reparametrized Gamma distribution for 'family'

[Reza Hajipour]

Hello

I want to use a reparametrized gamma distribution and use it as "family" in inla, as follows:

if Gamma (a, b) then y ~ Gamma (g(a), g(a,b)),   g(a) is a function of 'a' and g(a, b) is a function of 'a' and 'b'. 

formula <- y ~ 1+ X + f(ID.zone, model="bym", graph=graph) + f(ID.year, model="rw2") 

model <- inla (formula, family= "Gamma", 

                 data=data,
                 offset = log(E),
                 control.predictor=list(compute=TRUE),
                 control.compute= list(dic=TRUE, waic = TRUE))

How can I change the parameters of Gamma distribution to g(a) and g(a, b)?

[Havard Rue]

Can you send me the full details ?

-- 

Håvard Rue 

hr...@r-inla.org

--
You received this message because you are subscribed to the Google Groups "R-inla discussion group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to r-inla-discussion...@googlegroups.com.
To view this discussion on the web, visit https://groups.google.com/d/msgid/r-inla-discussion-group/4d657a1e-75ba-4d2b-a133-6fb87f284c82n%40googlegroups.com.

[Reza Hajipour]

I want to use the modal gamma regression with varying precision as mentioned in the "Bourguignon M, Leão J, Gallardo DI. Parametric modal regression with varying precision. Biom J. 2020 Jan;62(1):202-220. doi: 10.1002/bimj.201900132. Epub 2019 Oct 29. PMID: 31660649." page 3.

if Gamma (a, b) then y ~ Gamma (a', b')

a' = 1+ (sqrt(Q(Q+4))+Q)/2

b' = (sqrt(Q(Q+4))+Q)/2m
where m = (a-1)/b and Q = (a-1)^2/a

[Reza Hajipour]

Dear Prof. Havard,

I am seeking your assistance regarding reparameterizations for the gamma distribution in INLA. Could you please guide me on how to perform these reparameterizations and whether they are sensible?

Thank you in advance for your help.

[Helpdesk (Haavard Rue)]

I guess they are sensible if its based on the paper you share earlier.

> https://groups.google.com/d/msgid/r-inla-discussion-group/9c830ecc-bfb1-4341-bdb5-768d6ee3056en%40googlegroups.com
> .

--
Håvard Rue
he...@r-inla.org