norMmix {norMmix}

Constructor for Multivariate Normal Mixture Objects

Description

norMmix creates a multivariate normal (aka Gaussian) mixture object, conceptually a mixture of k multivariate (p-dimensional) Gaussians \mathcal{N}(\mu_j, \Sigma_j), for j=1, \dots, k.

Usage

norMmix(mu, Sigma = NULL, weight = rep(1/k, k), name = NULL,
        model = c("EII", "VII", "EEI", "VEI", "EVI",
                  "VVI", "EEE", "VEE", "EVV", "VVV"))

Arguments

mu

matrix of means, or a vector in which case k = 1 is assumed. Otherwise use as.matrix(mu).

Sigma

NULL, number, numeric, vector (length = k), matrix (dim = p x k), or array (p x p x k). See details.

weight

weights of mixture model components

name

gives the option of naming mixture

model

see ‘Details’

Details

model must be specified by one of the (currently 10) character strings shown in the default. (In a future version, model may become optional).

norMmix as a few nifty ways of constructing simpler matrices from smaller givens. This happens according to the dimension of the given value for the Sigma argument:

0.

for a single value d or NULL, norMmix() assumes all covariance matrices to be diagonal with entries d or 1, respectively.

1.

for a vector v, norMmix assumes all matrices to be diagonal with the i-th matrix having diagonal entries v[i].

2.

for a matrix m, norMmix assumes all matrices to be diagonal with diagonal vector m[,i], i.e., it goes by columns.

3.

an array is assumed to be the covariance matrices, given explicitly.

FIXME ... give "all" the details ... (from Bachelor's thesis ???)

Value

currently, a list of class "norMmix", with a name attribute and components

model

three-letter character string, specifying the Sigma-parametrization

mu

(p x k) matrix of component means mu[,j], j=1,\dots,k.

Sigma

(p x p x k) array of component Covariance matrices Sigma[,,j].

weight

p-vector of mixture probability weights; non-negative, summing to one: sum(weight) == 1.

k

integer, the number of components

dim

integer, the dimension p.

Author(s)

Nicolas Trutmann

References

__ TODO __

See Also

norMmixMLE() to fit such mixture models to data (an n \times p matrix).

“Marron-Wand”-like examples (for testing, etc), such as MW21.

Examples

## Some of the "MW" objects : % --> ../R/zmarrwandnMm.R

# very simple 2d:
M21 <- norMmix(mu = cbind(c(0,0)), # 2 x 1 ==> k=2, p=1
               Sigma = 1, model = "EII")
stopifnot(identical(M21, # even simpler, Sigma = default :
                    norMmix(mu = cbind(c(0,0)), model = "EII")))

m2.2 <- norMmix(mu = cbind(c(0, 0), c(5, 0)), Sigma = c(1, 10),
                weight = c(7,1)/8, model = "EVV")

m22 <- norMmix(
    name = "one component rotated",
    mu = cbind( c(0,0) ),
    Sigma = array(c(55,9, 9,3), dim = c(2,2, 1)),
    model = "EVV")
stopifnot( all.equal(MW22, m22) )

m213 <- norMmix(
    name = "#13 test VVV",
    weight = c(0.5, 0.5),
    mu = cbind( c(0,0), c(30,30) ),
    Sigma = array(c( 1,3,3,11, 3,6,6,13 ), dim=c(2,2, 2)),
    model = "VVV")
stopifnot( all.equal(MW213, m213) )
str(m213)

m34 <- norMmix(
    name = "#4 3d VEI",
    weight = c(0.1, 0.9),
    mu = matrix(rep(0,6), 3,2),
    Sigma = array(c(diag(1:3), 0.2*diag(3:1)), c(3,3, 2)),
    model = "VVI" )
stopifnot( all.equal(MW34, m34) )