how to know if random factors are significant?

There was a related question from Mariana Martinez a day or two ago.   
Before removing a random term that background knowledge or past  
experience with similar data suggests is likely, check what difference  
it makes to the p-values for the fixed  effects that are of interest.   
If it makes a substantial difference, caution demands that it be left  
it in.

To pretty much repeat my earlier comment:
If you omit the component then you have to contemplate the alternatives:
1) the component really was present but undetectable
2) the component was not present, or so small that it could be  
ignored, and the inference from the model that omits it is valid.

If (1) has a modest probability, and it matters whether you go with  
(1) or (2), going with (2) leads to a very insecure inference. The p- 
value that comes out of the analysis is unreasonably optimistic; it is  
wrong and misleading.

If you do anyway want a Bayesian credible interval, which you can  
treat pretty much as a confidence interval, for the random component,  
check Douglas Bates' message of a few hours ago, the first of two  
messages with the subject "lme4::mcmcsamp + coda::HPDinterval", re the  
use of the function HPDInterval().

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.


On 2 Apr 2008, at 4:02 AM, Leonel Arturo Lopez Toledo wrote:

Dear all:
I?m new to mixed models and I?m trying to understand the output from  
?lme? in the nlme
package. I hope my question is not too basic for that list-mail.  
Really sorry if that
is the case.
Especially I have problems to interpret the random effect output. I  
have only one
random factor which is ?Site?. I know the ?Variance and Stdev?  
indicate variation by
the random factor, but are they indicating any significance? Is  
there any way to
obtain a p-value for the random effects? And in case is not  
significant, how can I
remove it from the model? With ?update (model,~.-)??

The variance in first case (see below) is very low and in the second  
example is more
considerable, but should I consider in the model or do I remove it?

Thank you very much for your help in advance.

EXAMPLE 1
Linear mixed-effects model fit by maximum likelihood
Data: NULL
      AIC      BIC    logLik
 277.8272 287.3283 -132.9136

Random effects:
Formula: ~1 | Sitio
        (Intercept) Residual
StdDev: 0.0005098433 9.709515

EXAMPLE 2
Generalized linear mixed model fit using Laplace
Formula: y ~Canopy*Area + (1 | Sitio)
  Data: tod
Family: binomial(logit link)
  AIC   BIC logLik deviance
50.93 54.49 -21.46    42.93

Random effects:
Groups Name        Variance Std.Dev.
Sitio  (Intercept) 0.25738  0.50733
number of obs: 18, groups: Sitio, 6


Leonel Lopez
Centro de Investigaciones en Ecosistemas-UNAM
MEXICO




-- 
Este mensaje ha sido analizado por MailScanner
en busca de virus y otros contenidos peligrosos,
y se considera que est? limpio.
For all your IT requirements visit: http://www.transtec.co.uk