# Undirected Gaussian graphical Markov model

### Description

The `"UGgmm"`

class is the class of undirected Gaussian graphical
Markov models defined within the `qpgraph`

package to store
simulate and manipulate this type of graphical Markov models (GMMs).

An undirected Gaussian GMM is a family of multivariate normal distributions sharing a set of conditional independences encoded by means of an undirected graph. Further details can be found in the book of Lauritzen (1996).

### Objects from the Class

Objects can be created by calls of the form `UGgmm(g, ...)`

corresponding
to constructor methods or `rUGgmm(n, g, ...)`

corresponding to random
simulation methods.

### Slots

`p`

:Object of class

`"integer"`

storing the dimension of the undirected Gaussian GMM corresponding to the number of random variables.`g`

:Object of class

`graphBAM-class`

storing the associated undirected labeled graph.`mean`

:Object of class

`"numeric"`

storing the mean vector.`sigma`

:Object of class

`dspMatrix-class`

storing the covariance matrix.

### Methods

`UGgmm(g)`

Constructor method where

`g`

can be either an adjacency matrix or a`graphBAM-class`

object.`rUGgmm(n, g)`

Constructor simulation method that allows one to simulate undirected Gaussian GMMs where

`n`

is the number of GMMs to simulate and`g`

can be either a graphParam object, an adjacency matrix or a`graphBAM-class`

object.`names(x)`

Accessor method to obtain the names of the elements in the object

`x`

that can be retrieved with the`$`

accessor operator.`$`

Accessor operator to retrieve elements of the object in an analogous way to a

`list`

.`dim(x)`

Dimension of the undirected Gaussian GMM corresponding to the total number of random variables.

`dimnames(x)`

Names of the random variables in the undirected Gaussian GMM.

`show(object)`

Method to display some bits of information about the input undirected Gaussian GMM specified in

`object`

.`summary(object)`

Method to display a sumamry of the main features of the input undirected Gaussian GMM specified in

`object`

.`plot(x, ...)`

Method to plot the undirected graph associated to the the input undirected Gaussian GMM specified in

`x`

. It uses the plotting capabilities from the`Rgraphviz`

library to which further arguments specified in`...`

are further passed.

### Author(s)

R. Castelo

### References

Lauritzen, S.L. *Graphical models*. Oxford University Press, 1996.

### See Also

HMgmm