  
typeE       -1.493e-01  3.888e-01  -0.384 0.704284    
cons65       1.087e+00  2.967e-01   3.665 0.001224 ** 
cons70       1.500e+00  3.721e-01   4.031 0.000487 ***
cons75       8.545e-01  4.568e-01   1.871 0.073628 .  
op75         7.284e-01  2.246e-01   3.243 0.003461 ** 
ags          6.697e-05  1.411e-05   4.746 7.92e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

(Dispersion parameter for quasipoisson family taken to be 2.740679)

    Null deviance: 614.539  on 33  degrees of freedom
Residual deviance:  70.498  on 24  degrees of freedom
  (6 observations deleted due to missingness)
AIC: NA

Number of Fisher Scoring iterations: 5