mat.Vpred {dae} | R Documentation |

## Calculates the variances of a set of predicted effects from a mixed model

### Description

For `n`

observations, `w`

effects to be predicted,
`f`

nuiscance fixed effects and `r`

nuisance random effects,
the variances of a set of predicted effects is calculated using
the incidence matrix for the effects to be predicted and, optionally,
a variance matrix of the effects, an incidence matrix for the
nuisance fixed factors and covariates, the variance matrix of the nuisance
random effects in the mixed model and the residual variance matrix.

This function has been superseded by `mat.Vpredicts`

, which
allows the use of both matrices and `formula`

e.

### Usage

`mat.Vpred(W, Gg = 0, X = matrix(1, nrow = nrow(W), ncol = 1), Vu = 0, R, eliminate)`

### Arguments

`W` |
The |

`Gg` |
The |

`X` |
The |

`Vu` |
The |

`R` |
The residual variance |

`eliminate` |
The |

### Details

Firstly the information matrix is calculated as

`A <- t(W) %*% Vinv %*% W + ginv(Gg) - A%*%ginv(t(X)%*%Vinv%*%X)%*%t(A)`

,
where `Vinv <- ginv(Vu + R)`

, `A = t(W) %*% Vinv %*% X`

and ginv(B) is the unique Moore-Penrose inverse of B formed using the eigendecomposition of B.

If `eliminate`

is set and the effects to be predicted are fixed then the reduced information matrix is calculated as `A <- (I - eliminate) Vinv (I - eliminate)`

.

Finally, the variance of the predicted effects is calculated: `Vpred <- ginv(A)`

.

### Value

A `w x w`

`matrix`

containing the variances and covariances of the
predicted effects.

### Author(s)

Chris Brien

### References

Smith, A. B., D. G. Butler, C. R. Cavanagh and B. R. Cullis (2015).
Multi-phase variety trials using both composite and individual replicate
samples: a model-based design approach.
*Journal of Agricultural Science*, **153**, 1017-1029.

### See Also

`designAmeasures`

, `mat.Vpredicts`

.

### Examples

```
## Reduced example from Smith et al. (2015)
## Generate two-phase design
mill.fac <- fac.gen(list(Mrep = 2, Mday = 2, Mord = 3))
field.lay <- fac.gen(list(Frep = 2, Fplot = 4))
field.lay$Variety <- factor(c("D","E","Y","W","G","D","E","M"),
levels = c("Y","W","G","M","D","E"))
start.design <- cbind(mill.fac, field.lay[c(3,4,5,8,1,7,3,4,5,8,6,2),])
rownames(start.design) <- NULL
## Set up matrices
n <- nrow(start.design)
W <- model.matrix(~ -1+ Variety, start.design)
ng <- ncol(W)
Gg<- diag(1, ng)
Vu <- with(start.design, fac.vcmat(Mrep, 0.3) +
fac.vcmat(fac.combine(list(Mrep, Mday)), 0.2) +
fac.vcmat(Frep, 0.1) +
fac.vcmat(fac.combine(list(Frep, Fplot)), 0.2))
R <- diag(1, n)
## Calculate the variance matrix of the predicted random Variety effects
Vp <- mat.Vpred(W = W, Gg = Gg, Vu = Vu, R = R)
designAmeasures(Vp)
## Calculate the variance matrix of the predicted fixed Variety effects,
## elminating the grand mean
Vp.reduc <- mat.Vpred(W = W, Gg = 0, Vu = Vu, R = R,
eliminate = projector(matrix(1, nrow = n, ncol = n)/n))
designAmeasures(Vp.reduc)
```

*dae*version 3.2.28 Index]