Dear Jana,

>An anova(lm1, lm2)  lm1<-lmer(y~x1+x2+...+(1|region)+(1|region:farm));
lm2<-lmer(y+x1+x2+...+(1|farm)) said models did not differ significantly and
AIC was about the same. So I know there is no additional explanatory power
including the region term.

>Yet, I would like to keep the region effect in the model to separate and
compare the effect size of region vs. farm. Is it valid to do so even if
 some of the regions are only represented by one farm?

I don't think you have the data to ask questions about differences between
regions as distinct from differences between farms. Look at it this way. If
you were just doing a normal comparison between regions and you only looked
at 1 or 2 farms per region, would you have the statistical power to say that
differences were due to region rather than farm? Answer = No.

Similarly, are the differences between the farms because they are in
different regions or just normal variation between farms? Well you only have
2 farms per region so it's hard to tell. Maybe you just have enough data if
pairs of farms within regions are always very similar and differences
between regions large.

Also. Fitting random effects with fewer than 5 levels is dodgy, and you only
have 2 levels of farm per region, sometimes 1.

Perhaps you could look at it this way.

compare

m1 <- lmer (y~(1|region))
m2 <- lmer (y~(1|farm))

If m2 is better then there is variation between farms within regions, if
there's no difference then region accounts for most of the variation. BUT
you've not got much power to detect farm effects within regions, so a null
result is not strong evidence for the absence of farm variation within
regions.


Andy.



andydolman@gmail.com

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