[R] lmer fixed effects, SE, t . . . and p

[John Sorkin]

 Bert,
I appreciate you comments, and I have read Doug Bates writing about p values in mixed effects regression. It is precisely because I read Doug's material that I asked "how are we to interpret the estimates" rather than "how can we compute a p value". My question is a simple question whose answer is undoubtedly complex, but one that needs an answer. Without p values, or confidence intervals, I am not certain what to make of the results of my analysis. Does my analysis suggest, or does it not suggest that there is a relation between time and y? If I can't answer this question after running the analysis, I don't have any more information than I did before I ran the analysis, and a fair question would be why did I run the analysis? I am asking for help not in calculation a p value or a CI, but rather to know what I can and can't say about the results of the analysis. If this basic question can not be answered, I am at a loss to interpret my results. 
Thank you,
John




John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> Bert Gunter <gunter.berton at gene.com> 9/9/2010 11:21 PM >>>
John:

Search on this issue in the list archives. Doug Bates has addressed it
at length. Basically, he does not calculate CI's or p-values because
he does not know how to reliably do so.

However, the key remark in your query was:

> (2) lmer does not give p values or confidence intervals for the fixed effects. How we are to interpret the estimates given that no p value or CI is given for the estimates?

Think about it. A statistical analysis -- ANY statistical analysis --
treats the data in isolation: it is not informed by physics,
thermodynamics, biology,  other similar data, prior experience, or,
indeed, any part of the body of relevant scientific knowledge. Do you
really think that any such analysis, especially when predicated upon
often tenuous or even (necessarily) unverifiable assumptions and
simplifications should be considered authoritative? Classical
statistical inference is just another piece of the puzzle, and not
even particularly useful when, as if typically the case, hypotheses
are formulated AFTER seeing the data (this invalidates the probability
calculations -- hypotheses must be formulated before seeing the data
to be meaningfully assessed). Leo Breiman called this statistics'
"quiet scandal" something like 20 years ago, and he was no dummy.

It is comforting, perhaps, but illusory to believe that statistical
inference can be relied on to give sound, objective scientific
results. True, without such a framework, science seems rather
subjective, perhaps closer to religion and arbitrary cultural
archetypes than we care to admit. But see Thomas Kuhn and Paul
Feuerabend for why this is neither surprising nor necessarily a bad
thing.

Cheers,
Bert Gunter




On Thu, Sep 9, 2010 at 8:00 PM, John Sorkin <jsorkin at grecc.umaryland.edu> wrote:
> windows Vista
> R 2.10.1
>
>
> (1) How can I get the complete table of for the fixed effects from lmer. As can be seen from the example below, fixef(fit2) only give the estimates and not the SE or t value
>
>> fit3<- lmer(y~time + (1|Subject) + (time|Subject),data=data.frame(data))
>> summary(fit3)
> Linear mixed model fit by REML
> Formula: y ~ time + (1 | Subject) + (time | Subject)
>   Data: data.frame(data)
>    AIC    BIC logLik deviance REMLdev
>  -126.2 -116.4   70.1   -152.5  -140.2
> Random effects:
>  Groups   Name        Variance   Std.Dev.   Corr
>  Subject  (Intercept) 2.9311e+01 5.41396385
>  Subject  (Intercept) 0.0000e+00 0.00000000
>          time        0.0000e+00 0.00000000   NaN
>  Residual             8.1591e-07 0.00090328
> Number of obs: 30, groups: Subject, 10
>
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept) 14.998216   1.712046       9
> time        -0.999779   0.000202   -4950
>
> Correlation of Fixed Effects:
>     (Intr)
> time -0.001
>> fixef(fit3)
> (Intercept)        time
>  14.9982158  -0.9997793
>
> (2) lmer does not give p values or confidence intervals for the fixed effects. How we are to interpret the estimates given that no p value or CI is given for the estimates?
>
>
>
>
> John David Sorkin M.D., Ph.D.
> Chief, Biostatistics and Informatics
> University of Maryland School of Medicine Division of Gerontology
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> (Phone) 410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>
> Confidentiality Statement:
> This email message, including any attachments, is for ...{{dropped:25}}