gof_sim {multigraphr}

Goodness of fit test simulations for random multigraph models

Description

Goodness of fits test simulations of specified multigraph models using Pearson (S) and information divergence (A) test statistics under the random stub matching (RSM) and the independent edge assignments (IEA) model, where the latter is either independent edge assignments of stubs (IEAS) or independent stub assignment (ISA).

These can be used to check the reliability of the tests by examining the exact probability distributions of the test statistics and their fit to their asymptotic chi^2-distributions. Only practical for small multigraphs as exact distributions are calculated.

Usage

gof_sim(m, model, deg.mod, hyp, deg.hyp)

Arguments

m

integer giving number of edges in multigraph.

model

character string representing assumed model, either 'RSM', 'IEAS' or 'ISA'.

deg.mod

vector of integers with the sum equal to 2m representing the degree sequence of the multigraph under specified model.

hyp

character string representing the hypothesized null model, either 'IEAS' or 'ISA'.

deg.hyp

vector of integers with the sum equal to to 2m representing the hypothetical degree sequence of the multigraph under the null model:
- if hyp = 'IEAS', then simple IEAS hypothesis with fully specified degree sequence deg.hyp
- if hyp = 'ISA', then simple ISA hypothesis with with fully specified stub assignment probabilities deg.hyp/2m
- if hyp = 'IEAS' and deg.hyp = 0, then composite IEAS hypothesis with edge multiplicity sequence estimated from data
- if hyp = 'ISA' and deg.hyp = 0, then composite ISA hypothesis with edge multiplicity sequence estimated from data

Details

The tests are performed using goodness-of-fit measures between simulated edge multiplicity sequence of a multigraph according to an RSM or IEA model, and the expected multiplicity sequence according to a simple or composite IEA hypothesis.

Test statistics of Pearson type (S) and of information divergence (A) type are used and summary of tests given these two statistics are given as output. The adjusted statistics and chi^2-distributions are useful for better power calculations.

Value

Output is generated from function gof_stats:

test.summary

Expected value and variances of test statistics (stat), critical values (cv) according to asymptotic chi^2-distribution and according to cdf's of test statistics, significance level (alpha) according to asymptotic chi^2 distribution, power of tests (P(stat>cv)), critical values and power according to the distributions of test statistics (cv(stat) and P(Stat>cv(Stat))).

degrees.of.freedom

Degrees of freedom for tests performed.

probS

Probability distributions of Pearson statistic S.

probA

Probability distributions of information divergence statistic A.

adjusted.stats

Expected values and variances for adjusted test statistics, preferred adjusted statistics.

adjusted.chi2

Degrees of freedom for adjusted chi^2-distribution.

power.apx

Power approximations according to adjusted statistics.

Author(s)

Termeh Shafie

References

Shafie, T. (2015). A Multigraph Approach to Social Network Analysis. Journal of Social Structure, 16.

Shafie, T. (2016). Analyzing Local and Global Properties of Multigraphs. The Journal of Mathematical Sociology, 40(4), 239-264.

See Also

gof_stats,get_edge_assignment_probs, nsumk,rsm_model

Examples

# Testing a simple IEAS hypothesis with degree sequence [6,6,6] against
# an IEAS model with degree sequence [14,2,2] on a multigraph with n = 3 nodes and m = 9 edges
deg.mod <- c(14,2,2)
deg.hyp <- c(6,6,6)
test1 <- gof_sim(9, 'IEAS', deg.mod, 'IEAS', deg.hyp)

# Non-null distributions (pdf's and cdf's) of test statistics S and A are given by
test1$probS
test1$probA

# Testing a simple ISA hypothesis with degree sequence [6,6,6] against
# an IEAS model with degree sequence [12,3,3] on a multigraph with n = 3 nodes and m = 9 edges
deg.mod <- c(12,3,3)
deg.hyp <- c(6,6,6)
test2 <- gof_sim(9, 'IEAS', deg.mod, 'ISA', deg.hyp)

# Testing a composite IEAS hypothesis against
# an RSM model with degree sequence [6,6,6,6] on a multigraph with n = 4 nodes and m = 20 edges.
deg.mod <- c(6,6,6,6)
test3 <- gof_sim(12, 'RSM', deg.mod, 'IEAS', deg.hyp = 0)