[R-sig-ME] lmer and truncated gaussian distributions

[Ben Bolker]

Dan McCloy <drmccloy at ...> writes:

> 
> Hello folks,
> Is it ok to use lmer() when the distribution of the response data resembles
> a truncated gaussian?  I have data where the response variable is
> constrained in [0,15] but has a mean of 12.63 and a S.D. of 2.25, based on
> 130 observations.  Graphs of dnorm() look symmetrical near the mean and
> log-transformation doesn't help; thus I think the data is best treated as
> truncated rather than skewed.


  (1) is your marginal distribution truncated normal or is it the
distribution of residuals that is truncated normal?  The latter is what
matters more ...

  (2) as a very vague general point, mild non-normality doesn't matter
as much as people seem to think it does.  It's very hard to say
whether "it's OK" in a particular case -- it depends how much accuracy
you need, how hard you are willing to work on alternatives, etc. etc.
(either JAGS/WinBUGS or AD Model Builder could handle this case, I
think).  The only way I can think of to know for sure would be to run
simulations of similar cases to see how much it matters, and decide
whether the size of the attendant error (bias, change in type I error
away from nominal, etc.)  is acceptable in your application.  Or you
may be able to bootstrap (but you have to be careful to preserve
the dependence structure, e.g. bootstrapping by groups (and
maybe individuals within groups rather than by individuals).