I want to fit a Tweedie GlM to a response variable but with a dispersion parameter (phi) set to 1 for all the records in my data. So all the parameters get estimated using Maximum Likelihood Estimator except for phi.
Thank you.
You can do this by using the map argument in glmmTMB.
Example setup:
library(glmmTMB)
library(tweedie)
nobs <- 2000; mu <- 4; phi <- 2; p <- 1.7
set.seed(101)
y <- rtweedie(nobs, mu=mu, phi=phi, power=p)
Fit the unconstrained model:
twm <- glmmTMB(y ~ 1, family=tweedie(), data = NULL)
sigma(twm) ## 2.0188, close to the true value of 2
(sigma() is the general accessor method for the dispersion parameter; its definition varies by family, see ?sigma.glmmTMB)
Constrained:
twm2 <- update(twm,
map = list(betad=factor(NA)),
start = list(betad = 0))
sigma(twm2) ## 1
Explanation:
map specifies sets of parameters to be held fixed to their starting values (if NA), or sets of parameters to be constrained to be equal to each other (i.e. sharing a factor level): see glmmTMB. In this case the dispersion parameter is a single value (it could have length > 1 if dispformula was specified), so we make it a factor of length 1 containing NA.start specifies starting values (which are the values that map uses for fixed parameters). The dispersion parameter is fitted on a log scale, so we set the starting value to 0 (exp(0) = 1). In this case we don't really need to specify the value, since the default is 0 anyway, but it's clearer this way.