[R-sig-ME] nAGQ > 1 in lme4::glmer gives unexpected likelihood
Vaida, Florin
|v@|d@ @end|ng |rom he@|th@uc@d@edu
Fri Apr 24 23:05:11 CEST 2020
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]]
>>>>
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>>>>
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>>>
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