[R] decision about random effects in lme

[Thomas Petzoldt]

Hello,

in an experimental field study my collegue made a design with samples on 
two manipulated sampling sites (site: control, treatment). Within each 
site she sampled 3 traps (trap)  at day and night (light: light, dark) 
at 3 consecutive days (day).

We applied lme models with abundance as response variable, site * light 
as fixed effects and day and trap as random effects.

I assumed, the following model may be adequate:

m1 <- lme(ab ~ site * light, data = dat,
           random = ~1|site/day/trap, method="ML")

or alternatively:

m2 <- update(m1, random = ~1|site/trap)

and I get a significant interaction effect, but (as expected) NaN for 
site as there are not enough df. With several alternative assumptions 
about random effects I get both, the significant interaction and an 
effect of site, but m1 is remains the "best" model measured by AIC and BIC.

If I however simplify down to a linear model without random effects

m3 <- lm(ab ~ site * light, data=dat)

the models m1 and m3 are "not very different" (AIC, BIC, p-value):

 > anova(m1, m2, m3)
    Model df       AIC      BIC    logLik   Test  L.Ratio p-value
m1     1  8  96.54522 111.5148 -40.27261
m2     2  7 100.42958 113.5280 -43.21479 1 vs 2 5.884358  0.0153
m3     3  5  98.05421 107.4102 -44.02711 2 vs 3 1.624633  0.4438

and with m3 I get a very strong effect of site and also the interaction 
effect. Both, site and interaction effects are plausible if plotted with 
bwplot, but I am still confused, whether one of these two is a good 
model, and how to decide this.

Please help me

Thomas P.