atm {cssTools}

Estimate a Network Using the Adaptive Threshold Method

Description

Estimate a network of interest by aggregating the sampled CSS slices using the adaptive threshold method. This requires setting a tolerable level of type 1 error.

Usage

atm(d, sampled, alpha)

Arguments

d

Sampled CSS slices in cssTools package format.

sampled

A vector indicating which network individuals are sampled.

alpha

Tolerable type 1 error.

Details

Given a random sample of observed CSS slices and a tolerable type 1 error, the atm function uses the adaptive threshold method (ATM) of Siciliano et. al. (2012) to aggregate the observed slices and provides an estimate for the network of interest.

Value

estimatedNetwork

An estimate of the network of interest.

threshold

The threshold value required to reach the given type 1 error rate.

Author(s)

Deniz Yenigun, Gunes Ertan, Michael Siciliano

References

M.D. Siciliano, D. Yenigun, G. Ertan (2012). Estimating network structure via random sampling: Cognitive social structures and adaptive threshold method. Social Networks, Vol. 34, No. 4, 585-600. http://dx.doi.org/10.1016/j.socnet.2012.06.004

See Also

ftm, rtm

Examples

# Consider the example in Siciliano et. al. (2012),
# a network with five actors A, B, C, D, E
sA=matrix(c(0,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0),5,5)
sB=matrix(c(0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0),5,5)
sC=matrix(c(0,1,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0),5,5)
sD=matrix(c(0,0,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0),5,5)
sE=matrix(c(0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0),5,5)
d=array(dim=c(5,5,5))
d[,,1]=sA
d[,,2]=sB
d[,,3]=sC
d[,,4]=sD
d[,,5]=sE

# Suppose you randomly sampled A, D, and E
sampled=c(1,4,5)

# Then all you have is the following three sampled slices of A, D and E
dSampled=d[,,sampled]

# For a given alpha value, say 0.2, we can combine these slices as follows,
# which gives an estimate of the complete network 
atm(dSampled,sampled,0.2)