Description Usage Arguments Details Value Author(s) References See Also Examples

Function that determines the support of a partial correlation/precision matrix by thresholding and sparsifies it accordingly.

1 2 3 |

`P` |
(Possibly regularized) precision |

`threshold` |
A |

`absValueCut` |
A |

`FDRcut` |
A |

`top` |
A |

`output` |
A |

`verbose` |
A |

The function transforms the possibly regularized input precision matrix to a partial correlation matrix.
Subsequently, the support of this partial correlation matrix is determined.
Support determination is performed either by simple thresholding on the absolute values of matrix entries (`threshold = "absValue"`

) or by usage of local FDR (`threshold = "localFDR"`

).
A third option is to retain a prespecified number of matrix entries based on absolute values.
For example, one could wish to retain those entries representing the ten strongest absolute partial correlations (`threshold = "top"`

).
As a variation on this theme, a fourth option (`threshold = "connected"`

) retains the top edges such that the resulting graph is connected (this may result in dense graphs in practice).
The argument `absValueCut`

is only used when `threshold = "absValue"`

.
The argument `top`

is only used when `threshold = "top"`

.
The argument `FDRcut`

is only used when `threshold = "localFDR"`

.

The function is to some extent a wrapper around certain fdrtool functions when `threshold = "localFDR"`

.
In that case a mixture model is fitted to the nonredundant partial correlations by fdrtool.
The decision to retain elements is then based on the argument `FDRcut`

.
Elements with a posterior probability *≥q* FDRcut (equalling 1 - local FDR) are retained.
See Schaefer and Strimmer (2005) for further details on usage of local FDR in graphical modeling.

If the input `P`

is a standardized precision (or partial correlation) matrix the function returns a sparsified
precision (or partial correlation) `matrix`

whenever `output = "heavy"`

.
If the input `P`

is an unstandardized precision matrix the function returns an object of class `list`

whenever `output = "heavy"`

:

`sparseParCor` |
A |

`sparsePrecision` |
A |

When `output = "light"`

, only the (matrix) positions of the zero and non-zero elements are returned in
an object of class `list`

:

`zeros` |
A |

`nonzeros` |
A |

Carel F.W. Peeters <[email protected]>, Wessel N. van Wieringen

Schaefer, J., and Strimmer, K. (2005). A shrinkage approach to large-scale covariance estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4:32.

`ridgeP`

, `optPenalty.aLOOCV`

, `optPenalty.LOOCV`

1 2 3 4 5 6 7 8 9 10 11 12 | ```
## Obtain some (high-dimensional) data
p = 25
n = 10
set.seed(333)
X = matrix(rnorm(n*p), nrow = n, ncol = p)
colnames(X)[1:25] = letters[1:25]
## Obtain regularized precision under optimal penalty
OPT <- optPenalty.LOOCV(X, lambdaMin = .5, lambdaMax = 30, step = 100)
## Determine support regularized (standardized) precision under optimal penalty
sparsify(OPT$optPrec, threshold = "localFDR")
``` |

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