qpPathWeight: Calculation of path weights
In qpgraph: Estimation of genetic and molecular regulatory networks from high-throughput genomics data

Description Usage Arguments Details Value Author(s) References Examples

Calculates the path weight for a path of an undirected graph.

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## S4 method for signature 'matrix'
qpPathWeight(X, path, Q=integer(0), M=integer(0),
                                normalized=TRUE, R.code.only=TRUE)

`X`	covariance matrix.
`path`	character vector of consecutive vertex names defining a path in an undirected graph.
`Q`	indexes or names of the variables in `sigma` that should be used for conditioning.
`M`	indexes or names of the variables in `sigma` over which we want to marginalize.
`normalized`	logical; TRUE (default) when the calculated path weight should be normalized so that weights are comparable between paths with different endpoints, and false otherwise.
`R.code.only`	logical; if FALSE then the faster C implementation is used (not yet available); if TRUE then only R code is executed (default).

Calculation of path weights. This implementation is still under development and will give only correct results with either population covariance matrices or sample covariance matrices estimated from data with n >> p. Consult (Roverato and Castelo, 2017) for further details.

The calculated path weight for the given path.

R. Castelo and A. Roverato

Roverato, A. and Castelo, R. The networked partial correlation and its application to the analysis of genetic interactions. J. R. Stat. Soc. Ser. C-Appl. Stat., 66:647-665, 2017. http://dx.doi.org/10.1111/rssc.12166

## example in Figure 1 from (Castelo and Roverato, 2017)

## undirected graph on 9 vertices
edg <- matrix(c(1, 4,
                2, 4,
                3, 4,
                4, 5,
                5, 6,
                5, 7,
                8, 9),
            ncol=2, byrow=TRUE)

## create a corresponding synthetic precision matrix with
## partial correlation values set to -0.4 for all present edges
K <- matrix(0, nrow=9, ncol=9, dimnames=list(1:9, 1:9))
K[edg] <- -0.4
K <- K + t(K)
diag(K) <- 1

## calculate the corresponding covariance matrix
S <- solve(K)

## calculate networked partial correlations for all present
## edges
npc <- sapply(1:nrow(edg), function(i) qpPathWeight(S, edg[i, ]))

## note that while all partial correlations are zero for missing
## edges and are equal to -0.4 for present edges, the corresponding
## networked partial correlations are also zero for missing edges
## but may be different between them for present edges, depending on
## the connections between the vertices
cbind(edg, npc)