[R-sig-ME] to interpret the interactions of treatment factors in lme4

[Likan Zhan]

> Dear Dr. Maechler,

> I am writing to ask a clarification when I am trying to use "lme4" package in R.

> If in our experiment, both A and B are three levels treatment factors:
> A:1,2,3;
> B:1,2,3

> And we use the following model to fit our data:
> model=lmer(response~A*B+(1|subject)+(1|trial),data=xx)

> and the following is the result of the fixed-effects:

> Fixed-effects

> (Intercept)    t=100, p<.000
>  A2           t=1.0, p<.9
>  A3           t=1.0, p<.9
>  B2           t=10,  p<.008
>  B3           t=1.0, p<.9
>  A2:B3        t=100, p<.000   <===
>  A3:B3        t=1.8, p<.6
>  A3:B2        t=1.0, p<.7
>  A3:B3        t=1.0, p<.6

> Could you tell me what is the meaning of the significant effect of "A2:B3",
> what is the null hypothesis of it?

> Thank you very much.

> Likan