Cognitive Social Structure Tools

Description

Formalized by Krackhardt (1987), Cognitive Social Structure (CSS) network studies collect relational data on respondents direct ties and their cognition of ties among all other individuals in the network. This package provides a collection of tools for estimating a network from a random sample of CSS slices. The package also contains functions for evaluating a CSS in terms of various error types observed in each slice.

Details

The DESCRIPTION file:

Index of help topics:

atm                     Estimate a Network Using the Adaptive Threshold
                        Method
cssTools-package        Cognitive Social Structure Tools
cssTools2sna            Convert a CSS in 'cssTools' Format to a CSS in
                        'sna' Format
ftm                     Aggregate CSS Slices for a Fixed Threshod
highTechManagers        High Tech Managers Data Set
rtm                     Estimate a Network Using the ROC Based
                        Threshold Method
rtmPlot                 Plots for the ROC Based Threshold Method for
                        Estimating Networks
s14                     Calculate s14 Similarity Index
sliceQuality            Evaluate Several Characteristics of Slices from
                        a CSS
sna2cssTools            Convert a CSS in 'sna' Format to a CSS in
                        'cssTools' Format

Author(s)

Deniz Yenigun, Gunes Ertan, Michael Siciliano Maintainer: Deniz Yenigun <deniz.yenigun@bilgi.edu.tr>

References

Krackhardt, D. (1987). Cognitive social structures. Social Networks 9, 109-134. http://dx.doi.org/10.1016/0378-8733(87)90009-8

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, cssTools2sna, ftm, highTechManagers, rtm, rtmPlot, s14, sliceQuality, sna2cssTools

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

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

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)

Convert a CSS in cssTools Format to a CSS in sna Format

Description

Converts a CSS in cssTools package format to a CSS in sna package format.

Usage

cssTools2sna(d)

Arguments

Details

In cssTools package, a CSS d is coded in a three dimensional array such that d[,,i] is the i-th slice. In sna package, the same object is coded in a three dimensional array such that d[i,,] is the i-th slice. The cssTools2sna function transforms cssTools format to sna format.

Value

The same CSS coded in sna format.

Author(s)

Deniz Yenigun, Gunes Ertan, Michael Siciliano

See Also

sna2cssTools

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

# Here d is coded in cssTools package format
# Switching between sna and cssTools formats
e=cssTools2sna(d)
f=sna2cssTools(e)

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

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

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)

High Tech Managers Data Set

Description

Krackhardt (1987) reports the CSS data collected from 21 managers in a high tech machinery firm. Perceptions of all individuals on the whole network is provided.

Usage

data(highTechManagers)

Format

A 21 by 21 by 21 array of zeroes (nonexistence of tie) and ones (existence of tie), where the perception slice of the i-th individual correspons to highTechManagers[,,i].

Details

In a CSS data set, each actor not only reports his or her self-ties, but also answers questions on all possible ties in the network. Then a CSS for a network involving N individuals may be represented by a three dimensional array R_{i,j,m} (i,j,m=1,...,N), where i is the sender, j is the receiver, and m is the perceiver of the relationship. This data set contains the CSS given in Krackhardt (1987), which reports the perceptions of all individuals in a network of 21 managers in a high tech machinery firm. In the original data 17th slice is problematic since row 17 in this slice consists of ones only. To overcome this, we replaced row 17 with column 17.

References

Krackhardt, D. (1987). Cognitive social structures. Social Networks 9, 109-134. http://dx.doi.org/10.1016/0378-8733(87)90009-8

Examples

data(highTechManagers)
sliceQuality(highTechManagers)

Estimate a Network Using the ROC Based Threshold Method

Description

Estimate a network of interest by aggregating the sampled CSS slices using the ROC based threshold method.

Usage

rtm(d, sampled)

Arguments

Details

Given a random sample of observed CSS slices, the rtm function uses the density weighted ROC based threshold method (RTM) of Yenigun et. al. (2016) to aggregate the observed slices, and provides an estimate for the network of interest. Slice densities are computed by the gden function in the sna package.

Value

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, ftm

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]

# We can combine these slices as follows, 
# which gives an estimate of the complete network
rtm(dSampled,sampled)

Plots for the ROC Based Threshold Method for Estimating Networks

Description

Visualisation of the ROC based threshold method for estimating networks, implemented by the rtm function.

Usage

rtmPlot(rtmOutput)

Arguments

Details

The function rtm uses the density weighted ROC based threshold method (RTM) of Yenigun et. al. (2016) for estimating networks from a random sample of CSS slices. The output from rtm is visualized by the function rtmPlot, which displays the ROC curve, as well as the type 1 and type 2 error counts for each threshold value.

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

rtm

Examples

# Load the highTechManagers data given in cssTools package
data(highTechManagers)

# There are 21 CSS slices in the complete data 
# Suppose we only observed the 10 slices with the following indexes
sampled=c(2,4,5,8,9,10,11,14,18,19)

# Then the observed data is the following
dSampled=highTechManagers[,,sampled]

# Apply the ROC based threshold method to estimate the network
y=rtm(dSampled,sampled)

# Now plot the ROC curve and the error types for various threshold values
rtmPlot(y)

Calculate s14 Similarity Index

Description

Computes the S_{14} similarity index between two network matrices.

Usage

s14(d1, d2)

Arguments

Details

Given two networks of interest, a common measure of similarity is the S_{14} index introduced by Gower and Lagendre (1986). The function s14 computes this similarity measure for two networks having the same dimensions.

Value

The S_{14} similarity index.

Author(s)

Deniz Yenigun, Gunes Ertan, Michael Siciliano

References

Gower, J.C., Legendre, P. (1986). Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5-48. http://dx.doi.org/10.1007/BF01896809

See Also

sliceQuality

Examples

# Consider two matrices representing networks, d1 and d2
d1=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)
d2=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)

# The similarity index between d1 and d2
s14(d1,d2)

Evaluate Several Characteristics of Slices from a CSS

Description

Given a fully observed CSS, this function evaluates the quality of each slice by comparing them with the true network obtained by LAS intersection.

Usage

sliceQuality(d)

Arguments

Details

A common way of defining a true network for a given CSS is the LAS intersection (see, for example, Siciliano et. al. 2012, or Krackhardt, 1987). For a given CSS, the function sliceQuality first computes the true network by LAS intersection, and then compares each slice with the true network. The considered quantities are matching zeros, matching ones, type 1 errors, type 2 errors, S_{14} similarity index, error proportion and correlation.

Value

Author(s)

Deniz Yenigun, Gunes Ertan, Michael Siciliano

References

Krackhardt, D. (1987). Cognitive social structures. Social Networks 9, 109-134. http://dx.doi.org/10.1016/0378-8733(87)90009-8

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

s14

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

# Compute the quality of CSS slices
sliceQuality(d)

Convert a CSS in sna Format to a CSS in cssTools Format

Description

Converts a CSS in sna package format to a CSS in cssTools package format.

Usage

sna2cssTools(d)

Arguments

Details

In sna package, a CSS d is coded in a three dimensional array such that d[i,,] is the i-th slice. In cssTools package, the same object is coded in a three dimensional array such that d[,,i] is the i-th slice. The sna2cssTools function transforms sna format to cssTools format.

Value

The same CSS coded in cssTools format.

Author(s)

Deniz Yenigun, Gunes Ertan, Michael Siciliano

See Also

cssTools2sna

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

# Here d is coded in cssTools package format
# Switching between sna and cssTools formats
e=cssTools2sna(d)
f=sna2cssTools(e)