aSHD {MRPC}

Adjusted structural hamming distance (aSHD)

Description

The SHD as implemented in the R package pcalg (Kalisch et al., 2012) and bnlearn(Scutari, 2010), counts how many differences exist between two directed graphs. This distance is 1 if an edge exists in one graph but is missing in the other, or if the direction of an edge is different between the two graphs. The larger this distance is the more different the two graphs are. We adjusted the SHD to reduce the penalty of having the wrong direction of an edge to 0.5. For example, between two graphs V –> T1 <– T2 and V –> T1 –> T2, the SHD is 1 and the aSHD is 0.5.

Usage

aSHD(g1, g2, GV,edge.presence = 1.0, edge.direction = 0.5)

Arguments

g1

First graph object

g2

Second graph object

GV

The number of genetic variants (SNPs/indels/CNV/eQTL) in the input data matrix. For example, if the data has one genetic variant, first column, then GV = 1, if 2, 1st and 2nd column, then GV = 2, and so on.

edge.presence

The weight for an edge being present.

edge.direction

The weight for the edge direction.

Author(s)

Md Bahadur Badsha ([e-mail])

References

1. Kalisch M, Machler M, Colombo D, Maathuis MH and Buhlmann P (2012). Causal Inference Using Graphical Models with the R Package pcalg. Journal of Statistical Software, 47, 26.

2. Scutari M (2010). Learning Bayesian Networks with the bnlearn R Package. Journal of Statistical Software, 35(3), 1-22.

Examples

# True model (V1 --> T1 --> T2 --> T3)
tarmat_s1 <- matrix(0,
                    nrow = 4,
                    ncol = 4)
                    
colnames(tarmat_s1) <- c("V1", "T1", "T2", "T3")

rownames(tarmat_s1) <- colnames(tarmat_s1)

# Create an adjacency matrix for the true graph
tarmat_s1[1, 2] <- 1
tarmat_s1[2, 3] <- 1
tarmat_s1[3, 4] <- 1

# Graph object of the true graph
Truth <- as(tarmat_s1,
            "graphNEL")


# Inferred graph (V1 --> T1 <-- T2 --> T3)
tarmat_s2 <- matrix(0,
                    nrow = 4,
                    ncol = 4)
                    
colnames(tarmat_s2) <-c ("V1", "T1", "T2", "T3")

rownames(tarmat_s2) <- colnames(tarmat_s2)

# Create an adjacency matrix for the inferred graph
tarmat_s2[1, 2] <- 1
tarmat_s2[3, 2] <- 1
tarmat_s2[3, 4] <- 1

# Graph objects for the inferred graph
Inferred <- as(tarmat_s2,
               "graphNEL")

Distance <- aSHD(Truth,
                 Inferred,
                 GV = 1,
                 edge.presence = 1.0,
                 edge.direction = 0.5)