designTwophaseAnatomies {dae} | R Documentation |

## Given the layout for a design and three structure formulae, obtain the anatomies for the (i) two-phase, (ii) first-phase, (iii) cross-phase, treatments, and (iv) combined-units designs.

### Description

Uses `designAnatomy`

to obtain the four species of designs, described by Brien (2019), that are associated with a standard two-phase design: the anatomies for the (i) two-phase, (ii) first-phase, (iii) cross-phase, treatments, and (iv) combined-units designs. (The names of the last two designs in Brien (2019) were cross-phase and second-phase designs.) For the standard two-phase design, the first-phase design is the design that allocates first-phase treatments to first-phase units. The cross-phase, treatments design allocates the first-phase treatments to the second-phase units and the combined-units design allocates the the first-phase units to the second-phase units. The two-phase design combines the other three species of designs. However, it is not mandatory that the three formula correspond to second-phase units, first-phase units and first-phase treatments, respectively, as is implied above; this is just the correspondence for a standard two-phase design. The essential requirement is that three structure formulae are supplied. For example, if there are both first- and second-phase treatments in a two-phase design, the third formula might involve the treatment factors from both phases. In this case, the default anatomy titles when printing occurs will not be correct, but can be modifed using the `titles`

argument.

### Usage

```
designTwophaseAnatomies(formulae, data, which.designs = "all",
printAnatomies = TRUE, titles,
orthogonalize = "hybrid",
marginality = NULL,
which.criteria = c("aefficiency", "eefficiency",
"order"), ...)
```

### Arguments

`formulae` |
An object of class |

`data` |
A |

`which.designs` |
A |

`printAnatomies` |
A |

`titles` |
A |

`orthogonalize` |
A |

`marginality` |
A Each component of the |

`which.criteria` |
A |

`...` |
further arguments passed to |

### Details

To produce the anatomies, `designAnatomy`

is called. The
two-phase anatomy is based on the three `formulae`

supplied in `formulae`

,
the first-phase anatomy uses the second and third `formulae`

, the cross-phase,
treatments anatomy derives from the first and third `formulae`

and the combined-units
anatomy is obtained with the first and second `formulae`

.

### Value

A `list`

containing the components `twophase`

, `first`

,
`cross`

and `combined`

.Each contains the `pcanon.object`

for one of the four designs produced by `designTwophaseAnatomies`

, unless it is
`NULL`

because the design was omitted from the `which.designs`

argument. The returned `list`

has an attribute `titles`

, being a
`character`

vector of length four and containing the titles used in
printing the anatomies.

### Author(s)

Chris Brien

### References

Brien, C. J. (2017) Multiphase experiments in practice: A look back.
*Australian & New Zealand Journal of Statistics*, **59**, 327-352.

Brien, C. J. (2019) Multiphase experiments with at least one later
laboratory phase . II. Northogonal designs.
*Australian & New Zealand Journal of Statistics***61**,
234-268.

### See Also

`designAnatomy`

,
`pcanon.object`

, `p2canon.object`

,
`summary.pcanon`

, `efficiencies.pcanon`

,

`pstructure`

,
`projs.2canon`

, `proj2.efficiency`

, `proj2.combine`

,
`proj2.eigen`

,

`efficiency.criteria`

, in package dae,
`eigen`

.

`projector`

for further information about this class.

### Examples

```
#'## Microarray example from Jarrett & Ruggiero (2008) - see Brien (2019)
jr.lay <- fac.gen(list(Set = 7, Dye = 2, Array = 3))
jr.lay <- within(jr.lay,
{
Block <- factor(rep(1:7, each=6))
Plant <- factor(rep(c(1,2,3,2,3,1), times=7))
Sample <- factor(c(rep(c(2,1,2,2,1,1, 1,2,1,1,2,2), times=3),
2,1,2,2,1,1))
Treat <- factor(c(1,2,4,2,4,1, 2,3,5,3,5,2, 3,4,6,4,6,3,
4,5,7,5,7,4, 5,6,1,6,1,5, 6,7,2,7,2,6,
7,1,3,1,3,7),
labels=c("A","B","C","D","E","F","G"))
})
jr.anat <- designTwophaseAnatomies(formulae = list(array = ~ (Set:Array)*Dye,
plot = ~ Block/Plant/Sample,
trt = ~ Treat),
which.designs = c("first","cross"),
data = jr.lay)
## Three-phase sensory example from Brien and Payne (1999)
## Not run:
data(Sensory3Phase.dat)
Sensory.canon <- designTwophaseAnatomies(formulae = list(
eval= ~ ((Occasions/Intervals/Sittings)*Judges)/Positions,
field= ~ (Rows*(Squares/Columns))/Halfplots,
treats= ~ Trellis*Method),
data = Sensory3Phase.dat)
## End(Not run)
```

*dae*version 3.2.28 Index]