[R-sig-ME] magnitude of random effect vs significance

[Peter Dalgaard]

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             Øster 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