[R-sig-ME] nAGQ > 1 in lme4::glmer gives unexpected likelihood
Vaida, Florin
|v@|d@ @end|ng |rom he@|th@uc@d@edu
Sat Apr 25 16:10:14 CEST 2020
No spoiler, I agree.
When comparing across multiple models, each with their own "off by" constant, having the exact log-likelihood is important.
> On Apr 25, 2020, at 5:33 AM, Martin Maechler <maechler using stat.math.ethz.ch> wrote:
>
>
>> I think they're both 'correct' in the sense of being proportional to
>> the likelihood but use different baselines, thus incommensurate (see the
>> note pointed out below).
>
> Well, I'm sorry to be a spoiler here, but I think we should
> acknowledge that (log) likelihood is uniquely well defined
> function.
> I remember how we've fought with the many definitions of
> deviance and have (in our still unfinished glmm-paper -- hint!!)
> very nicely tried to define the many versions
> (conditional/unconditional and more), but I find it too sloppy
> to claim that likelihoods are only defined up to a constant
> factor -- even though of course it doesn't matter of ML (and
> REML) if the objective function is "off by constant factor".
>
> Martin
>
>> On 4/24/20 5:05 PM, Vaida, Florin wrote:
>>> One can figure out which likelihood version is correct (Laplace or nAGQ>1) by doing a simulation with random effects variance -> 0.
>>> I'll do that if I find time.
>>> Florin
>>>
>>>> On Apr 24, 2020, at 7:59 AM, Ben Bolker <bbolker using gmail.com> wrote:
>>>>
>>>>
>>>> I found the note I was looking for. In ?deviance.glmerMod it says:
>>>>
>>>> If adaptive Gauss-Hermite quadrature is used, then
>>>> ‘logLik(object)’ is currently only proportional to the
>>>> absolute-unconditional log-likelihood.
>>>>
>>>> (see the discussion on this page for more context); see also https://github.com/lme4/lme4/blob/master/misc/logLikGLMM/logLikGLMM.R
>>>>
>>>>
>>>> On 4/24/20 10:24 AM, Douglas Bates wrote:
>>>>> Having said that, I do see that the fits in the MixedModels package for
>>>>> Julia produce similar values of the deviance with the Laplace approximation
>>>>> and nAGQ = 7
>>>>>
>>>>> julia> m1 = fit(MixedModel, @formula(y ~ 1 + (1|group)), dd, Poisson())
>>>>> Generalized Linear Mixed Model fit by maximum likelihood (nAGQ = 1)
>>>>> y ~ 1 + (1 | group)
>>>>> Distribution: Poisson{Float64}
>>>>> Link: LogLink()
>>>>>
>>>>> Deviance: 193.5587
>>>>>
>>>>> Variance components:
>>>>> Column Variance Std.Dev.
>>>>> group (Intercept) 3.9577026 1.9893975
>>>>>
>>>>> Number of obs: 100; levels of grouping factors: 10
>>>>>
>>>>> Fixed-effects parameters:
>>>>> ──────────────────────────────────────────────────
>>>>> Estimate Std.Error z value P(>|z|)
>>>>> ──────────────────────────────────────────────────
>>>>> (Intercept) 2.65175 0.632317 4.19 <1e-4
>>>>> ──────────────────────────────────────────────────
>>>>>
>>>>> julia> m1 = fit(MixedModel, @formula(y ~ 1 + (1|group)), dd, Poisson(),
>>>>> nAGQ=7)
>>>>> Generalized Linear Mixed Model fit by maximum likelihood (nAGQ = 7)
>>>>> y ~ 1 + (1 | group)
>>>>> Distribution: Poisson{Float64}
>>>>> Link: LogLink()
>>>>>
>>>>> Deviance: 193.5104
>>>>>
>>>>> Variance components:
>>>>> Column Variance Std.Dev.
>>>>> group (Intercept) 3.9577026 1.9893975
>>>>>
>>>>> Number of obs: 100; levels of grouping factors: 10
>>>>>
>>>>> Fixed-effects parameters:
>>>>> ──────────────────────────────────────────────────
>>>>> Estimate Std.Error z value P(>|z|)
>>>>> ──────────────────────────────────────────────────
>>>>> (Intercept) 2.65175 0.632317 4.19 <1e-4
>>>>> ──────────────────────────────────────────────────
>>>>>
>>>>> As the person who wrote the first version of the nAGQ code in R I would not
>>>>> be surprised if there was a constant dropped somewhere. It is difficult
>>>>> code.
>>>>>
>>>>> And the results here in the Julia package make me uncomfortable because the
>>>>> values of the parameter estimates are identical in the two fits. I would
>>>>> expect them to be close but not identical.
>>>>>
>>>>> Isn't it good to know that there is still room for research in this area?
>>>>> :-)
>>>>>
>>>>> On Fri, Apr 24, 2020 at 9:05 AM Douglas Bates <bates using stat.wisc.edu> wrote:
>>>>>
>>>>>> There's a lot of variability in your lambdas
>>>>>>
>>>>>>> exp(3 + random_effects)
>>>>>> [1] 91.5919358 6.9678749 4.1841478 78.0771666 890.6931394
>>>>>> 20.8558107
>>>>>> [7] 3.0037864 0.3049416 2.1675995 40.6209684
>>>>>>
>>>>>> Do you really expect that some groups will have a mean count of nearly 900
>>>>>> whereas others will have a mean count less than 1?
>>>>>>
>>>>>>
>>>>>> On Wed, Apr 22, 2020 at 5:58 PM Ben Goldstein <ben.goldstein using berkeley.edu>
>>>>>> wrote:
>>>>>>
>>>>>>> Hi all,
>>>>>>>
>>>>>>> I'm using lme4::glmer to estimate Poisson mixed models in a very simple
>>>>>>> context (single random effect). I'm interested in the model
>>>>>> likelihood/AIC
>>>>>>> across many simulated datasets.
>>>>>>>
>>>>>>> To investigate whether the Laplace approximation was appropriate for my
>>>>>>> data context, I explored using the argument nAGQ to improve the accuracy
>>>>>> of
>>>>>>> the likelihood estimation. When I changed nAGQ to a value > 1, I saw an
>>>>>>> unexpectedly huge change in the likelihood; log-likelihoods tended to be
>>>>>>> off by ~200. Other statistics packages (e.g. GLMMadaptive) yield
>>>>>> estimates
>>>>>>> that agree with lme4's Laplace approximation, as did a manual likelihood
>>>>>>> estimate, and not with the nAGQ > 2 estimate.
>>>>>>>
>>>>>>> The following code reproduces the problem I'm encountering.
>>>>>>>
>>>>>>> *# r-sig-mixed-models GLMM question*
>>>>>>> library(lme4)
>>>>>>> set.seed(51)
>>>>>>>
>>>>>>> *# Simulate some random effect-driven Poisson data*
>>>>>>> random_effects <- rnorm(10, 0, 2)
>>>>>>> group <- rep(1:10, 10)
>>>>>>> simulated_data <- data.frame(y = rpois(n = 100, lambda = exp(3 +
>>>>>>> random_effects[group])),
>>>>>>> group = group)
>>>>>>>
>>>>>>> *# Fit models with Laplace (nAGQ = 1) and nAGQ = 11*
>>>>>>> fit_Laplace <- glmer(y ~ (1|group), data = simulated_data, family =
>>>>>>> poisson())
>>>>>>> fit_AGQ <- glmer(y ~ (1|group), data = simulated_data, family =
>>>>>> poisson(),
>>>>>>> nAGQ = 11)
>>>>>>>
>>>>>>> logLik(fit_Laplace)
>>>>>>> logLik(fit_AGQ)
>>>>>>> logLik(fit_Laplace) - logLik(fit_AGQ) *# Huge difference!*
>>>>>>>
>>>>>>> When I execute the above code, I see a difference in likelihood of
>>>>>>> -218.8894. I've tested across many simulations and on 2 different
>>>>>> machines
>>>>>>> (Mac and Linux). My version of lme4 is up to date.
>>>>>>>
>>>>>>> Has anyone run into this issue before? Am I using the glmer function
>>>>>> wrong,
>>>>>>> or is it possible there's something going on under the hood?
>>>>>>>
>>>>>>> Thanks,
>>>>>>> Ben
>>>>>>>
>>>>>>> [[alternative HTML version deleted]]
>>>>>>>
>>>>>>> _______________________________________________
>>>>>>> R-sig-mixed-models using r-project.org mailing list
>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>>>>>
>>>>>> [[alternative HTML version deleted]]
>>>>>>
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