marginality: Extracts the marginality matrix (matrices) from a...

In dae: Functions Useful in the Design and ANOVA of Experiments

Extracts the marginality matrix (matrices) from a pstructure.object or a pcanon.object.

Description

Produces (i) a marginality matrix for the formula in a call to pstructure.formula or (ii) a list containing the marginlity matrices, one for each formula in the formulae argument of a call to designAnatomy.

A marginality matrix for a set of terms is a square matrix with a row and a column for each ternon-aliased term. Its elements are zeroes and ones, the entry in the ith row and jth column indicates whether or not the ith term is marginal to the jth term i.e. the column space of the ith term is a subspace of that for the jth term and so the source for the jth term will be orthogonal to that for the ith term.

Usage

## S3 method for class 'pstructure'
marginality(object, ...)
## S3 method for class 'pcanon'
marginality(object, ...)

Arguments

object	A pstructure.object produced by pstructure.formula or pcanon.object produced by designAnatomy.
...	Further arguments passed to or from other methods. Unused at present.

Value

If object is a pstructure.object then a matrix containing the marginality matrix for the terms obtained from the formuula in the call to pstructure.formula.

If object is a pcanon.object then a list with a component for each formula, each component having a marginality matrix that corresponds to one of the formulae in the call to designAnatomy. The components of the list will have the same names as the componeents of the formulae list and so will be unnamed if the components of the latter list are unnamed.

Author(s)

Chris Brien

See Also

pstructure.formula, designAnatomy, summary.pcanon, proj2.efficiency, proj2.combine, proj2.eigen,
pstructure in package dae, eigen.

projector for further information about this class.

Examples

## PBIBD(2) from p. 379 of Cochran and Cox (1957) Experimental Designs. 
## 2nd edn Wiley, New York
PBIBD2.unit <- list(Block = 6, Unit = 4)
PBIBD2.nest <- list(Unit = "Block")
trt <- factor(c(1,4,2,5, 2,5,3,6, 3,6,1,4, 4,1,5,2, 5,2,6,3, 6,3,4,1))
PBIBD2.lay <- designRandomize(allocated = trt, 
                              recipient = PBIBD2.unit, 
                              nested.recipients = PBIBD2.nest)

##obtain pstructure.object and extract marginality matrix
unit.struct <- pstructure(~ Block/Unit, data = PBIBD2.lay)
unit.marg <- marginality(unit.struct)

##obtain combined decomposition and extract marginality matrices
unit.trt.canon <- designAnatomy(list(unit=~ Block/Unit, trt=~ trt), data = PBIBD2.lay)
marg <- marginality(unit.trt.canon)

dae documentation built on Aug. 21, 2025, 5:56 p.m.