Details
for the R programs used in the
article by Tsai and Gilmour (2007)
Three-level designs in 18 runs
Save level3.zip
for the program files.
Save r18dat.zip
for the three-level non-isomorphic designs in 18 runs with 3 to 7
quantitative factors that Tsai et al. generated by their columnwise
procedure
unzip the
two files to your computer.
Under R console open the
source code design18.r
> source("design18.r")
# specified noRun=18
noF= #number of factors 3~7
noF=4
Read 13 items
Read 129 records
study design= #
which of the 129 four-factor designs in 18 run to be studied.
study design=3
Output for the
design plan and their GWC
-----------------------------------------------------------------
There are 129 main effects designs for 18-run designs
with 4 factors.
The design of
interest is Design 3
1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3
1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 3
1 2 1 3 2 3 2 3 1 3 1 2 1 3 2 2 1 3
1 2 3 1 2 3 3 3 2 2 1 1 2 1 1 3 3 2
Generalised word
count
(#noF, order , Lin, Quad
: b_k(i,j))
1
2 0
1 0
1
1 1
0 0
2
4 0
2 0
2
3 1
1 0
2
2 2
0 0
3
6 0
3 0.875
3
5 1
2 0.75
3
4 2
1 1.125
3
3 3
0 0.0833
4
8 0
4 0
4
7 1
3 0
4
6 2
2 0
4
5 3
1 0.6667
4
4 4
0 0
GMA-aberration
A 1 : 0
A 2 : 0
A 3 : 2.8333
A 4 : 0.6667
beta-aberration
B 1 : 0
B 2 : 0
B 3 : 0.0833
B 4 : 1.125
B 5 : 1.4167
B 6 : 0.875
B 7 : 0
B 8 : 0
Q second-order
: 0.3646
-----------------------------------------------------
WorList for the generalised
word count in Tsai and Gilmour (2007)
word.A for the word length
pattern given by the ANOVA-type generalized minimum aberration
criterion defined by Xu and Wu (2002)
word.B for the word length pattern
given by the ß-aberration criterion defined by Cheng and Ye (2004)
Q.2nd is the value of Q for
the second-order maximal model given by Tsai et al (2000)
Other
useful information can be obtained from these programs
For any three-level
design
for a given design plan
Design=
[1,] 1 1
1 1
[2,] 1 1
2 2
[3,] 1 2
1 3
[4,] 1 2
3 1
[5,] 1 3
2 2
[6,] 1 3
3 3
[7,] 2 1
2 3
[8,] 2 1
3 3
[9,] 2 2
1 2
[10,] 2 2
3 2
[11,] 2 3
1 1
[12,] 2 3
2 1
[13,] 3 1
1 2
[14,] 3 1
3 1
[15,] 3 2
2 1
[16,] 3 2
2 3
[17,] 3 3
1 3
[18,] 3 3
3 2
Use the program gwc.r
worList is the
generalized word count for the design
delta.mod(a, b, c, noF) gives the number of
eligible models for
the second-order maximal models for designs with noF factors
in which a factors' linear effects, b of the a factors' quadratic
effects and c
linear×linear interactions of the a factors are included.
For example delta.mod(3,0,1,3)=32, delta.mod(3,0,2,3)=16
and delta.mod(3,1,1,3)=16
as for the calculation of the Q criterion for three-factor designs in
18 runs.
delta.mod(3,0,1,4)=544,
delta.mod(3,0,2,4)=272
and delta.mod(3,1,1,4)=272
as for the calculation of the Q criterion for four-factor designs in 18
runs.
delta.mod(3,0,15)=17334, delta.mod(3,0,2,5)=8626
and delta.mod(3,1,1,5)=8628
as for the calculation of the Q criterion for five-factor designs in 18
runs.
delta.mod(3,0,1,6)=667068,
delta.mod(3,0,2,6)=287228
and delta.mod(3,1,1,6)=287228
as for the calculation of the Q criterion for six-factor designs in 18
runs.
delta.mod(3,0,1,7)=
10758936, delta.mod(3,0,2,7)=
10758936 and delta.mod(3,1,1,7)=
10758936 as for the calculation of the Q criterion for seven-factor
designs in 18 runs.