lsmi_dd {snowboot}

Network Degree Distribution Estimated from Labeled Snowball Sample with Multiple Inclusion (LSMI)

Description

lsmi_dd computes an empirical network degree distribution and estimates mean degree based on data from an LSMI sample from a network; see Equations 6 and 7 by Thompson et al. (2016) and Equation 1 by Chen et al. (2018) on the details of the calculations.

Usage

lsmi_dd(x = NULL, net, ...)

Arguments

x

the LSMI sample obtained from the network net, for example, with lsmi function or as a subset of the output by lsmi_union.

net

a network object that is a list containing:

degree

the degree sequence of the network, which is an integer vector of length n;

edges

the edgelist, which is a two-column matrix, where each row is an edge of the network;

n

the network order (i.e., number of nodes in the network).

The network object can be simulated by random_network, selected from the networks available in artificial_networks, converged from an igraph object with igraph_to_network, etc.

...

arguments passed to the lsmi function (ignored if x is specified, see Details).

Details

The samples produced with lsmi or lsmi_union contain just node IDs arranged into lists of seeds and waves (no details on the node degrees or other node features). This information is sufficient to study some properties of a network (e.g., network motifs – not yet implemented in the package). To estimate a degree distribution or mean degree, both the LSMI sample and the original network object are required. If the LSMI object x is not supplied, the function will attempt sampling an LSMI automatically, using the arguments supplied in "..." that will be passed to the lsmi function.

Value

A list object of class "snowboot" consisting of:

fk

A named numeric vector with estimated probabilities \hat{f}(k) of degrees k, where k = 0, 1, \ldots, max(c(ds, dns)) (i.e., k ranges from 0 to the maximum node degree observed in the LSMI sample). The names of the vector elements are k.

mu

An estimate of the mean degree.

ds

An integer vector of degrees of seed nodes.

dns

An integer vector of degrees of non-seed nodes (i.e., nodes recorded in the waves of neighbors).

References

Chen Y, Gel YR, Lyubchich V, Nezafati K (2018). “Snowboot: bootstrap methods for network inference.” The R Journal, 10(2), 95–113. doi: 10.32614/RJ-2018-056.

Thompson ME, Ramirez Ramirez LL, Lyubchich V, Gel YR (2016). “Using the bootstrap for statistical inference on random graphs.” Canadian Journal of Statistics, 44(1), 3–24. doi: 10.1002/cjs.11271.

See Also

lsmi, lsmi_union, boot_dd

Examples

net <- artificial_networks[[1]]

#Obtain an LSMI sample and, at the next step,
#use it to estimate the degree distribution:
lsmiSample <- lsmi(net, n.seed = 5, n.wave = 3)
fkEstimate1 <- lsmi_dd(lsmiSample, net)$fk

#Obtain an LSMI sample and estimate the degree
#distribution in a single step:
fkEstimate2 <- lsmi_dd(net = net, n.seed = 5, n.wave = 3)$fk

#Use the output of lsmi_union to get the estimate:
lsmiUnionSample <- lsmi_union(net, n.seeds = c(5, 10), n.wave = 3)
fkEstimate3 <- lsmi_dd(lsmiUnionSample$lsmi_big, net)$fk