[R-sig-ME] [R] False convergence of a glmer model

[Doran, Harold]

I agree with Doug. But, agreeing with Doug is like agreeing that the Pope is Catholic. Quick small thing. I don't like using the term "convergence" with MCMC methods. I don't think MCMC converges in the same sense as ML methods do; they reach a stationary distribution.

Also, I only partly recall the OP on this, but from what I recall the differences in the log-likelihood and parameter estimates in the final iterations were nominal at best. I think many software programs would declare convergence given that differences in the log-likelihood are no longer larger than some predetermined criterion (e.g., 1e-3). So, reaching a stopping point w.r.t. an algorithm is (or may be) different than reaching the MLE of an objective function.

-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Douglas Bates
Sent: Wednesday, February 17, 2010 9:09 AM
To: Shige Song
Cc: R Mixed Models
Subject: Re: [R-sig-ME] [R] False convergence of a glmer model

On Tue, Feb 16, 2010 at 6:41 PM, Shige Song <shigesong at gmail.com> wrote:
> Hi Ben,
>
> As I stated earlier, Stata's xtlogit and xtmelogit did reach
> convergence and gave reasonable results, so did MCMCglmm; so this
> seems to be a unique problem with R's ML optimizer.

Bear in mind that declaring convergence and converging are different
things.  One way to check on the estimates from the Stata procedures
is to use them as starting estimates in glmer and see whether glmer
proceeds to reduce the deviance from those estimates.

For generalized linear mixed models and even more for nonlinear mixed
models I have for several years been advocating that rather than
comparing parameter estimates from different procedures on which
method provided convergence, etc., we should agree on a method for
evaluating the log-likelihood or deviance from a model/data
set/parameter value combination.  The method could be quite
computationally intensive and unsuitable for use in optimizing the
parameter estimates but suitable as a "gold standard" deviance
evaluation.  Then when software developers want to play the "my
estimates are better than your estimates" game, the standard for
comparing the estimates from different software systems could be to
evaluate the log-likelihood or deviance at those estimates and see
which set provides a lower value of the deviance.

It is quite possible that there are reasonable parameter estimates
corresponding to very low predicted probabilities but that the maximum
likelihood estimates don't exist because they would correspond to
negative infinity for some of the parameters.

> Shige
>
> On Tue, Feb 16, 2010 at 7:00 PM, Ben Bolker <bolker at ufl.edu> wrote:
>> Douglas Bates wrote:
>>> On Tue, Feb 16, 2010 at 2:23 PM, Shige Song <shigesong at gmail.com> wrote:
>>>> Dear Doug,
>>>>
>>>> Your argument makes a lot sense: after all, infant mortality is a rare
>>>> event! I have two questions:
>>>>
>>>> 1) Is there a way to change the convergence criterion in a glmer model
>>>> (to make it more tolerant)?
>>>
>>> I'm not sure that is a good idea.  If the linear predictor produces
>>> probabilities that are so small that the deviance is insensitive to
>>> the parameter values, what would it mean to quote estimates of those
>>> parameters?
>>>
>>>> 2) Do you see a better approach than mixed logistic regression model
>>>> in estimating infant morality, given the fact that infant mortality is
>>>> a rare event?
>>>
>>> I don't know of other approaches myself.  Others on the list (Ben?)
>>> may have suggestions.
>>
>>  I would think that a Bayesian approach would help here (by ruling out
>> probabilities of exactly zero): however, generally harder to implement
>> -- don't know if MCMCglmm offers possibilities for priors on fixed
>> effect parameters -- WinBUGS (possibly via glmmBUGS), ADMB may be
>> solutions.  (Also maybe harder to convince reviewers of.)
>>
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>
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