mat.random {dae}R Documentation

Calculates the variance matrix for the random effects from a mixed model, based on a supplied formula or a matrix.


For n observations, compute the variance matrix of the random effects. The matrix can be specified using a formula for the random effects and a list of values of the variance components for the terms specified in the random formula. If a matrix specifying the variances of the nuisance random effects is supplied then it is returned as the value from the function.


mat.random(random, G, design, keep.order = TRUE)



A formula or a matrix. If a formula, it specifies the random effects from which the matrix for the contribution of the random effects to the variance matrix can be generated. If it is a matrix, it must be an n x n matrix and will be passed through as the required variance matrix for the random effects. The default is 0, which implies that there are no random effects.


This term only needs to be set if random is a formula. Then it is set to a list, in which each component is either a single value or a matrix; there needs to be a component for each term in the expanded formula, with the order of the terms and components matching. If it is a single value, a diagonal matrix of dimension equal to the product of the numbers of levels of the factors in its term. If it is a matrix, its dimension must be equal to the product of the numbers of levels of the factors in its term.


A data.frame containing the design to be used in an experiment and for which the variane matrix is required. It is not required when the only formula specified is an intercept-only formula.


A logical indicating whether the terms should keep their position in the expanded formula projector, or reordered so that main effects precede two-factor interactions, which precede three-factor interactions and so on.


If \bold{Z}_i is the is incidence matrix for the random nuisance effects in \bold{u}_i for a term in random and \bold{u}_i has variance matrix \bold{G}_i so that the contribution of the random effectst to the variance matrix for \bold{Y} is \bold{V}_u = \Sigma (\bold{Z}_i\bold{G}_i(\bold{Z}_i)^T).


A n x n matrix containing the variance matrix for the random effects.


Chris Brien

See Also



## 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")) <- cbind(mill.fac, field.lay[c(3,4,5,8,1,7,3,4,5,8,6,2),])
rownames( <- NULL

## Set gammas
terms <- c("Variety", "Frep", "Frep:Fplot", "Mrep", "Mrep:Mday", "Mrep:Mday:Mord")
gammas <- c(1, 0.1, 0.2, 0.3, 0.2, 1)
names(gammas) <- terms

## Specify matrices to calculate the variance matrix of the predicted fixed Variety effects 
Vu <- with(, fac.vcmat(Mrep, gammas["Mrep"]) + 
                         fac.vcmat(fac.combine(list(Mrep,Mday)), gammas["Mrep:Mday"]) + 
                         fac.vcmat(Frep, gammas["Frep"]) + 
                         fac.vcmat(fac.combine(list(Frep,Fplot)), gammas["Frep:Fplot"]))

## Calculate the variance matrix of the predicted random Variety effects using formulae
Vu <- mat.random(random = ~ -1 + Mrep/Mday + Frep/Fplot, 
                 G = as.list(gammas[c(4,5,2,3)]), 
                 design =

[Package dae version 3.2.19 Index]