# Tests of conditional independence

### Description

Performs a test of conditional independence for every pair of variables.

### Usage

1 2 3 4 5 6 7 | ```
## S4 method for signature 'matrix'
qpAllCItests(X, I=NULL, Q=NULL, pairup.i=NULL, pairup.j=NULL,
long.dim.are.variables=TRUE, exact.test=TRUE,
use=c("complete.obs", "em"), tol=0.01,
return.type=c("p.value", "statn", "all"), verbose=TRUE,
R.code.only=FALSE, clusterSize=1, estimateTime=FALSE,
nAdj2estimateTime=10)
``` |

### Arguments

`X` |
data set from where to estimate the non-rejection rates. It can be an ExpressionSet object, a data frame or a matrix. |

`I` |
indexes or names of the variables in |

`Q` |
indexes or names of the variables in |

`pairup.i` |
subset of vertices to pair up with subset |

`pairup.j` |
subset of vertices to pair up with subset |

`long.dim.are.variables` |
logical; if |

`exact.test` |
logical; if |

`use` |
a character string defining the way in which calculations are done in the
presence of missing values. It can be either |

`tol` |
maximum tolerance controlling the convergence of the EM algorithm employed
when the argument |

`return.type` |
type of value returned by this function. By default |

`verbose` |
show progress on the calculations. |

`R.code.only` |
logical; if |

`clusterSize` |
size of the cluster of processors to employ if we wish to
speed-up the calculations by performing them in parallel. A value of 1
(default) implies a single-processor execution. The use of a cluster of
processors requires having previously loaded the packages |

`estimateTime` |
logical; if |

`nAdj2estimateTime` |
number of adjacencies to employ when estimating the
time of calculations ( |

### Details

When `I`

is set different to `NULL`

then mixed graphical model theory
is employed and, concretely, it is assumed that the data comes from an homogeneous
conditional Gaussian distribution. By default, with `exact.test=TRUE`

, an
exact test for conditional independence is employed, otherwise an asymptotic one
will be used. Full details on these features can be found in Tur, Roverato and Castelo (2014).

### Value

A list with three entries called `p.value`

, `statistic`

and `n`

corresponding to a `dspMatrix-class`

symmetric matrix of p-values for the null
hypothesis of coindtional independence with the diagonal set to `NA`

values,
an analogous matrix of the statistics of each test and of the sample sizes, respectively.
These returned values, however, depend on the setting of argument `return.type`

which,
by default, enables only returning the matrix of p-values.
If arguments `pairup.i`

and `pairup.j`

are employed, those cells outside
the constrained pairs will get also a `NA`

value.

Note, however, that when `estimateTime=TRUE`

, then instead of the matrix
of estimated non-rejection rates, a vector specifying the estimated number of
days, hours, minutes and seconds for completion of the calculations is returned.

### Author(s)

R. Castelo, A. Roverato and I. Tur

### 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.

Tur, I., Roverato, A. and Castelo, R. Mapping eQTL networks with mixed graphical models.
*Submitted*, http://arxiv.org/abs/1402.4547, 2014.

### See Also

`qpCItest`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
library(mvtnorm)
nVar <- 50 ## number of variables
maxCon <- 3 ## 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))
alltests <- qpAllCItests(X, verbose=FALSE)
## distribution of p-values for the present edges
summary(alltests$p.value[upper.tri(alltests$p.value) & A])
## distribution of p-values for the missing edges
summary(alltests$p.value[upper.tri(alltests$p.value) & !A])
``` |

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