Goodness of fit statistics for unipartite networks — gof_stats

Calculates goodness of fit statistics specifically for unipartite (square) networks, evaluating second-order (dyadic) and third-order (triadic) dependence patterns.

Usage

gof_stats_unipartite(Y)

Arguments

Y: a square n x n relational data matrix where Y[i,j] represents the relationship from node i to node j. Missing values (NA) are allowed and will be handled appropriately. Diagonal values are typically NA for non-self-loop networks.

Value

A named numeric vector containing five goodness-of-fit statistics:

sd.rowmean: Standard deviation of row means. Measures the heterogeneity in out-degree centrality (sender effects).
sd.colmean: Standard deviation of column means. Measures the heterogeneity in in-degree centrality (receiver effects).
dyad.dep: Dyadic dependence/reciprocity correlation. Measures the correlation between Y[i,j] and Y[j,i], capturing reciprocity patterns.
cycle.dep: Cyclic triadic dependence. Measures the tendency for directed cycles (i->j->k->i) in the network.
trans.dep: Transitive triadic dependence. Measures the tendency for transitivity (if i->j and j->k, then i->k) in the network.

Details

This function computes network statistics that capture different aspects of network structure beyond simple density. These statistics are particularly useful for evaluating how well a model captures the observed network patterns.

The dyadic dependence statistic captures reciprocity - the tendency for relationships to be mutual. The triadic statistics capture different forms of triadic closure that are common in social networks.

Missing values in Y are handled by pairwise deletion for correlations and are excluded from matrix products in triadic calculations.

Author

Cassy Dorff, Shahryar Minhas, Tosin Salau

Examples


# Create a random unipartite network
Y <- matrix(rnorm(100), 10, 10)
diag(Y) <- NA
gof_stats_unipartite(Y)
#>   sd.rowmean   sd.colmean     dyad.dep    cycle.dep    trans.dep 
#>  0.226494520  0.280922809 -0.131141047 -0.056931045 -0.003309911