R help - Oct 2010 - Confidence interval for response variable in mixed effects models

HI,

I am using lmer() for a simple mixed effects model. The model is of the form
logit(y)~ x + (1|z), where x is an indicator variable and z a multi-level
factor.

I would like an estimate of the response variable (either y or logit y) with
an associated confidence interval for a given value of x.

There does not appear to be a predict function written for lmer().

The output for the fixed effects gives a standard error for the intercept,
the coefficient of x and the correlation. For n observations, I transform
the std errors to variances, and with the correlation, I think I can use the
formula Var(intercept + x) = Var(intercept) + Var(x) + 2Cov(x,intercept) to
get the variance of the fixed effects component of the response variable.

However, I would like to include the random effects component of the
variance, so I may derive a standard error and confidence interval for the
variance.

Does anyone know how to do this? Is there a ready made function like
predict() or does anyone know how to incorporate the variance of random
effects term to derive the std error of the response variable?

Regards,

Brian

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Brian Willis <brian.willis <at> manchester.ac.uk> writes:
> I am using lmer() for a simple mixed effects model. The model is of the
form
> logit(y)~ x + (1|z), where x is an indicator variable and z a multi-level
> factor.
> 
> I would like an estimate of the response variable (either y or logit y)
with
> an associated confidence interval for a given value of x.
[snippage: sorry to remove context, but I am posting via gmane, which
will complain if I have too much quoted context ...]
> Does anyone know how to do this? Is there a ready made function like
> predict() or does anyone know how to incorporate the variance of random
> effects term to derive the std error of the response variable?
  You should search the r-sig-mixed-models archive for answers, and
post there if you don't find what you need.  The problem is that it
can actually be a bit tricky to define these things properly for mixed
models, decide which random effects to include (or not) in the prediction
of the mean and include (or not) in the definition of the variance.
So far there has not been a confluence of people who want this,
people who know enough to construct a nice general solution, and
people who have time to do it ...

  Ben Bolker

On Oct 30, 2010, at 11:33 AM, Brian Willis wrote:
> HI,
>
> I am using lmer() for a simple mixed effects model. The model is of  
> the form
> logit(y)~ x + (1|z), where x is an indicator variable and z a multi- 
> level
> factor.
>
> I would like an estimate of the response variable (either y or logit  
> y)
There is a fitted method for objects of class "mer".

?"mer-class"
> .... with an associated confidence interval for a given value of x.
That is the sticking point as I understand it. See
below.
>
> There does not appear to be a predict function written for lmer().
>
> The output for the fixed effects gives a standard error for the  
> intercept,
> the coefficient of x and the correlation. For n observations, I  
> transform
> the std errors to variances, and with the correlation, I think I can  
> use the
> formula Var(intercept + x) = Var(intercept) + Var(x) +  
> 2Cov(x,intercept) to
> get the variance of the fixed effects component of the response  
> variable.
>
> However, I would like to include the random effects component of the
> variance, so I may derive a standard error and confidence interval  
> for the
> variance.
>
> Does anyone know how to do this? Is there a ready made function like
> predict() or does anyone know how to incorporate the variance of  
> random
> effects term to derive the std error of the response variable?
I see Ben Bolker has offered a suggestion that you search the mixed  
models list.

An earlier question on this topic elicited this citation (from Bolker):

http://glmm.wikidot.com/faq

One of the available choices in Baron's search page is R-sig-mixed- 
models and here are a few links to threads (by people who know more  
than me) that may offer at least informed commentary and options if  
not a general solution (from  both R-help and the SIG-ME archives):

http://search.r-project.org/cgi-bin/namazu.cgi?query=+confidence+intervals+lmer&max=100&result=normal&sort=score&idxname=functions&idxname=Rhelp08&idxname=Rhelp10&idxname=R-sig-mixed-models&idxname=Rhelp02

http://finzi.psych.upenn.edu/Rhelp10/2008-May/161516.html

http://rwiki.sciviews.org/doku.php?id=guides:lmer-tests

http://finzi.psych.upenn.edu/R/Rhelp02/archive/76742.html

http://finzi.psych.upenn.edu/R/Rhelp02/archive/81237.html

http://finzi.psych.upenn.edu/R/Rhelp02/archive/82567.html

-- 

David Winsemius, MD
West Hartford, CT