how to know if random factors are significant?
On 02/04/2008, John Maindonald <john.maindonald at anu.edu.au> 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.
I think this is a question of strategy. Leonel did put emphasis on the random effect, and he might just be interested in the size and significance of the random effect rather than the fixed effects. Estimating and testing the random effect seems reasonable to me in this case, although confidence intervals, as you mention below also provides good inference. It is always possible to discuss how much non-data information to include in an analysis and I believe the answer depends very much on the purpose of the research. If the research question regards the size and "existence" of the variance of 'Site', then he might conclude that it is so small compared to other effects in the model/data, that it has no place in the model. I think the question regarding "existence" of some effect can be misleading in many cases, because one can always claim that any effect is really there, and had we observed enough data, we would be able to estimate the effect reliably. Leaving too many variables in the model on which there is too little information also results in bias in parameter estimates, so it is a trade off. We often speak of appropriate models, but the appropriateness depends on the purpose - do we seek inference for a specific (set of) parameter(s), the system as a whole or do we want to use it for prediction? /Rune
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 > > _______________________________________________ > R-sig-mixed-models at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
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