ftm {cssTools}

Aggregate CSS Slices for a Fixed Threshod

Description

Estimate a network of interest by aggregating the sampled CSS slices for a fixed threshold.

Usage

ftm(d, sampled, k)

Arguments

d

Sampled CSS slices in cssTools package format.

sampled

A vector indicating which network individuals are sampled.

k

A threshold for aggregating the CSS slices.

Details

Given a random sample of observed CSS slices and a fixed threshold value k for aggregation, the ftm function aggregates the observed slices and provides an estimate for the network of interest by using the fixed threshold method (FTM) given in Yenigun et. al. (2016). The function also returns the estimated type 1 and type 2 errors.

Value

estimatedNetwork

An estimate of the network of interest.

type1Error

Estimated type 1 error rate.

type2Error

Estimated type 2 error rate.

type1Count

Total number of type 1 errors committed.

type1Instances

Number of instances for a potential type 1 error. In other words, number of zeros in the knowledge region of the true network. Here by knowledge region we mean the ties in the network such that both actors are sampled, and the tie is estimated by the intersection of the self reports from both actors. Note that type1Error equals type1Count divided by type1Instances.

type2Count

Total number of type 2 errors committed.

type2Instances

Number of instances for a potential type 2 error. In other words, number of ones in the knowledge region of the true network. Note that type2Error equals type2Count divided by type2Instances.

Author(s)

Deniz Yenigun, Gunes Ertan, Michael Siciliano

References

D. Yenigun, G. Ertan, M.D. Siciliano (2016). Omission and commission errors in network cognition and estimation using ROC curve. arXiv:1606.03245 [stat.CO] https://arxiv.org/abs/1606.03245

See Also

atm, 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 threshold, say 2, we can combine these slices as follows,
# which gives an estimate of the complete network 
ftm(dSampled,sampled,2)