Estimates partial correlation coefficients (PACs) for a Gaussian graphical model with undirected graph G and their corresponding p-values for the null hypothesis of zero-partial correlation.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
## S4 method for signature 'ExpressionSet'
qpPAC(X, g, return.K=FALSE, tol=0.001,
matrix.completion=c("HTF", "IPF"), verbose=TRUE,
R.code.only=FALSE)
## S4 method for signature 'data.frame'
qpPAC(X, g, return.K=FALSE, long.dim.are.variables=TRUE,
tol=0.001, matrix.completion=c("HTF", "IPF"),
verbose=TRUE, R.code.only=FALSE)
## S4 method for signature 'matrix'
qpPAC(X, g, return.K=FALSE, long.dim.are.variables=TRUE,
tol=0.001, matrix.completion=c("HTF", "IPF"),
verbose=TRUE, R.code.only=FALSE)
``` |

`X` |
data set from where to estimate the partial correlation coefficients. It can be an ExpressionSet object, a data frame or a matrix. |

`g` |
either a |

`return.K` |
logical; if TRUE this function also returns the concentration
matrix |

`long.dim.are.variables` |
logical; if TRUE it is assumed
that when |

`tol` |
maximum tolerance in the application of the IPF algorithm. |

`matrix.completion` |
algorithm to employ in the matrix completion operations
employed to construct a positive definite matrix with the
zero pattern specified in |

`verbose` |
show progress on the calculations. |

`R.code.only` |
logical; if FALSE then the faster C implementation is used (default); if TRUE then only R code is executed. |

In the context of maximum likelihood estimation (MLE) of PACs it is a necessary
condition for the existence of MLEs that the sample size `n`

is larger
than the clique number `w(G)`

of the graph `G`

. If the sample size
`n`

is larger than the maximum boundary of the input graph `bd(G)`

,
then the default matrix completion algorithm HTF by Hastie, Tibshirani and
Friedman (2009) can be used (see the function `qpHTF()`

for details),
which has the avantage that is faster than IPF (see the function
`qpIPF()`

for details).

The PAC estimation is done by first obtaining a MLE of the covariance matrix
using the `qpIPF`

function and the p-values are calculated based on
the estimation of the standard errors (see Roverato and Whittaker, 1996) and
performing Wald tests based on the asymptotic chi-squared distribution.

A list with two matrices, one with the estimates of the PACs and the other with
their p-values. If `return.K=TRUE`

then the MLE of the inverse covariance is
also returned as part of the list.

R. Castelo and A. Roverato

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.

Castelo, R. and Roverato, A. Reverse engineering molecular regulatory
networks from microarray data with qp-graphs. *J. Comp. Biol.*,
16(2):213-227, 2009.

Hastie, T., Tibshirani, R. and Friedman, J.H. *The Elements of Statistical Learning*,
Springer, 2009.

Roverato, A. and Whittaker, J. Standard errors for the parameters of graphical
Gaussian models. *Stat. Comput.*, 6:297-302, 1996.

`qpGraph`

`qpCliqueNumber`

`qpClique`

`qpGetCliques`

`qpIPF`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
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))
nrr.estimates <- qpNrr(X, verbose=FALSE)
qpg <- qpGraph(nrr.estimates, epsilon=0.5)
qpg$g
pac.estimates <- qpPAC(X, g=qpg, verbose=FALSE)
## distribution absolute values of the estimated
## partial correlation coefficients of the present edges
summary(abs(pac.estimates$R[upper.tri(pac.estimates$R) & A]))
## distribution absolute values of the estimated
## partial correlation coefficients of the missing edges
summary(abs(pac.estimates$R[upper.tri(pac.estimates$R) & !A]))
``` |

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