# Homogeneous mixed graphical Markov model

### Description

The `"HMgmm"`

class is the class of homogeneous mixed graphical
Markov models defined within the `qpgraph`

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

An homogeneous mixed GMM is a family of multivariate conditional Gaussian distributions on mixed discrete and continuous variables sharing a set of conditional independences encoded by means of a marked 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 `HMgmm(g, ...)`

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

corresponding to random
simulation methods.

### Slots

`pI`

:Object of class

`"integer"`

storing the number of discrete random variables.`pY`

:Object of class

`"integer"`

storing the number of continuous random variables.`g`

:Object of class

`graphBAM-class`

storing the associated marked graph.`vtype`

:Object of class

`"factor"`

storing the type (discrete or continuous) of each random variable.`dLevels`

:Object of class

`"integer"`

storing the number of levels of each discrete random variable.`a`

:Object of class

`"numeric"`

storing the vector of additive linear effects on continuous variables connected to discrete ones.`rho`

:Object of class

`"numeric"`

storing the value of the marginal correlation between two continuous random variables.`sigma`

:Object of class

`dspMatrix-class`

storing the covariance matrix.`mean`

:Object of class

`"numeric"`

storing the mean vector.`eta2`

:Object of class

`"numeric"`

storing for each continuous variable connected to a discrete one, the fraction of variance of the continuous variable explained by the discrete one.

### Methods

`HMgmm(g)`

Constructor method where

`g`

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

object.`rHMgmm(n, g)`

Constructor simulation method that allows one to simulate homogeneous mixed GMMs where

`n`

is the number of GMMs to simulate and`g`

can be either a markedGraphParam 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 homogeneous mixed GMM corresponding to the number of discrete and continuous random variables.

`dimnames(x)`

Names of the discrete and continuous random variables in the homogeneous mixed GMM.

`show(object)`

Method to display some bits of information about the input homogeneous mixed GMM specified in

`object`

.`summary(object)`

Method to display a sumamry of the main features of the input homogeneous mixed GMM specified in

`object`

.`plot(x, ...)`

Method to plot the undirected graph associated to the the input homogeneous mixed 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

UGgmm