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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