magnitude of random effect vs significance
Mike Dunbar wrote:
Hi Peter Just to check I'm understanding you: So in the generic case where you have a nesting say A/B/C/D, if you want to test by removal of any factor that isn't the lowest in the hierarchy then you have to re-label that factor as including the levels of the next lowest factor. So for example testing by removing A, you must recode B as interaction(A,B) and test that against the full model. If so then I already understood this in the case of POLE and TRANSECT, I'd just forgotten it for the higher level factors.
Yes. Or put differently, using aov-like terms: If you remove A from A/B
you don't get B but A:B, because A/B==A+A:B by definition.
-p
(BTW. "Higher" and "lower" for model terms is a bit ambiguous. With your
convention, higher-order interactions describe lower-level terms. I
prefer "coarser" and "finer" as I was taught by Tue Tjur many years ago. )
regards Mike
Peter Dalgaard <p.dalgaard at biostat.ku.dk> 04/09/2007 20:53 >>>
Mike Dunbar wrote:
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 c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907