Thank you all for your help.

Daniel,

I want to know if I really understand your answer. I calculated each group
mean and sub mean as below:

> tapply(val,group,mean)
  group1   group2   group3
4.215670 5.664411 7.210819
> tapply(val,sub,mean)
       a        b        c        d
4.856927 5.199305 6.183979 6.547655

and
intercept (group=1 and sub=a) is: 3.506216 (see original post table)
average difference between group2 and group1 is: 5.664411 -
4.215670=1.448741
average difference between sub b and sub a is: 5.199305-4.856972=0.342333

therefore, if I understand this right,  the reference level for interaction
between sub=b and group=2  should be the sum of the above numbers, which is:
3.506216+1.448741+0.342333=5.29729

Am I right? Thank you vey much.


On Fri, Aug 28, 2009 at 7:02 PM, Daniel Malter <daniel@umd.edu> wrote:

> The intercept is group=1, sub=a,
>
> The interaction between sub=b and group=2 implies that both sub=b and
> group=2 direct effects are included. That is, with the direct effects only
> you are now at: intercept+group2+subb, which means the intercept (group1
> and
> sub=a) + the average difference between group=2 and group=1 + the average
> difference between sub=b and sub=a. This is the reference level for the
> interaction effect between group=2 and sub=b. This is not one-specific
> group
> in your experiment but rather a generic average group (average group=2,
> average sub=b). Your interaction effect now asks the question how much does
> group=2 with sub=b stand out from the average in its group and in its sub.
>
> To clarify your confusion, you may want to write out the model formula.
>
> Daniel
>
> -------------------------
> cuncta stricte discussurus
> -------------------------
>
> -----Ursprüngliche Nachricht-----
> Von: r-help-bounces@r-project.org [mailto:r-help-bounces@r-project.org] Im
> Auftrag von zrl
> Gesendet: Friday, August 28, 2009 6:49 PM
> An: r-help
> Betreff: [R] how to explain the interaction terms regarding
> "treatmentcontrast" of lm model
>
> Dear list,
>
> I am confused on how to explain the interaction term in the context of
> "treatment contrast".
>
> for example, I have an data frame as below:
>  sub  group      val
> 1    a group1 3.685625
> 2    a group1 3.407445
> 3    a group1 4.040920
> 4    a group1 2.890875
> 5    b group1 3.853280
> 6    b group1 4.113585
> 7    b group1 3.043250
> 8    b group1 3.800920
> 9    c group1 5.394305
> 10   c group1 5.004290
> 11   c group1 4.651435
> 12   c group1 4.286650
> 13   d group1 4.773440
> 14   d group1 3.982200
> 15   d group1 5.718690
> 16   d group1 4.803815
> .....
> 45   d group3 8.021240
> 46   d group3 7.641685
> 47   d group3 7.519445
> 48   d group3 9.514580
>
> then:
>
> >tapply(val,list(group,sub),mean)
>              a        b        c        d
> group1 3.506216 3.702759 4.834170 4.819536
> group2 4.831503 5.246833 5.930116 6.649191
> group3 6.233062 6.648325 7.787651 8.174238
>
> > summary(lm(val~group*sub))
>
> Call:
> lm(formula = val ~ group * sub)
>
> Residuals:
>     Min       1Q   Median       3Q      Max
> -1.24378 -0.50184 -0.03726  0.51748  1.34034
>
> Coefficients:
>                 Estimate Std. Error t value Pr(>|t|)
> (Intercept)        3.5062     0.3278  10.696 9.98e-13 ***
> groupgroup2        1.3253     0.4636   2.859  0.00703 **
> groupgroup3        2.7268     0.4636   5.882 9.98e-07 ***
> subb               0.1965     0.4636   0.424  0.67411
> subc               1.3280     0.4636   2.865  0.00693 **
> subd               1.3133     0.4636   2.833  0.00751 **
> groupgroup2:subb   0.2188     0.6556   0.334  0.74052
> groupgroup3:subb   0.2187     0.6556   0.334  0.74060
> groupgroup2:subc  -0.2293     0.6556  -0.350  0.72851
> groupgroup3:subc   0.2266     0.6556   0.346  0.73158
> groupgroup2:subd   0.5044     0.6556   0.769  0.44671
> groupgroup3:subd   0.6279     0.6556   0.958  0.34460
> ---
> Signif. codes:  0  ***  0.001  **  0.01  *  0.05  .  0.1     1
>
> Residual standard error: 0.6556 on 36 degrees of freedom
> Multiple R-squared: 0.8607,     Adjusted R-squared: 0.8182
> F-statistic: 20.22 on 11 and 36 DF,  p-value: 3.296e-12
>
>
> My question is:
> with "treatment contrast" in R, Coefficients, groupgroup2,groupgroup3,
> subb,
> subc,subd are the difference from Intercept 3.5062 (reference level for
> intercepts).
> But what is the reference level for the interaction terms? such as
> groupgroup2:subb,groupgroup3:subb,and etc.
>
> Thanks.
>
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>
>
>

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