[R-sig-ME] predict in lmer()?

[David Winsemius]

On Jul 31, 2011, at 1:34 PM, Douglas Bates wrote:

> On Sun, Jul 31, 2011 at 11:01 AM, David Winsemius
> <dwinsemius at comcast.net> wrote:
>>
>> On Jul 31, 2011, at 9:41 AM, Ewart Thomas wrote:
>>
>>> david, i'm now slogging thru the most informative thread!
>>>
>>> as dennis advised, one has to do the 'predict' part 'by hand' when
>>> using lmer.  this is done in the 2 lines:
>>> mm = model.matrix(terms(fm1),newdat)
>>> newdat$distance = mm %*% fixef(fm1)
>>> good luck - this thing is worth sticking with!
>>
>> The ongoing quest for prediction and confidence intervals is
>> chronicled in the mixed-effects Archive. The online discussion of
>> prediction intervals in lme4-derived models, i.e. objects of class
>> "mer" can be extracted with a Google search of the mixed-models
>> Archive at the "advanced search" page:
>>
>> http://www.google.com/search?q=lme4+OR+mer+%22prediction+intervals%22+site%3Ahttps%3A%2F%2Fstat.ethz.ch%2Fpipermail%2Fr-sig-mixed-models%2F&hl=en&num=50
>>
>> The other place to look is in Bates' drafts of the book he is writing
>> on lme4 methods. In chapter 1 of a 2010 draft he suggests plotting
>> prediction intervals (of the random effects)  thusly:
>>
>> dotplot(ranef(fm1ML,postVar=TRUE))
>>
>> And he continues using that method for the next few chapters (during
>> that year). I wonder if it makes sense to construct prediction
>> intervals without proper consideration of the fact that some of the
>> variability is assumed to arise from fixed effects. In his written
>> material it appears that Bates studiously avoids mixing random and
>> fixed effects in what he is calling "prediction intervals". There is
>> some discussion of this problem in his chapter 5 of the March 2011
>> material but the matrix math is too complex for me to follow and he
>> has no accompanying R code to go along with it.
>
> You're mixing two concepts.

It did seem that you consistently referred to estimates of  
"conditional random effects" and I drew the inference that the  
estimates were particular to the fixed aspects of the sampling or  
design.

>  The intervals to which you refer are not
> prediction intervals on future responses. They are intervals that
> contain the central 1-\alpha area under the (marginal) density curve
> for each component in the conditional distribution of the
> random-effects given the observed data and evaluated at the parameter
> estimates.  So the random effects are an unobserved vector-valued
> random vector.  The model is defined by the unconditional distribution
> of the random effects and the conditional distribution of the
> responses, given a value of the random effects.  From these two we can
> derive the joint distribution of the random effects and the responses.
> When we condition on the observed value of the responses we get a
> conditional density of the random effects, given the observed data.
> For a linear mixed model this is a multivariate Gaussian distribution.

That is what I understood and I apologize if my language was not  
precise. Just to test my understanding I am wondering if this addition  
to those two sentence preserves your meaning:

"When we condition on the observed value of the responses we get a
conditional density of the random effects, given the observed data  
[and the particular sampling choices for the fixed effects units of  
analysis].
For a linear mixed model this is a multivariate Gaussian distribution."

And for this sentence:

"If we look at the marginal distribution of a particular component of
the random effects vector [limited to one or more fixed factors], we  
get a univariate Gaussian with a mean and standard deviation that we  
can evaluate."

I see your apology below and assume it must be directed at others  
since it certainly doesn't apply to my case, and counter-offer my  
apology for asking possibly uneducated questions, since I am surely  
one of the least experienced in this statistical sub-domain.

-- 
David Winsemius


>  The 95% prediction interval
> on a particular component of the random effects vector, given the
> observed response, is this mean plus/minus 1.96 times the standard
> deviation.
>
> I know that's a mouthful and may seem pedantic but being a pedant is
> the only way that I have been able to reach an understanding of these
> models.  I need to trace everything back to the probability model and
> keep clear in my mind what are parameters, what are random variables
> and what are observed values.
>
> I apologize to the readers of the list for continually changing the
> descriptions and the underlying software.  I know this is an
> inconvenience to many, such as Harald Baayen whom I will see next
> week.  My understanding of the models and the available computational
> methods has evolved considerably and I hope the end result is worth
> the annoyance of the many changes that have gone on.  I'm just
> relieved that I work for an Open Source project and don't need to
> produce software under a deadline :-)
>
>
>>> On Jul 31, 2011, at 6:35 AM, David Winsemius wrote:
>>>
>>>>
>>>> On Jul 31, 2011, at 8:47 AM, Dennis Murphy wrote:
>>>>
>>>>> Hi:
>>>>>
>>>>> See http://glmm.wikidot.com/faq
>>>>>
>>>>> Go about 2/3 of the way down until you see the section  
>>>>> 'Predictions
>>>>> and/or confidence (or prediction) intervals on predictions'.
>>>>
>>>> Aren't objects created by lmer of class "mer"? Attempting to follow
>>>> your advice with the first example provided in ?lmer meets with
>>>> frustration:
>>>>
>>>> require(lme4)
>>>> (fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy))
>>>> newdat0 <- expand.grid(Reaction=c(200,300,400), Days=c(0,4,8),
>>>> Subject=c(5,10,15) )
>>>> newdat0$pred <- predict(fm1, newdat0, level = 0)
>>>>
>>>> Error in UseMethod("predict") :
>>>>  no applicable method for 'predict' applied to an object of class
>>>> "mer"
>>>>
>>>> I'm not even a journeyman use of ME methods, so this is just a
>>>> question. Do you have a fix? (There are predict methods listed in
>>>> nlme but none in the Index of lme4.
>>>>
>>>> --
>>>> David.
>>>>
>>>>
>>>>
>>>> David Winsemius, MD
>>>> West Hartford, CT
>>>>
>>>
>>
>> David Winsemius, MD
>> West Hartford, CT
>>
>>
>>        [[alternative HTML version deleted]]
>>
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>>

David Winsemius, MD
West Hartford, CT