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

[Ben Bolker]

  It's entirely possible there's something going on under the hood.  
IIRC there's a document somewhere that talks about how deviances and 
log-likelihoods are defined, and this may(?) still differ between nAGQ=1 
and nAGQ>1 ?

On 4/22/20 6:58 PM, Ben Goldstein 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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