build_mogen: Build Multi-Order Generative Model (MOGen)

In Nestimate: Network Estimation, Bootstrap, and Higher-Order Analysis

Build Multi-Order Generative Model (MOGen)

Description

Constructs higher-order De Bruijn graphs from sequential trajectory data and selects the optimal Markov order using AIC, BIC, or likelihood ratio tests.

Usage

build_mogen(
  data,
  max_order = 5L,
  criterion = c("aic", "bic", "lrt"),
  lrt_alpha = 0.01
)

Arguments

data	A data.frame (rows = trajectories, columns = time points) or a list of character/numeric vectors (one per trajectory).
max_order	Integer. Maximum Markov order to test (default 5).
criterion	Character. Model selection criterion: "aic" (default), "bic", or "lrt" (likelihood ratio test).
lrt_alpha	Numeric. Significance threshold for LRT (default 0.01).

Details

At order k, nodes are k-tuples of states and edges represent transitions between overlapping k-tuples. The model tests increasingly complex Markov orders and selects the one that best balances fit and parsimony.

Value

An object of class net_mogen with components:

optimal_order

Selected optimal Markov order.

criterion

Which criterion was used for selection.

orders

Integer vector of tested orders (0 to max_order).

aic

Named numeric vector of AIC values per order.

bic

Named numeric vector of BIC values per order.

log_likelihood

Named numeric vector of log-likelihoods.

dof

Named integer vector of cumulative DOF per model.

layer_dof

Named integer vector of per-layer DOF.

transition_matrices

List of transition matrices (index 1 = order 0).

states

Unique first-order states.

n_paths

Number of trajectories.

n_observations

Total number of state observations.

References

Scholtes, I. (2017). When is a Network a Network? Multi-Order Graphical Model Selection in Pathways and Temporal Networks. KDD 2017.

Gote, C. & Scholtes, I. (2023). Predicting variable-length paths in networked systems using multi-order generative models. Applied Network Science, 8, 62.

Examples

seqs <- list(c("A","B","C","D"), c("A","B","C","A"), c("B","C","D","A"))
mg <- build_mogen(seqs, max_order = 2)


trajs <- list(c("A","B","C","D"), c("A","B","D","C"),
              c("B","C","D","A"), c("C","D","A","B"))
m <- build_mogen(trajs, max_order = 3)
print(m)
plot(m)

Nestimate documentation built on April 20, 2026, 5:06 p.m.