lame (version 1.3.4)

gof_stats: Goodness of fit statistics

Description

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)

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

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.

Author

Cassy Dorff, Shahryar Minhas, Tosin Salau

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.

Examples

data(YX_nrm) 

# Auto-detect unipartite
gof_stats(YX_nrm$Y) 

# 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")

# 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)