proj2.efficiency {dae}

Computes the canonical efficiency factors for the joint decomposition of two projectors

Description

Computes the canonical efficiency factors for the joint decomposition of two projectors (James and Wilkinson, 1971).

Usage

proj2.efficiency(Q1, Q2)

Arguments

Q1

An object of class "projector".

Q2

An object of class "projector".

Details

The nonzero canonical efficiency factors are the nonzero eigenvalues of Q1 %*% Q2 %*% Q1 (James and Wilkinson, 1971). An eigenvalue is regarded as zero if it is less than daeTolerance, which is initially set to .Machine$double.eps ^ 0.5 (about 1.5E-08). The function set.daeTolerance can be used to change daeTolerance.

Value

A vector containing the nonzero canonical efficiency factors.

Author(s)

Chris Brien

References

James, A. T. and Wilkinson, G. N. (1971) Factorization of the residual operator and canonical decomposition of nonorthogonal factors in the analysis of variance. Biometrika, 58, 279-294.

See Also

efficiency.criteria, proj2.eigen, proj2.combine 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 sets of projectors
unit.struct <- pstructure(~ Block/Unit, data = PBIBD2.lay)
trt.struct <- pstructure(~ trt, data = PBIBD2.lay)

## save intrablock efficiencies
eff.intra <- proj2.efficiency(unit.struct$Q[["Block"]], trt.struct$Q[["trt"]])