Goodness of fit statistics — gof

Calculates goodness of fit statistics for relational data matrices, evaluating second-order (dyadic) and third-order (triadic) dependence patterns. Can handle both unipartite and bipartite networks.

Usage

gof_stats(Y, mode = NULL, custom_gof = NULL)

Arguments

Y: a relational data matrix. For unipartite networks, a square n x n matrix where Y\[i,j\] represents the relationship from node i to node j. For bipartite networks, an nA x nB matrix where Y\[i,j\] represents the relationship from node i in set A to node j in set B. Missing values (NA) are allowed and will be handled appropriately.
mode: character string specifying the network type: "unipartite" or "bipartite". If NULL (default), attempts to infer from matrix dimensions (rectangular = bipartite, square = unipartite). Note: square bipartite networks must specify mode="bipartite".
custom_gof: optional function or list of functions to compute custom GOF statistics. Each function should take Y as input and return a named numeric value or vector. Custom statistics will be added to the standard statistics.

Value

A named numeric vector containing goodness-of-fit statistics. For unipartite networks:

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.
cycle.dep: Cyclic/transitive triadic dependence.
trans.dep: Transitive triadic dependence.

For bipartite networks:

sd.rowmean: Standard deviation of row means (sender heterogeneity).
sd.colmean: Standard deviation of column means (receiver heterogeneity).
four.cycles: Count of four-cycles in the bipartite network.

If custom_gof is provided, additional statistics will be included with their user-specified names.

Naming note. The columns above are the internal names used by gof_stats() and stored on fit$GOF. gof_plot exposes a shorter user-facing alias for some of them; the mapping is:

internal (this column)	gof_plot alias
`sd.rowmean`	`sd.row`
`sd.colmean`	`sd.col`
`dyad.dep`	`dyad.dep`
`cycle.dep`	`triad.dep`
`trans.dep`	`trans.dep`
`four.cycles` (bipartite)	`four.cycles`

Details

The function computes network statistics that capture different aspects of network structure beyond simple density. These statistics are particularly useful for:

Model checking: comparing observed statistics to those from simulated networks
Model selection: choosing between models that better capture network dependencies
Descriptive analysis: summarizing key structural features of the network

For bipartite networks with square dimensions (nA = nB), you must explicitly specify mode="bipartite" to ensure correct statistics are calculated.

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


data(YX_nrm) 

# Auto-detect unipartite
gof_stats(YX_nrm$Y) 
#> sd.rowmean sd.colmean   dyad.dep  cycle.dep  trans.dep 
#> 0.93582644 0.27834223 0.65987298 0.03557144 0.04263373 

# Bipartite (rectangular) networks are auto-detected; mode can also
# be given explicitly (required when a bipartite network is square)
Y_bip <- matrix(rnorm(120), 10, 12)
gof_stats(Y_bip, mode = "bipartite")
#>   sd.rowmean   sd.colmean  four.cycles 
#>    0.3136781    0.4161703 2970.0000000 

# Custom GOF function
my_stat <- function(Y) { c(my_measure = sum(Y > 0, na.rm = TRUE)) }
gof_stats(YX_nrm$Y, custom_gof = my_stat)
#>   sd.rowmean   sd.colmean     dyad.dep    cycle.dep    trans.dep   my_measure 
#>   0.93582644   0.27834223   0.65987298   0.03557144   0.04263373 545.00000000