The following dummy data frame has factor Q (with 2 levels) nesting
factor P (with levels p1 and p2 nested under q1, and p3 and p4 nested
under q2), but both crossing the random variate s, which has 8
levels. The dependent measure is dv.
> # The data frame:
> testnest
dv s P Q
1 1 s1 p1 q1
2 2 s2 p1 q1
3 1 s3 p1 q1
4 2 s4 p1 q1
5 1 s5 p1 q1
6 3 s6 p1 q1
7 3 s7 p1 q1
8 4 s8 p1 q1
9 2 s1 p2 q1
10 3 s2 p2 q1
11 3 s3 p2 q1
12 1 s4 p2 q1
13 1 s5 p2 q1
14 2 s6 p2 q1
15 2 s7 p2 q1
16 3 s8 p2 q1
17 3 s1 p3 q2
18 3 s2 p3 q2
19 4 s3 p3 q2
20 1 s4 p3 q2
21 1 s5 p3 q2
22 1 s6 p3 q2
23 2 s7 p3 q2
24 2 s8 p3 q2
25 4 s1 p4 q2
26 3 s2 p4 q2
27 1 s3 p4 q2
28 2 s4 p4 q2
29 4 s5 p4 q2
30 1 s6 p4 q2
31 3 s7 p4 q2
32 1 s8 p4 q2
# The following aov() call is structurally correct with respect
# to the design, and appropriate error-terms, but, as can be seen,
# returns an error:
> testnest.aov=aov(dv~Q+P%in%Q+Error(s+s:Q+s:P:Q),data=testnest)
Warning message:
Error() model is singular in: aov(dv ~ Q + P %in% Q + Error(s + s:Q +
s:P:Q), data = testnest)
# However, applying the summary() method to the aov output, produces
the correct analysis:
> summary(testnest.aov)
Error: s
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 7 5.8750 0.8393
Error: s:Q
Df Sum Sq Mean Sq F value Pr(>F)
Q 1 0.1250 0.1250 0.068 0.8018
Residuals 7 12.8750 1.8393
Error: s:Q:P
Df Sum Sq Mean Sq F value Pr(>F)
Q:P 2 0.250 0.125 0.1111 0.8956
Residuals 14 15.750 1.125
I have tried many different ways of denoting the Error()
partitioning, but can't find one that produces both the correct
analysis *AND* no singularity error on the aov() call. Any suggestions?
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