I am using generalized mixed models using glmer function of the “lme4” package. Glmer() always uses Maximum Likelihood (ML) rather than REstricted Maximum Likelihood (REML) (http://glmm.wikidot.com/faq#reml-glmm). How can I fit a GLMM with REML to optimize the random effects structure? does it make sense?
The recommendation for fitting linear mixed effects models using lmer is to first determine the random effects structure using REML (with the full fixed effect structure), then to conduct LR tests (or model selection) for fixed effects structure using ML, and finally to make inferences from the final model selected fit with REML. However, when fitting a GLMM in lem4 there is no longer any REML option. I am confused about why this is and would really appreciate knowing some more of the theory behind it.
The optimizer for glmer is found with
glmerControl()$optimizer
Ben Bolker (on the R-sig-ME list, and it is worth reading the archive of their discussions) gives more details. For linear model they discuss this in their paper, http://arxiv.org/abs/1406.5823, and he said they are working on one for the glm case.
I would also recommend the appendices of Chapter 4 of Goldstein's "Multilevel statistics models, 3rd ed" (it may be a different chapter in other editions.
If you are not already on the listservs, try https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models if you are interested in the programming details and http://www.nursing.manchester.ac.uk/learning/staff/mcampbell/multilevel.html for general multilevel issues.
Also relevant, here is what it says on http://glmm.wikidot.com/faq (see another FAQ here for comparison of estimation methods):
REML for GLMMs?
While restricted maximum likelihood (REML) procedures (Wikipedia definition) are well established for linear mixed models, it is less clear how one should define and compute the equivalent criteria (integrating out the effects of fixed parameters) for GLMMs. Millar 2011 [22] and Berger et al 1999 [7] are possible starting points in the peer-reviewed literature, and there are mailing-list discussions of these issues here and here.
Note that in the current version of lme4, glmer silently ignores the REML specification (!)
The recommandation seems strange to me: why alternate between REML and ML, and what is the guarantee that such a random-then-fixed approach will be better than the other way round?
Other recommandations say that you should use the random effects structure as close as possible to your experimental design, with the limitation of the sample size/number of parameters; it is easiest to transpose to GLMM...
Some background
FIML or IGLS (MLwiN) estimates the variances as if the averages (fixed part) are known not estimates and vice versa
REML or RIGLS estimates the variances on the basis that the fixed part averages are estimates - this is like dividing by n-1 in a simple variance estimation (1 degree of freedom has been consumed in estimating the mean), but still estimates the means as if the variances are known
MCMC estimates have full error propagation and all estimates are treated as having uncertainty
None of this will make much differences if the variances are large and are based on a large number of groups.
Morrell (1998)) Likelihood ratio testing of variance components in the mixed-effects models using restricted maximum likelihood. Biometrics, 54(4),1560-1568
found the following in a simulation study
• In comparing models with different random effects, REML Type I error rates tended to be truer than FIML rates
.
• REML was especially superior for small group sizes (20 or below) and for more random effects (three/four vs. fewer).
• REML error rates decreased the more FIML error rates increased.
While REML is more realistic and is recommended, especially when the number of grouping is small (it may additionally help convergence), we need to be careful when using likelihood tests.
Strictly two models with nested fixed effects should be compared using likelihood-based methods if they are fit using FIML (not REML) . In contrast, models with the same fixed effect structure but different random effects should be compared by fitting with REML.
This suggests a twofold strategy.
1 Use FIML-based LRT model comparisons to decide which fixed effects to include in the model.
2 Switch to REML to decide which random effects to include and to obtain final estimates of random effects.
As I say - it should only make a difference in problematic cases and then I would use MCMC for a sensitivity analysis and compare models with DIC ( or some variant of that)
One idea is to have a focussed random effect information criterion rather like an AIC or BIC. This idea is akin to treating the other parameters in the model as nuisance. The approach has been developed for PH survival models with frailty. In the reference below the approach is developed using h-likelihood methods. So there is a strong connection with REML-type methods. As with other information It is not necessary that the frailty structures are nested.
A key reference is
Ha ID, Lee Y and MacKenzie G (2007). Model selection for multi-component frailty models. Statistics in Medicine, 26, 4790-4807.
Hi all!
Thanks for sharing. You have all made interesting and enriching contributions
Hi Francismeire
I am still working on it. I am not in a position to give you a clear answer.
It is important to be in mind that glmer ( ) do not have the REML specification. At the moment, as Emmanuel Curis suggested I just using the random effects structure as close as possible to me experimental design. This means that I am not optimising random effects structure.
Best regards,
:D Don't worry Francismeire
there is hope, try in http://glmm.wikidot.com/faq#reml-glmm. There is nice information inside of this web
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