Generalized non-rejection rate estimation

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Description

Estimates generalized non-rejection rates for every pair of variables from two or more data sets.

Usage

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## S4 method for signature 'ExpressionSet'
qpGenNrr(X, datasetIdx=1, qOrders=NULL, I=NULL, restrict.Q=NULL,
                                   fix.Q=NULL, return.all=FALSE, nTests=100, alpha=0.05,
                                   pairup.i=NULL, pairup.j=NULL, verbose=TRUE, identicalQs=TRUE,
                                   exact.test=TRUE, use=c("complete.obs", "em"), tol=0.01,
                                   R.code.only=FALSE, clusterSize=1, estimateTime=FALSE,
                                   nAdj2estimateTime=10)
## S4 method for signature 'data.frame'
qpGenNrr(X, datasetIdx=1, qOrders=NULL, I=NULL, restrict.Q=NULL,
                                fix.Q=NULL, return.all=FALSE, nTests=100, alpha=0.05,
                                pairup.i=NULL, pairup.j=NULL, long.dim.are.variables=TRUE,
                                verbose=TRUE, identicalQs=TRUE, exact.test=TRUE,
                                use=c("complete.obs", "em"), tol=0.01, R.code.only=FALSE,
                                clusterSize=1, estimateTime=FALSE, nAdj2estimateTime=10)
## S4 method for signature 'matrix'
qpGenNrr(X, datasetIdx=1, qOrders=NULL, I=NULL, restrict.Q=NULL,
                            fix.Q=NULL, return.all=FALSE, nTests=100, alpha=0.05,
                            pairup.i=NULL, pairup.j=NULL, long.dim.are.variables=TRUE,
                            verbose=TRUE, identicalQs=TRUE, exact.test=TRUE,
                            use=c("complete.obs", "em"), tol=0.01, R.code.only=FALSE,
                            clusterSize=1, estimateTime=FALSE, nAdj2estimateTime=10)

Arguments

X

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

datasetIdx

either a single number, or a character string, indicating the column in the phenotypic data of the ExpressionSet object, or in the input matrix or data frame, containing the indexes to the data sets. Alternatively, it can be a vector of these indexes with as many positions as samples.

qOrders

either a NULL value (default) indicating that a default guess on the q-order will be employed for each data set or a vector of particular orders with one for each data set. The default guess corresponds to the floor of the median value among the valid q orders of the data set.

I

indexes or names of the variables in X that are discrete. When X is an ExpressionSet then I may contain only names of the phenotypic variables in X. See details below regarding this argument.

restrict.Q

indexes or names of the variables in X that restrict the sample space of conditioning subsets Q.

fix.Q

indexes or names of the variables in X that should be fixed within every conditioning conditioning subsets Q.

return.all

logical; if TRUE all intervining non-rejection rates will be return in a matrix per dataset within a list; FALSE (default) if only generalized non-rejection rates should be returned.

nTests

number of tests to perform for each pair for variables.

alpha

significance level of each test.

pairup.i

subset of vertices to pair up with subset pairup.j

pairup.j

subset of vertices to pair up with subset pairup.i

long.dim.are.variables

logical; if TRUE it is assumed that when the data is a data frame or a matrix, the longer dimension is the one defining the random variables; if FALSE, then random variables are assumed to be at the columns of the data frame or matrix.

verbose

show progress on the calculations.

identicalQs

use identical conditioning subsets for every pair of vertices (default), otherwise sample a new collection of nTests subsets for each pair of vertices.

exact.test

logical; if FALSE an asymptotic conditional independence test is employed with mixed (i.e., continuous and discrete) data; if TRUE (default) then an exact conditional independence test with mixed data is employed.

use

a character string defining the way in which calculations are done in the presence of missing values. It can be either "complete.obs" (default) or "em".

tol

maximum tolerance controlling the convergence of the EM algorithm employed when the argument use="em".

R.code.only

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

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 snow and rlecuyer.

estimateTime

logical; if TRUE then the time for carrying out the calculations with the given parameters is estimated by calculating for a limited number of adjacencies, specified by nAdj2estimateTime, and extrapolating the elapsed time; if FALSE (default) calculations are performed normally till they finish.

nAdj2estimateTime

number of adjacencies to employ when estimating the time of calculations (estimateTime=TRUE). By default this has a default value of 10 adjacencies and larger values should provide more accurate estimates. This might be relevant when using a cluster facility.

Details

Note that when specifying a vector of particular orders q, these values should be in the range 1 to min(p,n-3), where p is the number of variables and n the number of observations for the corresponding data set. The computational cost increases linearly within each q value and quadratically in p. When setting identicalQs to FALSE the computational cost may increase between 2 times and one order of magnitude (depending on p and q) while asymptotically the estimation of the non-rejection rate converges to the same value.

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. In this setting further restrictions to the maximum value of q apply, concretely, it cannot be smaller than p plus the number of levels of the discrete variables involved in the marginal distributions employed by the algorithm. 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 containing the following two or more entries: a first one with name genNrr with a dspMatrix-class symmetric matrix of estimated generalized non-rejection rates with the diagonal set to NA values. When using the arguments pairup.i and pairup.j, those cells outside the constraint pairs will get also a NA value; a second one with name qOrders with the q-orders employed in the calculation for each data set; if return.all=TRUE then there will be one additional entry for each data set containing the matrix of the non-rejection rates estimated from that data set with the corresponding q-order, using the indexing value of the data set as entry name.

Note, however, that when estimateTime=TRUE, then instead of the list with matrices of estimated (generalized) 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 and A. Roverato

References

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

Tur, I., Roverato, A. and Castelo, R. Mapping eQTL networks with mixed graphical Markov models. Genetics, 198:1377-1393, 2014.

See Also

qpNrr qpAvgNrr qpEdgeNrr qpHist qpGraphDensity qpClique

Examples

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

set.seed(123)

## simulate two independent Gaussian graphical models determined
## by two undirected d-regular graphs
model1 <- rUGgmm(dRegularGraphParam(p=nVar, d=maxCon), rho=0.5)
model2 <- rUGgmm(dRegularGraphParam(p=nVar, d=maxCon), rho=0.5)

## simulate two independent data sets from the previous graphical models
X1 <- rmvnorm(nObs, model1)
dim(X1)
X2 <- rmvnorm(nObs, model2)
dim(X2)

## estimate generalized non-rejection rates from the joint data
nrr.estimates <- qpGenNrr(rbind(X1, X2),
                          datasetIdx=rep(1:2, each=nObs),
                          qOrders=c("1"=5, "2"=5),
                          long.dim.are.variables=FALSE, verbose=FALSE)

## create adjacency matrices from the undirected graphs
## determining the two Gaussian graphical models
A1 <- as(model1$g, "matrix") == 1
A2 <- as(model2$g, "matrix") == 1

## distribution of generalized non-rejection rates for the common present edges
summary(nrr.estimates$genNrr[upper.tri(nrr.estimates$genNrr) & A1 & A2])

## distribution of generalized non-rejection rates for the present edges specific to A1
summary(nrr.estimates$genNrr[upper.tri(nrr.estimates$genNrr) & A1 & !A2])

## distribution of generalized non-rejection rates for the present edges specific to A2
summary(nrr.estimates$genNrr[upper.tri(nrr.estimates$genNrr) & !A1 & A2])

## distribution of generalized non-rejection rates for the common missing edges
summary(nrr.estimates$genNrr[upper.tri(nrr.estimates$genNrr) & !A1 & !A2])

## compare with the average non-rejection rate on the pooled data set
avgnrr.estimates <- qpNrr(rbind(X1, X2), q=5, long.dim.are.variables=FALSE, verbose=FALSE)

## distribution of average non-rejection rates for the common present edges
summary(avgnrr.estimates[upper.tri(avgnrr.estimates) & A1 & A2])

## distribution of average non-rejection rates for the present edges specific to A1
summary(avgnrr.estimates[upper.tri(avgnrr.estimates) & A1 & !A2])

## distribution of average non-rejection rates for the present edges specific to A2
summary(avgnrr.estimates[upper.tri(avgnrr.estimates) & !A1 & A2])

## distribution of average non-rejection rates for the common missing edges
summary(avgnrr.estimates[upper.tri(avgnrr.estimates) & !A1 & !A2])

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