[R] glm with variance = mu+theta*mu^2?

Spencer Graves spencer.graves at pdf.com
Thu Jun 2 20:19:09 CEST 2005


	  How might you fit a generalized linear model (glm) with variance = 
mu+theta*mu^2 (where mu = mean of the exponential family random variable 
and theta is a parameter to be estimated)?

	  This appears in Table 2.7 of Fahrmeir and Tutz (2001) Multivariate 
Statisticial Modeling Based on Generalized Linear Models, 2nd ed. 
(Springer, p. 60), where they compare "log-linear model fits to cellular 
differentiation data based on quasi-likelihoods" between variance = 
phi*mu (quasi-Poisson), variance = phi*mu^2 (quasi-exponential), and 
variance = mu+theta*mu^2.  The "quasi" function accepted for the family 
argument in "glm" generates functions "variance", "validmu", and 
"dev.resids".  I can probably write functions  to mimic the "quasi" 
function.  However, I have two questions in regard to this:

	  (1) I don't know what to use for "dev.resids".  This may not matter 
for fitting.  I can try a couple of different things to see if it matters.

	  (2) Might someone else suggest something different, e.g., using 
something like optim to solve an appropriate quasi-score function?

	  Thanks,
	  spencer graves




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