magnitude of random effect vs significance

Following on from previous recent post, here is an example of a random effect which is tiny but highly significant. I've got no problem explaining a fixed effect which is tiny but significant (ie precisely estimated), but I'm struggling here!

regards

Mike



# read in temp3 first below
varcor.2h.crustacea.hf <- lme(log(crustdens+1) ~ HEIGHT, random=~1|MONTH/TIME/TRANSECT/POLE, data=temp3)
VarCorr(varcor.2h.crustacea.hf)

varcor.2h.crustacea.nomonth.hf <- lme(log(crustdens+1) ~ HEIGHT, random=~1|TIME/TRANSECT/POLE, data=invdens.bottommiddle)

anova(varcor.2h.crustacea.hf,varcor.2h.crustacea.nomonth.hf)
# month random effect of very low magnitude, yet it it highly significant: how can I explain this, or have I made a mistake!

  

I don't think those models are comparable. Let's ignore TRANSECT and 
POLE for now. In one model you have MONTH with 4 groups and TIME %in% 
MONTH with 16 groups,  and in the other you have TIME with 4 groups. Put 
differently the variance for that term in one case means main effect of 
TIME and in the other case ditto plus the interaction. If TIME really 
only makes sense as nested in MONTH, the former can give a substantially 
worse fit to data whether or not there is a MONTH term.  For 
comparability, try this:

 > temp3$MTIME <- interaction(temp3$MONTH,temp3$TIME)> 
varcor.2h.crustacea.nomonth2.hf <- lme(log(crustdens+1) ~ HEIGHT, 
random=~1|MTIME/TRANSECT/POLE, data=temp3)

anova(varcor.2h.crustacea.hf,varcor.2h.crustacea.nomonth2.hf)                             

Model df      AIC      BIC    logLik   Test
varcor.2h.crustacea.hf              1  7 1900.187 1929.923 -943.0935       

varcor.2h.crustacea.nomonth2.hf     2  6 1898.187 1923.675 -943.0935 1 vs 2
                                     L.Ratio p-value
varcor.2h.crustacea.hf                             
varcor.2h.crustacea.nomonth2.hf 3.202003e-07  0.9995

O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
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