I am trying to model some count data (clutch size) which are underdispersed. I want to account for different fixed and random (intercept) effects. My initial model was by using a random effect Poisson distribution with glmer {lme4} function, like this:
fm1<- glmer(clutchSize ~ fixef1 + fixef2 + fixef3 + (1|ranef1) + (1|ranef2) + (1|ranef3), data = data, poisson).
I estimated the dispersion of fm1 by:
dispersion_glmer(fm1) # 0.51
This suggests there is some underdispersion. After reading Lynch et al. (2014) I have understood that it is quite typical for this kind of data. I have looked for a way of dealing with these data and found the spaMM package which implements a function, HLfit, which allows to use the Conway-Maxwell-Poisson distribution in a GLMM model like the one I ran with glmer. I am asked to set a 'nu' parameter as an argument of an argument of the HLfit function but I cannot understand what value should I put - how may I calculate it? In particular, it should be:
fm2<- HLfit(clutchSize ~ fixef1 + fixef2 + fixef3 + (1|ranef1) + (1|ranef2) + (1|ranef3), data = data, COMPoisson(nu))
In the help page of HLfit it is stated that if nu>1 it means underdispersion, nu<1 means overdispersion and nu=1 is equivalent to a Poisson. According to the spaMM.pdf:
I am afraid I am missing the point somewhere but I cannot see where: may someone please help me?