[R-sig-ME] nAGQ > 1 in lme4::glmer gives unexpected likelihood

[Douglas Bates]

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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> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
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>
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