Comparing lme4 and glm?

Comments are interspersed.
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.

Dears lme4 and R users: I'm new to lme4 and starting to explore it.  
I have two questions on regard to model simplification and hope you  
can help me. I?m modelling the effect of timber harvesting on the  
number of individuals left in a forest and using two fixed factors  
and SITE as random factor with poisson family. My questions: 1.- How  
do I know a random factor is significant or not. I found very small  
variance and st dev for a random factor (SITE) and based on that I  
suppose random effect is not significant, but is there any test to  
determine it. I have seen some papers where chi square and p-values  
are shown (Svenning et al 2008 Oecologiqa), but do not know how they  
are obtained.

For reasons given under 2., maybe you do not want such tests.

2.- If the random factor is not significant can I remove it from the  
model? and run a simple glm with poisson family?

If this makes a difference to the inference that you draw, you should  
worry.  I take the view that if such a random component is likely to  
be present, then the model should accommodate it, irrespective of  
whether is it statistically significant.  This is an especially  
important point when the component in question is estimated with a  
rather small number of degrees of freedom, i.e., not much information  
to go on.

If you omit the component then you have to contemplate the alternatives
1) the effect really was present but undetectable
2) the effect was not present, or so small that it could be ignored,  
and my inference 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.  Your p- 
value is not, in truth, the one that comes out of the analysis!

Historical data can be useful.  Have you analysed other such data in  
the past?  With enough such samples, you can look at the distribution  
of estimates of the random component.

3.- Can I compare with ?anova? the lme4 model against that one from  
glm? I?ll be very grateful for your help. Mariana

If the random effects all reduce to zero, then you have a glm model.

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