[R] Marginal Predicitions from nlme and lme4

[Thomas Lumley]

On Tue, 22 Aug 2006, Rick Bilonick wrote:

> On Wed, 2006-08-23 at 06:43 +1000, Andrew Robinson wrote:
>> Rick,
>>
>> if by marginal prediction, you mean the prediction without random
>> effects, then use the "level" argument.  See ?predict.lme or ?fitted.lme
>>
>> If not then I don't know :)
>>
>> Cheers
>>
>> Andrew
> Thanks. I'm familiar with level in predict and fitted for lme. These
> allow you to select the fixed effects and/or the random effects. The
> marginal prediction integrates out the random effects and is what a GEE
> marginal model produces. From what I've read, the marginal effects seem
> to be less desirable than the fixed effects from an lme or a generalized
> lme. But I would still like to compute them for comparison.
>

I don't agree that they are less useful, but they are not in general easy 
to obtain from a GLMM.  For any linear link model or a log link model that 
has only random intercepts the marginal and conditional effects are the 
same.  For the probit model there is a conversion formula, but for other 
models they typically require high-dimensional integration to compute.

It's easy just to fit a marginal glm if you want marginal coefficients and 
a mixed model if you want conditional coefficients.

 	-thomas