[R-sig-ME] nAGQ > 1 in lme4::glmer gives unexpected likelihood
Ben Bolker
bbo|ker @end|ng |rom gm@||@com
Fri Apr 24 16:59:27 CEST 2020
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
>>>
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>>>
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>>>
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>>
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