atm: Estimate a Network Using the Adaptive Threshold Method In cssTools: Cognitive Social Structure Tools

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

 `1` ```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

`ftm`, `rtm`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```# 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) ```