binom.stat: Binomial Scan Statistic

In TunChiehHsu/SNscan: Scan Statistics in Social Networks

Description

The binomial scan statistic evaluate the statistic which compares the node attribute within the subgraph with that outside the subgraph while the node attribute follows the binomial distribution.

Usage

binom.stat(obs, pop, zloc)

Arguments

obs	Numeric vector of observation values.
pop	Numeric vector of population values.
zloc	Numeric vector of selected nodes.

Details

A network with interested attributes is denoted as G=(V,E,X), where X=(x_1,…,x_{|V|}) follows a defined distribution. Suppose a subgraph, Z, is selected.

λ_A(Z) =n_z \ln\big(\frac{p_{11}}{p_0}\big)+ (N_z-n_z) \ln\big(\frac{1-p_{11}}{1-p_0}\big) +(n_G-n_z) \ln\big(\frac{p_{10}}{p_0}\big) +[(N_G-N_z)-(n_G-n_z)] \ln\big(\frac{1-p_{10}}{1-p_0}\big),

where p_0=n_G/N_G, p_{10}=(n_G-n_z)/(N_G-N_z), and p_{11}=n_z/N_z, in which N_G and n_G are population sizes and number of successful cases respectively in the whole graph G, and N_Z and n_Z are similarly expressed in a selected subgraph Z, are estimated by the likelihood function.

Value

Three values will be returned. The first value is test statistic. The second is the estimated means which estimated outside the selected nodes. The third is estimated means estimated within the selected nodes.

Author(s)

Taichi Wang <[e-mail]>

References

Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics-Theory and methods, 26(6), 1481–1496.

Examples

binom.stat(obs=rbinom(n=100, size=10000, prob=0.0001),pop=rep(10000,100),zloc=1:5)

TunChiehHsu/SNscan documentation built on May 9, 2019, 5:15 p.m.