Dear listers,

I am evaluating an experiment in plant ecology. Since the experiment has both crossed and nested random factors and the data are unbalanced, I decided to use linear mixed effects models (lmer from lme4). Right now, I am struggling to determine the significance of the fixed factors. I tried to estimate the p-value for the fixed factors by dropping individual factors from the model and comparing the two models with anova (cf. code below). However, I run into trouble when I try to drop the factor Origin from the model which occurs also in the Origin:Soil interaction term. As can be seen from the output of R, the two models seem to be identical for R. (Although the formula given in the output is different, AIC, BIC, and logLik are exactly identical.)

So my question is: how can I estimate a p-value for Origin (as well as Soil) in this case? Should I remove the interaction term beforehand? However, this would then be a different model, would't it?

I use the following model formulation, with

RDiam: a continuous covariate.
Altitude, Origin, Soil: fixed factors.
Plot, Site, Population: random effects.
Origin:Soil: significant interaction term.

> library(lme4)
> f1 <- lmer(y ~ RDiam + Altitude + Origin + Soil + (1 | Plot) + (1 | Site) +
+             (1 | Population) + Origin:Soil, data = Ran,
+              na.action = na.exclude, REML=FALSE)
> f2 <- update(f1, .~. - Origin  , REML=FALSE)
> anova(f2,f1)
 
Data: Ran
Models:
f2:  y ~ RDiam + Altitude + Soil + (1 | Plot) + (1 | Site) +
f2:      (1 | Population) + Origin:Soil
f1:  y ~ RDiam + Altitude + Origin + Soil + (1 | Plot) + (1 | Site) +
f1:      (1 | Population) + Origin:Soil
     Df    AIC    BIC  logLik Chisq Chi Df Pr(>Chisq)   
f2   11 5382.6 5435.1 -2680.3                           
f1   11 5382.6 5435.1 -2680.3     0      0  < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Any advice is highly appreciated!
Thanks a lot,
Martin Heggli
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