[R-sig-ME] Logistisc regression (lmer) fitted by the Laplace approximation- references?

[Ken Beath]

On 23/07/2008, at 8:14 PM, R.S. Cotter wrote:

> Dear all,
>
> I have sucessfully run Logistic regression by using generalized linear
> mixed-effects model (lmer) fitted by the Laplace approximation (lme4
> package).
>
> Is there any limits that I should aware of by use of this model? I
> haven't found references for this model, could somone provide me with
> a reference from a article/book?
>
> My response is Yes or No and explanatory variables is categories
> (A,B,C and D), and random effect (ID, number of groups 7).
>

Accuracy of Laplace approximation is determined by size of clusters  
(larger is better) and variance of random effects (smaller is better).  
Unfortunately I don't know of a reference that describes when it does  
and doesn't work.

The only work I know is Pinheiro and Chao, Journal of Computational  
and Graphical Statistics vol 15 p58-81 which has some simulations for  
2-level models. My impression is that for random effect variances of 1  
or less and average cluster sizes of 6 or more then Laplace will work  
quite well for fixed effects but maybe not so well for estimates of  
the variance components, not that these are usually important. There  
may also be something on PQL in one of the papers by Rodriguez and  
Goldman, which as Laplace is better than PQL can be used as a guide.  
Generalized Latent Variable Modeling: Multilevel, Longitudinal, and  
Structural Equation Models by Skrondal and Rabe-Hesketh has an  
introduction to the integration methods.

Simulation could be used to show that the level of bias is small.

Ken