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
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