Help concerning GLMM estimation needed
This is going to be a bit of a challenge. glmer really depends on extensions of the machinery used in GLM (see e.g. McCullagh and Nelder or Barnett and Dobson or ...) *If* the distribution is in the exponential family, then you should be able to define a new family argument for it following the existing ones (binomial, Poisson, Gamma, etc.), which defines the mean-variance relationship. However, many extensions of the exponential family (e.g. negative binomial with an unspecified shape parameter) won't work without additional machinery. (You could do what glmer.nb does, wrapping an internal loop that estimates an exponential family model with a fixed parameter inside an outer loop ...) The machinery of Laplace approximation is described e.g. in Madsen, Henrik, and Poul Thyregod. Introduction to General and Generalized Linear Models. CRC Press, 2011. For mixed models using arbitrary conditional distributions, a better start might be the TMB or glmmTMB projects (see kaskr/adcomp and glmmTMB/glmmTMB on Github). Or you could look into generalized estimating equation machinery, which only needs to know the mean-variance relationship.
On 16-07-03 12:14 PM, Isaac Adeniyi wrote:
Dear all, Good day all. I have used lme4 quite a lot and i must say that it is a wonderful work. I would like to use glmer with other distributions like the generalized poisson and com-poisson distribution. I am having hard time understanding how to approximate the logliklihood and expressing the mathematics involved. I would love you to point me in a direction that will be helpful. Materials such as links to websites, papers and textbooks will be helpful. Also,can you give some hints on how I can modify the glmer codes to make it work for these distributions. Thanks a lot for the help.
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