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

[D. Rizopoulos]

On a related topic, it is not clear to me whether glmer() updates the location of the quadrature points at each iteration when nAGQ > 1.



-----Original Message-----
From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> On Behalf Of Ben Bolker
Sent: Thursday, April 23, 2020 1:30 AM
To: r-sig-mixed-models using r-project.org
Subject: Re: [R-sig-ME] nAGQ > 1 in lme4::glmer gives unexpected likelihood

  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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