[R-sig-ME] To interpret the interaction between treatment factors in lme4

[Chris Howden]

Hi Likan,

Interactions mean your main effects are having an impact that is more than
just the sum of their parts.

U need to look at the actual parameters to understand what it means. For
example, if its parameter was 5 then this means the average response in
this study goes up by 5 when both A2 and B3 occur. If its -5 then it means
the response goes down by 5 when A2 and B3 occur.

Keep in mind the total effect is the sum of all the relevant parameters ie
intercept + A2 + B3 + A2:B3.

The null being tested is that the parameter A2:B3 = 0.

But to get a better understanding of the effect in the population u can
calculate CI's for the total effect using predict().


Chris Howden B.Sc. (Hons) GStat.
Founding Partner
Evidence Based Strategic Development, IP Commercialisation and Innovation,
Data Analysis, Modelling and Training
(mobile) 0410 689 945
(fax) +612 4782 9023
chris at trickysolutions.com.au




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-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Likan Zhan
Sent: Thursday, 20 October 2011 10:09 AM
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] To interpret the interaction between treatment factors
in lme4

Hi all,

If 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

How could we interpret the significant effect of "A2:B3",
what is the null hypothesis of it?

Thank you very much.

Likan

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