[R-sig-ME] how to know if random factors are significant?

[John Maindonald]

Sure, I should have said:
"p-values (once one has worked out how to calculate them)"

Where was it said that degrees of freedom would necessarily help,  
especially for a generalized linear mixed model?
:-) John.

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 2:46 PM, Robert Kushler wrote:

>
> Wait a minute ... what p-values?  Have you informed Doug that the
> degrees of freedom police have resolved the issue?
>
> :-)    Rob Kushler
>
> (Sorry, couldn't resist.)
>
>
> John Maindonald wrote:
>> 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
>>>
>>>
>>>
>>>
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