[ADMB Users] NLMM Model Selection

[Chris Gast]

Conditional on the values of the main effects. I'm working from a reference
provided by Dr. Bolker:

Greven, Sonja, and Thomas Kneib. 2010. On the Behaviour of Marginal
and Conditional
Akaike Information Criteria in Linear Mixed
Models. Biometrika 97, no. 4: 773-789.
http://www.bepress.com/jhubiostat/paper202/.

where the marginal likelihood (for a LMM, not a GLMM or other nonlinear
mixed model) is as discussed above, y~N(XB,V) (REs have been integrated
over) and the conditional likelihood (at its optimum) is evaluated at the
MLEs and EB estimates of REs, y | b ~ B*XB + Zb, I*sigma^2) where the b's
are the REs.

So ADMB works with the marginal likelihood, and the optimum value is
provided in the .par file.  However, it would be nice (at least at this, the
exploratory model-selection phase of my work) to also have the conditional
likelihood value, which would be obtained (I believe) by plugging the RE
estimates and MLEs back into the likelihood function and evaluating. This
isn't done automatically by ADMB, but (I think) could be done by changing
the .par file to a .pin file, and re-evaluating the model and outputting the
first objective function value.  I haven't tested this idea yet, though.
 I'll probably play with it a bit with a GLMM for which I can compare AIC
values with other software to try and understand what precisely each is
doing.


Chris



-----------------------------
Chris Gast
cmgast at gmail.com


On Tue, Feb 22, 2011 at 9:30 AM, Mark Maunder <mmaunder at iattc.org> wrote:

> Conditional on what?
>
>
>
> Mark Maunder
>
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> -----Original Message-----
> From: users-bounces at admb-project.org [mailto:
> users-bounces at admb-project.org] On Behalf Of H. Skaug
> Sent: Tuesday, February 22, 2011 8:19 AM
> To: Chris Gast
> Cc: users at admb-project.org
> Subject: Re: [ADMB Users] NLMM Model Selection
>
> On Tue, Feb 22, 2011 at 5:10 PM, Chris Gast <cmgast at gmail.com> wrote:
> > I'm sorry, I must be getting confused.  My message from yesterday
> (question
> > 1) asked if the objective function value in the .par file was the
> > post-integration marginal likelihood, to which you responded in the
> > negative, but now it seems as if you're saying what I had originally
> > postulated is true. Maybe it's just a terminology difference.  It is my
> > understanding that the .par file contains the optimum loglikelihood value
> > obtained, where the loglikelihood value is marginalized over the random
> > effects.  Perhaps there is some miscommunication?  I think we're talking
> > about the same thing.
>
> Yes, we are. I misunderstood your original question.
>
> > Since the marginal likelihood is available in the .par file, is there a
> way
> > to output the conditional likelihood following optimization?
>
> No, not any direct way that I am aware of. It is possible that this
> is what you get before the random effects kick in (assuming those
> active in phase 2 or later).
>
> hans
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