I hadn't thought this would be a difficult question, but perhaps I was wrong. I'll try and rephrase in hopes of inspiring some more interest.<br clear="all"><br><div>1) Is it correct to say that the objective function value returned in the .par value of a RE model is the approximation to the marginal likelihood, post-integration?</div>
<div><br></div><div>2a) Is it correct to obtain the conditional likelihood value by re-evaluating the likelihood function at the MLEs (for fixed parameters) and empirical Bayes estimates of REs?</div><div><br></div><div>2b) If 2a is true, can this value be obtained in a single ADMB model-fit, or do I need to first fit the model, then re-run the model using the optimum values from the previous run and output an initial likelihood value to get the conditional likelihood?</div>
<div><br></div><div>3) Or am I way off here?</div><div><br></div><div>I used to output the objective function value to the report file, but I noticed that it did not match the value from the .par file (the former was not the minimum).</div>
<div><br></div><div><br></div><div><br></div><div>Thanks again,</div><div><br></div><div>Chris Gast</div><div><br></div><div><br></div><div><br></div><div><br></div><div>-----------------------------<br>Chris Gast<br><a href="mailto:cmgast@gmail.com" target="_blank">cmgast@gmail.com</a><br>
<br><br><div class="gmail_quote">On Wed, Feb 9, 2011 at 10:49 AM, Chris Gast <span dir="ltr"><<a href="mailto:cmgast@gmail.com" target="_blank">cmgast@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
So, ADMB reports the (optimal) marginal loglikelihood approximation in<br>
the .par file (correct?).<br>
<br>
In order to obtain the (maximum) conditional loglikelihood value, one<br>
would re-evaluate the likelihood function at the MLEs along with the<br>
empirical Bayes estimates of RE terms. Is that correct?<br>
<br>
If the latter statement is correct, could this be obtained by<br>
outputting the final objective function value (following SE<br>
estimation) in the report file? Or do I need to re-evaluate the<br>
function after fitting the model?<br>
<br>
<br>
<br>
Thanks again,<br>
<font color="#888888"><br>
Chris Gast<br>
</font><div><br>
<br>
<br>
-----------------------------<br>
Chris Gast<br>
<a href="mailto:cmgast@gmail.com" target="_blank">cmgast@gmail.com</a><br>
<br>
<br>
<br>
</div><div><div></div><div>On Sun, Feb 6, 2011 at 11:54 AM, Ben Bolker <<a href="mailto:bbolker@gmail.com" target="_blank">bbolker@gmail.com</a>> wrote:<br>
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> On 11-02-06 02:47 PM, dave fournier wrote:<br>
>> Something that has always bothered me about this random effects stuff<br>
>> is that if I fit a model with a neg bin dist it is just a parametric<br>
>> model with one more parameter than a Poisson with a Poisson at the<br>
>> end. I can do standard LR tests and random effects never come up. But<br>
>> that is just because one can do the integration analytically so that<br>
>> the RE nature or interpretation never comes up. How can that be? Why<br>
>> are other RE models different?<br>
><br>
> It really depends what you want to do. Dealing with random effects by<br>
> integrating them out (when that is possible) is called a marginal model,<br>
> and there are plenty of methods that take this approach (e.g.<br>
> generalized estimating equations). Sometimes you're actually interested<br>
> in estimates of the 'random effects', which disappear in the marginal<br>
> approach. In some cases the marginal approach doesn't give you separate<br>
> estimates for different processes (e.g. variances from different random<br>
> effects components) that you would ideally like to distinguish.<br>
> Sometimes you wouldn't mind a marginal approach but it's just too hard.<br>
> There are also differences in interpretation -- for example, estimated<br>
> slopes from marginal models (which give the overall expected,<br>
> unconditional slope) are shallower than those from 'non-marginal'<br>
> (conditional? don't know the right term) models, where one is estimating<br>
> the slope conditional on individuals within a group.<br>
><br>
> Alan Agresti's book on Categorical Data Analysis has a very nice<br>
> discussion of this stuff, I think.<br>
><br>
> Ben Bolker<br>
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