[R-sig-ME] contrasts vs. directly modelling differences: big diff?

[Guillaume Adeux]

Good afternoon everyone,

I have this recurring question of whether it is best to directly model the
response as % differences (e.g. Yield_loss=(Yield_without_weeds -
Yield_with_weeds)/(Yield_without_weeds)) or whether it is best to directly
model the response (e.g. Yield) and compute yield loss through post hoc
contrasts on the log scale.

I hope this following example can illustrate better:
Let's take two different weed communities: WC1 and WC2.
Each community is present on 6 fields, with multiple samples per field.
Next to each weedy sample of WC1 and WC2 within each of the 6 fields, there
is a hand weed control, inducing a hierarchical structure (paired data
within each field for each of the two weed communities).
The objective is to compute yield loss induced by the two communities and
to compare them.
One option could be to directly compute yield loss (e.g.
Yield_loss=(Yield_without_weeds - Yield_with_weeds)/(Yield_without_weeds))
for each weedy/weeded couple within each field and model
* mod0=glmer(Yield_loss~WC+(1|field)+(1|field:WC),family="binomial"),data=yl)*
(I
suppose beta or beta_binomial would also be a reasonable choice but it's
not the matter of today). Comparisons could then be made with
*cld(emmeans(mod0,~WC))*

Another option could be to directly model the response (e.g. Yield),
introduce a "Handweeding" (yes/no) variable and compute Yield loss through
the following code:
*mod1=lmer(log(Yield)~Handweeding*WC+(1|field)+(1|field:Handweeding)+(1|field:WC)+(1|field:Handweeding:WC),data=yl)*

*x=pairs(emmeans(mod1,~Handweeding|WC),reverse=TRUE)
y=regrid(x,transform="response")
*# differences on the log scale are exponentiated
*summary(y,infer=c(TRUE,TRUE),null=1) *# is yield loss significantly
different from 0 for each of the 2 community?
*cld(emmeans(y,~WC),adjust="mvt") *# is yield loss induced by WC1 different
from yield loss induced by WC2?

Are both these "procedures" correct? Which is preferable? Why?

Do not hesitate to request further information if I wasn't clear enough.
Thanks a lot.
Guillaume ADEUX

	[[alternative HTML version deleted]]