[R] how to explain the interaction terms regarding "treatmentcontrast" of lm model

Daniel Malter daniel at umd.edu
Sat Aug 29 02:02:42 CEST 2009

```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

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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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