# Function to support estimability requests for compromise designs

### Description

Addelman (1962) and Ke and Wu (2005) discuss compromise plans of different types. Their creation is supported by the function compromise.

### Usage

1 | ```
compromise(nfactors, G1, class=3, msg=TRUE)
``` |

### Arguments

`nfactors` |
overall number of factors |

`G1` |
vector with indices of factors in group G1 (cf. details) |

`class` |
class of compromise designs that is to be generated; 1, 2, 3, or 4, cf. details below |

`msg` |
logical stating whether the |

### Details

For compromise plans, the factors are decomposed into a group G1 and a group G2.
The different classes of compromise plans require estimability of different subsets
of 2fis in addition to main effects:

Class 1: all 2fis within group G1 are estimable

Class 2: all 2fis within group G1 are estimable,
as well as all 2fis within group G2

Class 3: all 2fis within group G1 are estimable,
as well as all 2fis between groups G1 and G2

Class 4: all 2fis between groups G1 and G2 are estimable

The function returns a list of four components (cf. section “Value”).
They can be used as input for the function `FrF2`

, if compromise
plans are to be created. Both distinct designs (Addelman 1962) and clear designs
(Ke, Tang and Wu 2005) can be constructed,
depending on the settings of option `clear`

in function
`FrF2`

. More explanations on specifying estimability requirements
for 2fis in general are provided under `estimable.2fis`

.

### Value

Value is a list of the four components `perms.full`

, `requirement`

,
`class`

, and `minnrun.clear`

. The last two components are purely imformative,
while the first two provide input parameters for function `FrF2`

.

`requirement`

can be used for specifying the required 2fis in the `estimable`

option,
both with `clear=FALSE`

and `clear=TRUE`

.
For `clear=FALSE`

, `perms.full`

can be used in the `perms`

option
for speeding up the search into a hopefully realistic time frame.

`minnrun.clear`

indicates the minimum number of runs needed for a clear design.

Note that the catalogue `catlg`

contains all designs needed for
accomodating existing clear compromise designs in up to 128 runs (even minimum aberration
among all existing clear compromise designs; for a catalogue of these, cf. Gr\"omping 2010).

### Author(s)

Ulrike Groemping

### References

Addelman, S. (1962). Symmetrical and asymmetrical fractional factorial plans.
*Technometrics* **4**, 47-58.

Gr\"omping, U. (2010). Creating clear designs: a graph-based algorithm and a
catalogue of clear compromise plans.
*Reports in Mathematics, Physics and Chemistry*, report 05/2010,
Department II, Beuth University of Applied Sciences Berlin.
(Preprint for IIE Transactions; IIE Transactions is available at
http://www.tandfonline.com.)

Ke, W., Tang, B. and Wu, H. (2005). Compromise plans with clear two-factor interactions.
*Statistica Sinica* **15**, 709-715.

### See Also

See Also `FrF2`

for creation of regular fractional factorial designs
as well as `estimable.2fis`

for statistical and algorithmic information on estimability of 2-factor interactions

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | ```
## seven factors two of which are in group G1
C1 <- compromise(7, c(2,4), class=1)
C1$perms.full ## the same for all classes
C1$requirement
C2 <- compromise(7, c(2,4), class=2)
C2$requirement
C3 <- compromise(7, c(2,4), class=3)
C3$requirement
C4 <- compromise(7, c(2,4), class=4)
C4$requirement
## Not run:
########## usage of estimable ###########################
## design with with BD clear in 16 runs
FrF2(16,7,estimable = C1$requirement)
## design with BD estimable on a distinct column in 16 runs (any design will do,
## if resolution IV!!!
FrF2(16,7,estimable = C1$requirement, clear=FALSE, perms=C1$perms.full)
## all four classes, mostly clear, for 32 runs
FrF2(32,7,estimable = C1$requirement)
FrF2(32,7,estimable = C2$requirement) ## requires resolution V
## as clear class 2 compromise designs do not exist due to Ke et al. 2005
FrF2(32,7,estimable = C2$requirement, clear=FALSE, perms=C2$perms.full)
FrF2(32,7,estimable = C3$requirement)
FrF2(32,7,estimable = C4$requirement)
## two additional factors H and J that do not show up in the requirement set
FrF2(32,9,estimable = C3$requirement)
## two additional factors H and J that do not show up in the requirement set
FrF2(32,9,estimable = C3$requirement, clear=FALSE)
## note that this is not possible for distinct designs in case perms is needed,
## because perms must have nfactors columns
## End(Not run)
``` |