/ vs : operators in model specifications

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On Mon, Mar 3, 2008 at 4:21 PM, Martin Eklund
Hi all,
 I'm new to mixed models and lme4 and would appreciate any help on
 specifying models in lme4. Specifically I'm wondering about
 specifying nested variables. As I understand it lmer is capable of
 determining the nesting structure by itself (as long as the nesting
 is not implicit in the factors), so is there ever a need for
 specifying the nesting structure in the model specification when
 using lmer? Assuming A and B are random factors, B is nested in A,
 and Y is a response. What would be the difference between the
 following model specifications?

 (i)     lmer(Y ~ (1|A) + (1|B))
 (ii)    lmer(Y ~ (1|A) + (1|A:B))
 (iii)   lmer(Y ~ (1|A) + (1|A/B))
They should be the same provided that the levels of B are not
implicitly nested in the levels of A, which is what you indicated
would be the case.

The specification (1|A) + (1|A/B) is redundant as (1|A/B) expands to
(1|A) + (1|A:B) so (iii) could be written as

lmer(Y ~ 1|A/B)
 On a different note: using the mcmcsamp method, is it possible to
 change the choice of priors? I understand that this is a longshot and
 that it is most likely not possible, but I'm still asking just to be
 sure. Is there another way this can be done (i.e. sampling from the
 posterior distribution of a mixed model but with a general choice of
 prior)?
Unfortunately, no, there is no convenient way of specifying an
arbitrary prior for the mcmcsamp function.  To make it practical to
use that function routinely, the sampling scheme is hard-wired into
compiled code and based upon having an improper, locally uniform prior
on the fixed effects and improper, locally uniform priors on the
logarithms of the variance components.
 Thank you very much!

 Best regards,

 Martin.

 ========================================
 Martin Eklund
 PhD Student
 Department of Pharmaceutical Biosciences
 Uppsala University, Sweden
 Ph: +46-18-4714281
 ========================================

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