[R-sig-ME] modelling saturated random effects with glmm

[Ben Bolker]

Greg Snow wrote:
> This is a basic property of the distributions.
> 
> The normal distribution has 2 parameters, the mean and the variance
> which are independent of each other.  Therefore in any type of model
> based on the normal distribution you need at least 1 degree of
> freedom left over after estimating the mean in order to estimate the
> variance.
> 
> The poisson distribution only has 1 parameter because the variance is
> equal to the mean in the poisson, so you can use all the degrees of
> freedom estimating the mean, and that gives you the variance, you
> don't need additional information to estimate it.
> 
> All this of course is dependent on your assumptions about the
> distributions being reasonable (the routines do what you tell them
> too whether they make sense or not).  And any model that uses all or
> even the majority of the degrees of freedom is unlikely to be very
> precise or informative even if you do get an "answer".
> 

  Yes, but ... modeling overdispersion in this way can definitely be
reasonable.  Adding a random-effect level per individual (e.g. assuming
a lognormal-Poisson model, in the Poisson/log link case) is not using
all or even the majority of the degrees of freedom ... there's still
plenty of room left for systematic departures from both the
deterministic and stochastic components of the model ...