qpBoundary {qpgraph} | R Documentation

## Maximum boundary size of the resulting qp-graphs

### Description

Calculates and plots the size of the largest vertex boundary as function of the non-rejection rate.

### Usage

    qpBoundary(nrrMatrix, n=NA, threshold.lim=c(0,1), breaks=5, vertexSubset=NULL,
               plot=TRUE, qpBoundaryOutput=NULL, density.digits=0, logscale.bdsize=FALSE,
               titlebd="Maximum boundary size as function of threshold", verbose=FALSE)

### Arguments

`nrrMatrix` | matrix of non-rejection rates.
`n` | number of observations from where the non-rejection rates were estimated.
`threshold.lim` | range of threshold values on the non-rejection rate.
`breaks` | either a number of threshold bins or a vector of threshold breakpoints.
`vertexSubset` | subset of vertices for which their maximum boundary size is calculated with respect to all other vertices.
`plot` | logical; if TRUE makes a plot of the result; if FALSE it does not.
`qpBoundaryOutput` | output from a previous call to `qpBoundary`. This allows one to plot the result changing some of the plotting parameters without having to do the calculation again.
`density.digits` | number of digits in the reported graph densities.
`logscale.bdsize` | logical; if TRUE then the scale for the maximum boundary size is logarithmic which is useful when working with more than 1000 variables; FALSE otherwise (default).
`titlebd` | main title to be shown in the plot.
`verbose` | show progress on calculations.

### Details

The maximum boundary is calculated as the largest degree among all vertices of a given qp-graph.

### Value

A list with the maximum boundary size and graph density as function of threshold, the threshold on the non-rejection rate that provides a maximum boundary size strictly smaller than the sample size n and the resulting maximum boundary size.

### Author(s)

R. Castelo and A. Roverato

### References

Castelo, R. and Roverato, A. A robust procedure for Gaussian graphical model search from microarray data with p larger than n. J. Mach. Learn. Res., 7:2621-2650, 2006.

### See Also

`qpHTF` `qpGraphDensity`

### Examples

    require(mvtnorm)

    nVar <- 50  ## number of variables
    maxCon <- 5 ## maximum connectivity per variable
    nObs <- 30  ## number of observations to simulate

    set.seed(123)

    A <- qpRndGraph(p=nVar, d=maxCon)
    Sigma <- qpG2Sigma(A, rho=0.5)
    X <- rmvnorm(nObs, sigma=as.matrix(Sigma))

    ## the higher the q the less complex the qp-graph

    nrr.estimates <- qpNrr(X, q=1, verbose=FALSE)

    qpBoundary(nrr.estimates, plot=FALSE)

    nrr.estimates <- qpNrr(X, q=5, verbose=FALSE)

    qpBoundary(nrr.estimates, plot=FALSE)

[Package qpgraph version 2.21.2 Index]