[R-sig-ME] Help concerning GLMM estimation needed

Ben Bolker bbolker at gmail.com
Mon Jul 4 04:03:05 CEST 2016

  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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