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

[Robert Kushler]

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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