Tools for Multilayer and Single Layer Network Modeling

Description

Tools for estimating and analyzing single layer and multilayer networks using Mixed Graphical Models (MGMs), accommodating continuous, count, and categorical variables. In the multilayer setting, layers may comprise different types and numbers of variables, and users can explicitly impose a predefined multilayer topology to constrain the estimation of inter and intralayer connections. The package implements bootstrap procedures to derive quantile regions for edge weights and node-level centrality and bridge metrics, and provides tools to assess the stability of node community membership. In addition, subject-level community scores can be computed to summarize the latent dimensions identified through network clustering.

Author(s)

Maria De Martino, Caterina Gregorio, Adrien Perigord

maria.demartino@uniud.it

References

De Martino, M., Triolo, F., Perigord, A., Ornago, A. M., Vetrano, D. L., Gregorio, C. (2026). MixMashNet: An R Package for Single and Multilayer Networks. https://arxiv.org/abs/2602.05716

Christensen, A. P., & Golino, H. (2021). Estimating the Stability of Psychological Dimensions via Bootstrap Exploratory Graph Analysis: A Monte Carlo Simulation and Tutorial. Psych, 3(3), 479–500. doi:10.3390/psych3030032

Christensen, A. P., Golino, H., Abad, F. J., & Garrido, L. E. (2025). Revised network loadings. Behavior Research Methods, 57(4), 114. doi:10.3758/s13428-025-02640-3

Epskamp, S., Borsboom, D., & Fried, E. I. (2018). Estimating psychological networks and their accuracy: A tutorial paper. Behavior Research Methods, 50(1), 195–212. doi:10.3758/s13428-017-0862-1

Haslbeck, J. M. B., & Waldorp, L. J. (2020). mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data. Journal of Statistical Software, 93(8). doi:10.18637/jss.v093.i08

Jones, P. J., Ma, R., & McNally, R. J. (2021). Bridge Centrality: A Network Approach to Understanding Comorbidity. Multivariate Behavioral Research, 56(2), 353–367. doi:10.1080/00273171.2019.1614898

See Also

Useful links:

• https://arcbiostat.github.io/MixMashNet/

• Report bugs at https://github.com/ARCbiostat/MixMashNet/issues

Bacteremia example dataset for single layer network analysis

Description

Clinical bacteremia dataset used to illustrate single-layer network estimation with MixMashNet. This dataset contains 7240 patients with clinical suspicion of bacteremia who underwent blood culture testing at the Vienna General Hospital.

Usage

data(bacteremia)

Format

A data frame with 7420 rows and 16 variables:

AGE

Age (numeric).

WBC

White blood cell (numeric).

NEU

Neutrophil counts (numeric).

HGB

Hemoglobin (numeric).

PLT

Platelet count (numeric).

CRP

C-reactive protein (numeric).

APTT

Activated partial thromboplastin time (numeric).

FIB

Fibrinogen (numeric).

CREA

Creatinine (numeric).

BUN

Blood urea nitrogen (numeric).

GLU

Glucose (numeric).

ALAT

High-sensitivity C-reactive protein (numeric).

GBIL

Total bilirubin (numeric).

ALB

Albumin (numeric).

SEX

Sex with 0=male and 1=female.

BloodCulture

Positive blood culture results with 0=no and 1=yes.

References

Ratzinger, F., Dedeyan, M., Rammerstorfer, M., Perkmann, T., Burgmann, H., Makristathis, A., Dorffner, G., Loetsch, F., Blacky, A., & Ramharter, M. (2014). A risk prediction model for screening bacteremic patients: A cross sectional study. PLoS ONE, 9(9), e106765. doi:10.1371/journal.pone.0106765

Bridge metrics for nodes across communities

Description

Computes bridge centrality measures for nodes with an assigned community. This function is used internally by mixMN() and multimixMN(). Specifically, the function computes bridge strength as the sum of absolute edge weights connecting a node to nodes in other communities; bridge expected influence of order one (EI1) as the signed sum of direct connections to nodes in other communities; bridge expected influence of order two (EI2) as the signed influence that propagates indirectly to nodes in other communities via one intermediate neighbor (i.e., through paths of length two); bridge betweenness as the number of times a node lies on shortest paths between nodes belonging to different communities; and bridge closeness as the inverse of the mean shortest-path distance to nodes in other communities.

Usage

bridge_metrics(g, membership)

Arguments

Details

Bridge betweenness and closeness are computed on the positive-weight subgraph only, with weights converted to distances as d = 1/w.

Value

A data.frame with columns: node, community, bridge_strength, bridge_ei1, bridge_ei2, bridge_betweenness, bridge_closeness.

References

Jones, P. J., Ma, R., & McNally, R. J. (2021). Bridge Centrality: A Network Approach to Understanding Comorbidity. Multivariate Behavioral Research, 56(2), 353–367. doi:10.1080/00273171.2019.1614898

Bridge metrics for nodes excluded from communities

Description

Computes bridge centrality measures for nodes that are not assigned to any community. This function is used internally by mixMN() and multimixMN(). For these excluded nodes, the function computes bridge strength, bridge closeness, bridge betweenness, and bridge expected influence of order one and two (EI1 and EI2), quantifying their role in connecting nodes across different communities.

Usage

bridge_metrics_excluded(g, membership)

Arguments

Details

Bridge betweenness excluded and closeness excluded are computed on the positive-weight subgraph only, with weights converted to distances as d = 1/w.

Value

A data.frame with columns: node, bridge_strength, bridge_closeness, bridge_betweenness, bridge_ei1, bridge_ei2.

References

Jones, P. J. (2025). networktools: Tools for identifying important nodes in networks. R package version 1.6.1. https://github.com/paytonjjones/networktools

Compute community scores from a fitted MixMashNet model

Description

Computes subject-level community scores. Community scores are obtained as weighted sums of the variables belonging to each detected community, where weights correspond to the standardized community loadings estimated via EGAnet::net.loads and stored in the fitted mixMN_fit object. Scores are computed using the dataset provided via the data argument. If data = NULL, the original dataset used to fit the model (fit$model$data) is used by default. Errors if both are NULL. Optionally, percentile bootstrap quantile regions for the community scores can be computed if bootstrap community loadings are available in fit$community_loadings$boot. Community scores are only available if community loadings were computed in the fitted model. This requires that all variables in the community subgraph are of MGM type Gaussian ("g"), Poisson ("p"), or binary categorical ("c" with level == 2).

Usage

community_scores(
  fit,
  data = NULL,
  layer = NULL,
  scale = TRUE,
  quantile_level = NULL,
  return_quantile_region = FALSE,
  na_action = c("stop", "omit")
)

Arguments

Details

The function requires that fit$community_loadings$true exists and that the input data contains all required variables in fit$community_loadings$nodes. It errors otherwise.

The returned object has class "community_scores" and implements print() and summary() methods for quick inspection and descriptive summaries of the scores.

Value

A list with class "community_scores" containing:

call

The matched call.

settings

List with scale, quantile_level, and na_action.

ids

Character vector of subject IDs (rownames of data).

communities

Character vector of community score names.

scores

Numeric matrix of scores (n × K).

quantile_region

If requested and available, a list with lower and upper matrices (n × K) for percentile bootstrap quantile regions; otherwise NULL.

details

List containing nodes_used, loadings_true, loadings_boot_available, and scaling parameters (center, scale).

If fit is a mixMN_fit (or a multimixMN_fit with layer specified), returns a "community_scores" object. If fit is a multimixMN_fit and layer = NULL, returns a named list of community_scores objects for all scoreable layers. If no layer is scoreable, the function errors.

References

Christensen, A. P., Golino, H., Abad, F. J., & Garrido, L. E. (2025). Revised network loadings. Behavior Research Methods, 57(4), 114. doi:10.3758/s13428-025-02640-3

Examples

data(bacteremia)

vars <- c("WBC", "NEU", "HGB", "PLT", "CRP")
df <- bacteremia[, vars]

fit <- mixMN(
  data = df,
  lambdaSel = "EBIC",
  reps = 0,
  seed_model = 42,
  compute_loadings = TRUE,
  progress = FALSE,
  save_data = TRUE
)

# Compute community scores on the original data
scores <- community_scores(fit)
summary(scores)

Bridge profiles of a node across communities

Description

Identifies which communities contribute most to the bridge role of a given node, by decomposing its bridge connectivity into community-specific contributions, excluding its own community when assigned. The function is designed as an interpretative companion to bridge_metrics() and bridge_metrics_excluded(), providing the components underlying the corresponding overall bridge indices.

Bridge connectivity is summarized using five complementary profiles: bridge strength, bridge EI1, bridge EI2, bridge closeness, and bridge betweenness.

For single layer fits (mixMN_fit), profiles are computed directly on the supplied fitted object.

For multilayer fits (multimixMN_fit), profiles are computed within the selected layer only, by applying the same single layer procedure to the corresponding intralayer fit stored in fit$layer_fits[[layer]].

Usage

find_bridge_communities(fit, node, layer = NULL)

Arguments

Details

Bridge profiles are computed using only connections from the focal node to nodes in communities different from its own. If the focal node is not assigned to any community, i.e. excluded, connections to all assigned nodes in communities are considered.

Bridge betweenness is computed by counting all shortest paths between pairs of nodes in different communities that pass through the focal node as an intermediate vertex. When multiple shortest paths exist, each path is counted separately.

The returned object has class "bridge_profiles" and provides a dedicated print() method. By default, all bridge profiles are displayed; a specific profile can be selected through the statistic argument.

Value

An object of class "bridge_profiles" (a named list) with the following components:

bridge_strength

Bridge strength. List with overall, the total value across all other communities, and by_comm, a tibble with community-specific contributions (community, sum_abs_w).

bridge_ei1

Bridge expected influence (order 1). List with overall and by_comm (community, sum_signed_w).

bridge_ei2

Bridge expected influence (order 2). List with overall and by_comm (community, sum_signed_w2).

bridge_closeness

Bridge closeness. List with overall and by_comm (community, inv_mean_dist).

bridge_betweenness

Bridge betweenness. List with overall and by_pair, a tibble with contributions by community pair (Ci, Cj, hits).

Bridge profiles of a node across layers

Description

Identifies which layers contribute most to the interlayer bridge role of a given node, by decomposing its interlayer connectivity into layer-specific contributions. The function is designed as an interpretative companion to the interlayer node-level indices returned by multimixMN(), providing the components underlying the corresponding overall interlayer indices.

Interlayer connectivity is summarized using four complementary profiles: interlayer strength, interlayer expected influence (order 1), interlayer closeness, and interlayer betweenness.

Usage

find_bridge_layers(fit, node, layer)

Arguments

Details

The function operates on the interlayer-only graph, i.e. on the graph containing only edges between nodes belonging to different layers.

For a focal node in the selected layer, the function decomposes:

• interlayer strength into contributions toward each layer;

• interlayer expected influence (order 1) into signed contributions toward each layer;

• interlayer closeness into additive harmonic-distance contributions toward each layer;

• interlayer betweenness into additive contributions from shortest paths between layer pairs, using the standard fraction \sigma_{st}(v) / \sigma_{st}.

Contributions are defined so that they sum to the corresponding overall interlayer index.

The returned object has class "bridge_layer_profiles" and provides a dedicated print() method. By default, all interlayer profiles are displayed; a specific profile can be selected through the statistic argument.

Value

An object of class "bridge_layer_profiles" (a named list) with the following components:

bridge_strength

List with overall and by_layer, where by_layer is a tibble with columns target_layer and sum_abs_w.

bridge_ei1

List with overall and by_layer, where by_layer is a tibble with columns target_layer and sum_signed_w.

bridge_closeness

List with overall and by_layer, where by_layer is a tibble with columns target_layer and contribution.

bridge_betweenness

List with overall and by_pair, where by_pair is a tibble with columns Li, Lj, and contribution.

Extract node-level centrality indices

Description

Extracts node-level centrality indices from fitted objects returned by mixMN() and multimixMN() in a long-format data frame.

For single layer fits of class "mixMN_fit", only intralayer node-level indices are available.

For multilayer fits of class "multimixMN_fit", what = "intra" returns intralayer node-level indices, whereas what = "inter" returns node-level indices computed on the interlayer-only graph. If what is not specified for a multilayer fit, both intralayer and interlayer node-level indices are returned by default, unless layer or pairs imply a specific scope.

The function returns the original estimates and, when available, bootstrap means, standard errors, and bootstrap quantile regions.

Usage

get_centrality(object, ...)

## S3 method for class 'mixMN_fit'
get_centrality(
  object,
  what = "intra",
  statistics = NULL,
  digits = NULL,
  drop_na_boot = TRUE,
  ...
)

## S3 method for class 'multimixMN_fit'
get_centrality(
  object,
  what = c("intra", "inter"),
  statistics = NULL,
  layer = NULL,
  pairs = NULL,
  digits = NULL,
  drop_na_boot = TRUE,
  ...
)

Arguments

Details

The returned data frame is in long format, with one row per node-statistic combination.

For single layer fits, only what = "intra" is available.

For multilayer fits, layer can be used to subset intralayer output, whereas pairs can be used to subset interlayer output.

The set of admissible statistics depends on what and on the class of object. In particular, bridge-related indices are available only for intralayer output.

Value

A tibble in long format with one row per node-statistic combination. It contains the columns:

• node

• layer

• scope

• metric

• estimated

When available, the output also contains bootstrap summary columns:

• mean.bootstrap

• SE.bootstrap

• quantile.lower.bootstrap

• quantile.upper.bootstrap

The quantile level used to compute the bootstrap quantile region is stored as the "quantile_level" attribute of the returned tibble.

Extract edge-level summaries

Description

Extracts edge-level summaries from fitted objects returned by mixMN() and multimixMN() in a long-format data frame.

For single layer fits of class "mixMN_fit", only intralayer edges are available.

For multilayer fits of class "multimixMN_fit", what = "intra" returns intralayer edges, whereas what = "inter" returns interlayer edges. If what is not specified for a multilayer fit, both scopes are returned by default, unless layer or pairs imply a specific scope.

The function returns the original edge weights and, when available, bootstrap means, standard errors, and bootstrap quantile regions.

Usage

get_edges(object, ...)

## S3 method for class 'mixMN_fit'
get_edges(object, what = "intra", digits = NULL, drop_na_boot = TRUE, ...)

## S3 method for class 'multimixMN_fit'
get_edges(
  object,
  what = c("intra", "inter"),
  layer = NULL,
  pairs = NULL,
  digits = NULL,
  drop_na_boot = TRUE,
  ...
)

Arguments

Details

The returned data frame is in long format, with one row per edge.

For single layer fits, only what = "intra" is available.

For multilayer fits, layer can be used to subset intralayer output, whereas pairs can be used to subset interlayer output.

Value

A tibble in long format with one row per edge. It contains the columns:

• edge

• layer for intralayer edges

• pairs for interlayer edges

• scope

• estimated

When available, the output also contains bootstrap summary columns:

• mean.bootstrap

• SE.bootstrap

• quantile.lower.bootstrap

• quantile.upper.bootstrap

The quantile level used to compute the bootstrap quantile region is stored as the "quantile_level" attribute of the returned tibble.

Extract a single layer from a multilayer MixMashNet object

Description

Extracts one layer from a fitted multilayer multimixMN_fit object returned by multimixMN().

The selected layer is returned as the corresponding single layer mixMN_fit object stored in layer_fits.

Usage

layer_slice(object, ...)

## S3 method for class 'multimixMN_fit'
layer_slice(object, layer, ...)

Arguments

Value

An object of class "mixMN_fit" corresponding to the selected layer.

Node stability from bootstrap community assignments

Description

Computes per-node stability given the empirical community structure and the homogenized bootstrap memberships contained in a mixMN_fit object. Stability is expressed as the proportion of bootstrap replications that assign each node to its empirical (original) community.

Usage

membershipStab(fit)

Arguments

Details

Bootstrap community labels are first aligned to the empirical solution using EGAnet::community.homogenize(). Stability is then computed node-wise as the proportion of bootstrap runs in which the node's community matches its empirical assignment.

The returned object has class "membershipStab" and provides print(), summary(), and plot() methods for quick inspection, descriptive summaries, and visualization of node stability.

Value

An object of class c("membershipStab"), with components:

membership

List with:

empirical

Named integer vector of empirical community labels

bootstrap

Matrix of homogenized bootstrap labels (reps × p)

membership.stability

List with:

empirical.dimensions

Named numeric vector of node-level stability (proportion assigned to empirical community)

all.dimensions

Matrix (p × K) with proportions of assignment to each community

community_palette

Named vector of colors for communities, if available

References

Christensen, A. P., & Golino, H. (2021). Estimating the Stability of Psychological Dimensions via Bootstrap Exploratory Graph Analysis: A Monte Carlo Simulation and Tutorial. Psych, 3(3), 479–500. doi:10.3390/psych3030032

Estimate single layer MGM network with bootstrap centrality, bridge metrics, clustering, and (optionally) community score loadings

Description

Estimates a single layer Mixed Graphical Model (MGM) network on the original data, using the estimation framework implemented in the mgm package, and performs non-parametric bootstrap (row resampling) to compute centrality indices, bridge metrics, clustering stability, and quantile regions for node metrics and edge weights. Optionally, the function computes community score loadings (for later prediction on new data) and can bootstrap the corresponding loadings.

Usage

mixMN(
  data,
  reps = 100,
  scale = TRUE,
  lambdaSel = c("CV", "EBIC"),
  lambdaFolds = 5,
  lambdaGam = 0.25,
  alphaSeq = 1,
  alphaSel = "CV",
  alphaFolds = 5,
  alphaGam = 0.25,
  k = 2,
  ruleReg = "AND",
  threshold = "LW",
  overparameterize = FALSE,
  thresholdCat = TRUE,
  quantile_level = 0.95,
  covariates = NULL,
  exclude_from_cluster = NULL,
  treat_singletons_as_excluded = FALSE,
  seed_model = NULL,
  seed_boot = NULL,
  cluster_method = c("louvain", "edge_betweenness", "fast_greedy", "infomap",
    "label_prop", "leading_eigen", "leiden", "optimal", "spinglass", "walktrap"),
  cluster_args = list(),
  compute_loadings = TRUE,
  boot_what = c("general_index", "bridge_index", "excluded_index", "community",
    "loadings"),
  save_data = FALSE,
  progress = TRUE
)

Arguments

Details

This function does not call future::plan(). To enable parallel bootstrap, set a plan (e.g. future::plan(multisession)) before calling mixMN(). If boot_what is "none" and reps > 0, node-level metrics are not bootstrapped but edge-weight bootstrap and corresponding quantile regions are still computed.

Value

An object of class "mixMN_fit", that is a list with the following top-level components:

call

The matched function call.

settings

List of main settings used in the call, including reps, cluster_method, cluster_args, covariates, exclude_from_cluster, treat_singletons_as_excluded, and boot_what.

data_info

List with information derived from the input data used for model setup: mgm_type_level (data frame with one row per variable, reporting the original R class and the inferred MGM type and level, as used in the call to mgm::mgm), and binary_recode_map (named list describing the mapping from original binary labels to the internal {0,1} coding used for model fitting).

model

List with: mgm (the fitted mgm object), nodes (character vector of all node names), n (number of observations), p (number of variables), and data (if save_data = TRUE).

graph

List describing the graph: igraph (an igraph object built on keep_nodes_graph, with edge attributes weight, abs_weight, sign and vertex attribute membership for communities), keep_nodes_graph (nodes retained in the graph and all node-level metrics), and keep_nodes_cluster (nodes used for community detection).

communities

List describing community structure with: original_membership (integer vector of community labels on keep_nodes_cluster), groups (factor of community labels actually used for bridge metrics, optionally with singletons treated as excluded), palette (named vector of colors per community), and boot_memberships (list of bootstrap memberships if "community" is requested in boot_what, otherwise an empty list).

statistics

List with node- and edge-level summaries: node is a list with: true (data frame with one row per node in keep_nodes_graph, containing the node name and metrics strength, ei1, closeness, betweenness, bridge_strength, bridge_betweenness, bridge_closeness, bridge_ei1, bridge_ei2, and for nodes treated as excluded from communities also bridge_strength_excluded, bridge_betweenness_excluded, bridge_closeness_excluded, bridge_ei1_excluded, bridge_ei2_excluded); boot (list of bootstrap matrices for each metric, each of dimension reps x length(keep_nodes_graph), possibly NULL if the metric was not requested or if reps = 0); and quantile_region (list of quantile regions for each node metric, one p x 2 matrix per metric, with columns corresponding to the lower and upper quantile bounds implied by quantile_level, or NULL if no bootstrap was performed).

edge is a list with: true (data frame with columns edge and weight for all unique undirected edges among keep_nodes_graph); boot (matrix of bootstrap edge weights of dimension n_edges x reps); and quantile_region (matrix of quantile regions for edge weights, n_edges x 2, with columns corresponding to the lower and upper bootstrap quantile bounds, or NULL if reps = 0).

community_loadings

List containing community-loading information (based on EGAnet::net.loads) for later community-score computation on new data: nodes(nodes used for loadings), wc (integer community labels aligned with nodes), true (matrix of standardized loadings, nodes x communities, or NULL if loadings were not computed.), boot (list of bootstrap loading matrices, one per replication, or NULL if not bootstrapped), available (logical indicating whether loadings were computed), reason (character string explaining why loadings were not computed, or NULL if available = TRUE), non_scorable_nodes (character vector of nodes in the community subgraph that prevented loadings from being computed (e.g., categorical variables with >2 levels), otherwise empty).

References

Haslbeck, J. M. B., & Waldorp, L. J. (2020). mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data. Journal of Statistical Software, 93(8). doi:10.18637/jss.v093.i08

Loh, P. L., & Wainwright, M. J. (2012). Structure estimation for discrete graphicalmodels: Generalized covariance matrices and their inverses. NIPS

Examples

data(bacteremia)
df <- bacteremia[, !names(bacteremia) %in% "BloodCulture"]

fit <- mixMN(
  data = df,
  lambdaSel = "EBIC",
  lambdaGam = 0.25,
  reps = 0,
  seed_model = 42,
  cluster_method = "louvain",
  covariates = c("AGE", "SEX"),
  compute_loadings = FALSE,
  progress = FALSE
)
fit

# Plot the estimated network
set.seed(1)
plot(fit)


fit_b <- mixMN(
  data = df,
  lambdaSel = "EBIC",
  lambdaGam = 0.25,
  reps = 5,
  seed_model = 42,
  seed_boot =42,
  cluster_method = "louvain",
  covariates = c("AGE", "SEX"),
  boot_what = "community",
  compute_loadings = FALSE,
  progress = FALSE
)

# Plot the membership stability
plot(fit_b, what = "stability", cutoff = 0.7)

Multilayer MGM with bootstrap, intra/interlayer metrics, and quantile regions

Description

Estimates a multilayer Mixed Graphical Model (MGM) using the estimation framework implemented in the mgm package, with a masking scheme that enforces which cross-layer edges are allowed according to layer_rules. Within each layer, the function computes community structure and performs non-parametric row-bootstrap to obtain node centrality indices, edge weights, and bridge metrics, including metrics for nodes treated as excluded. Optionally, within-layer community loadings can also be estimated and bootstrapped. The function additionally returns interlayer-only node metrics and summaries of cross-layer edge weights.

Usage

multimixMN(
  data,
  layers,
  layer_rules,
  scale = TRUE,
  reps = 100,
  lambdaSel = c("CV", "EBIC"),
  lambdaFolds = 5,
  lambdaGam = 0.25,
  alphaSeq = 1,
  alphaSel = "CV",
  alphaFolds = 5,
  alphaGam = 0.25,
  k = 2,
  ruleReg = "AND",
  threshold = "LW",
  overparameterize = FALSE,
  thresholdCat = TRUE,
  quantile_level = 0.95,
  covariates = NULL,
  exclude_from_cluster = NULL,
  seed_model = NULL,
  seed_boot = NULL,
  treat_singletons_as_excluded = FALSE,
  cluster_method = c("louvain", "edge_betweenness", "fast_greedy", "infomap",
    "label_prop", "leading_eigen", "leiden", "optimal", "spinglass", "walktrap"),
  cluster_args = list(),
  compute_loadings = TRUE,
  boot_what = c("general_index", "interlayer_index", "bridge_index", "excluded_index",
    "community", "loadings"),
  save_data = FALSE,
  progress = TRUE
)

Arguments

Details

This function does not call future::plan(). To enable parallel bootstrap, set a plan (e.g. future::plan(multisession)) before calling multimixMN(). If "none" is the only element of boot_what and reps > 0, node-level metrics are not bootstrapped, but intra and interlayer edge-weight bootstrap and the corresponding quantile regions are still computed.

Value

An object of class "multimixMN_fit". The returned list contains at least the following components:

call

The matched function call.

settings

List of main settings used in the call, including reps, cluster_method, cluster_args, covariates, exclude_from_cluster, treat_singletons_as_excluded, boot_what).

data_info

List with information derived from the input data used for model setup: mgm_type_level (data frame with one row per variable, reporting the original R class and the inferred MGM type and level, as used in the call to mgm::mgm), and binary_recode_map (named list describing the mapping from original binary labels to the internal {0,1} coding used for model fitting).

model

List with: mgm (the fitted mgm object), nodes (character vector of all node names), n (number of observations), p (number of variables), and data (if save_data = TRUE))

layers

List describing the multilayer structure (assignment of nodes to layers, layer_rules matrix used and color of each layer in palette).

layer_fits

Named list (one element per layer) with single layer fits, including community structure, node-level statistics, edge-level statistics, bridge metrics, and (optionally) community loadings with bootstrap information.

interlayer

List collecting interlayer-only node metrics (strength, expected influence, closeness, betweenness, with or without bootstrap) and cross-layer edge summaries for each allowed pair of layers.

graph

List containing a global igraph object built on the retained nodes (keep_nodes_graph), with vertex attributes such as name, layer, membership, and edge attributes such as weight, abs_weight, sign, type (intra vs inter) and layer_pair.

References

Haslbeck, J. M. B., & Waldorp, L. J. (2020). mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data. Journal of Statistical Software, 93(8). doi:10.18637/jss.v093.i08

Examples

data(nhanes)

bio_vars  <- c("ALT", "AST", "HDL", "HbA1c")
ant_vars  <- c("BMI", "Waist", "ArmCirc", "LegLength")
life_vars <- c("Smoke", "PhysicalActivity", "Drug")
covs      <- c("Age", "Gender", "MonInc")

df <- nhanes[, c(bio_vars, ant_vars, life_vars, covs)]

# Layer assignment (must cover all columns except covariates)
layers <- c(
  setNames(rep("bio",  length(bio_vars)),  bio_vars),
  setNames(rep("ant",  length(ant_vars)),  ant_vars),
  setNames(rep("life", length(life_vars)), life_vars)
)

# Allow cross-layer edges bio<->ant and ant<->life; disallow bio<->life
layer_rules <- matrix(0, nrow = 3, ncol = 3,
                      dimnames = list(c("bio","ant","life"),
                                      c("bio","ant","life")))
layer_rules["bio","ant"]  <- 1
layer_rules["ant","life"] <- 1

fitM <- multimixMN(
  data = df,
  layers = layers,
  layer_rules = layer_rules,
  covariates = covs,
  lambdaSel = "EBIC",
  lambdaGam = 0.25,
  reps = 5,
  seed_model = 42,
  seed_boot = 42,
  compute_loadings = FALSE,
  progress = FALSE
)
fitM

# Plot the estimated network
set.seed(1)
plot(fitM, color_by = "layer")

NHANES-derived dataset for multilayer network analysis

Description

Example dataset derived to illustrate multilayer network estimation in MixMashNet. This dataset contains 29 variables derived from the National Health and Nutrition Examination Survey (NHANES)

Usage

data(nhanes)

Format

A data frame with 2759 rows and 29 variables:

TotChol

Total Cholesterol (numeric).

HDL

High-density lipoprotein cholesterol (numeric).

Creatinine

Creatinine (numeric).

UricAcid

Uric acid (numeric).

ALT

Alanine aminotransferase (numeric).

AST

Aspartate aminotransferase (numeric).

GGT

Gamma-glutamyl transferase (numeric).

Bilirubin

Bilirubin (numeric).

Albumin

Albumin (numeric).

TotProtein

Total protein (numeric).

HbA1c

Glycated hemoglobin (numeric).

hsCRP

High-sensitivity C-reactive protein (numeric).

BMI

Body mass index (numeric).

Waist

waist circumference (numeric).

Height

Height (numeric).

ArmCirc

Arm circumference (numeric).

HipCirc

Hip circumference (numeric).

LegLength

Leg length (numeric).

ArmLength

Arm Length (numeric).

TroubleSleep

Trouble Sleep with 0=no and 1=yes.

PhysicalActivity

Physical Activity with 0=no and 1=yes.

Smoke

Smoking with 0=no and 1=yes.

Drug

Drug use with 0=no and 1=yes.

Diet

Dietary quality with 1=Poor, 2=Fair, 3=Good, 4=Very good, 5=Excellent.

Alcohol

Alcohol consumption with 0=no and 1=yes.

Work

Employment status with 1=working, 2=employed but absent, 3=seeking work, 4=not working.

MonInc

Monthly income category (1–12), where higher values indicate higher income.

Gender

Gender with 0=male and 1=female.

Age

Age (numeric).

References

Centers for Disease Control and Prevention (CDC) & National Center for Health Statistics (NCHS). (2020). National Health and Nutrition Examination Survey data. https://www.cdc.gov/nchs/nhanes/

Plot method for single layer MixMashNet objects

Description

Plotting interface for objects returned by mixMN().

Depending on what, the method can:

• what = "network": plot the estimated single-layer network;

• what = "intra": plot node-level metrics or edge weights with bootstrap quantile regions at the level stored in the object;

• what = "stability": plot node stability within communities based on bootstrap community assignments.

Usage

## S3 method for class 'mixMN_fit'
plot(x, what = c("network", "intra", "stability"), ...)

Arguments

Details

Network plots (what = "network"): Supported arguments (via ...):

color_by

Node coloring: c("community","none").

edge_color_by

Edge coloring: c("sign","none").

edge_scale

Numeric scaling factor for edge widths (multiplied by abs(weight)).

graphics::plot.igraph arguments

e.g., vertex.size, vertex.label.cex, edge.width, vertex.label.color, etc.

Within-network statistics (what = "intra"): Plots node-level metrics or edge weights with bootstrap quantile regions.

Supported arguments (via ...):

statistics

Character vector of metrics. Options include: "strength", "expected_influence", "closeness", "betweenness", bridge metrics "bridge_strength", "bridge_ei1", "bridge_ei2", "bridge_closeness", "bridge_betweenness", excluded bridge metrics "bridge_strength_excluded", "bridge_ei1_excluded", "bridge_ei2_excluded", "bridge_closeness_excluded", "bridge_betweenness_excluded", and "edges". Different metric families cannot be mixed in the same call (e.g., "edges" cannot be combined with node metrics).

ordering

Node ordering: c("value","alphabetical","community").

standardize

Logical; if TRUE, z-standardize the displayed values within the panel.

exclude_nodes

Optional character vector of node names to remove before plotting.

color_by_community

Logical; if TRUE, color nodes by community when available.

edges_top_n

Integer; when statistics = "edges", keep the top edges by absolute weight.

title

Optional plot title.

Community membership stability (what = "stability"): Plots node stability by community.

Supported arguments (via ...):

title

Plot title. Default: "Node Stability by Community".

cutoff

Optional numeric threshold in [0,1] shown as a dashed vertical line. Use NULL to hide the line. Default: 0.7.

The quantile region level is taken from the fitted object (x$settings$quantile_level); if missing or invalid, a default of 0.95 is used.

Value

If what != "network", the function returns a ggplot object. If what = "network", the network is plotted directly.

See Also

mixMN

Plot method for multilayer MixMashNet objects

Description

Plotting interface for objects returned by multimixMN().

Depending on what, the method can:

• what = "network": plot the estimated multilayer network, or a single layer if layer is specified;

• what = "intra": plot intralayer node-level metrics or edge weights with bootstrap quantile regions;

• what = "inter": plot interlayer node metrics or interlayer edge weights with bootstrap quantile regions;

• what = "stability": plot node stability within communities based on bootstrap community assignments.

Usage

## S3 method for class 'multimixMN_fit'
plot(x, what = c("network", "intra", "inter", "stability"), layer = NULL, ...)

Arguments

Details

Network plots (what = "network"): Supported arguments (via ...):

color_by

Node coloring: c("layer","community","none").

edge_color_by

Edge coloring: c("sign","none").

edge_scale

Numeric scaling factor for edge widths (multiplied by abs(weight)).

graphics::plot.igraph arguments

e.g., vertex.size, vertex.label.cex, edge.width, vertex.label.color, etc.

Intralayer statistics (what = "intra"): Plots node-level metrics or edge weights with bootstrap quantile regions. If layer is provided, only that layer is plotted. If layer is NULL, all layers are plotted, one panel per layer.

Supported arguments (via ...):

statistics

Character vector of metrics. Options include: "strength", "expected_influence", "closeness", "betweenness", bridge metrics "bridge_strength", "bridge_ei1", "bridge_ei2", "bridge_closeness", "bridge_betweenness", excluded bridge metrics "bridge_strength_excluded", "bridge_ei1_excluded", "bridge_ei2_excluded", "bridge_closeness_excluded", "bridge_betweenness_excluded", and "edges". Different metric families cannot be mixed in the same call (e.g., "edges" cannot be combined with node metrics).

ordering

Node ordering: c("value","alphabetical","community").

standardize

Logical; if TRUE, z-standardize the displayed values within each panel.

exclude_nodes

Optional character vector of node names to remove before plotting.

color_by_community

Logical; if TRUE, color nodes by community when available.

edges_top_n

Integer; when statistics = "edges", keep the top edges by absolute weight.

title

Optional plot title. If omitted and multiple layers are shown, layer-specific titles are added automatically.

Interlayer summaries (what = "inter"): Plots interlayer node metrics or interlayer edge weights with bootstrap quantile regions.

Supported arguments (via ...):

statistics

Character vector. Node metrics: c("strength","expected_influence","closeness","betweenness"), or "edges" for interlayer edge weights. Node metrics and "edges" cannot be combined.

pairs

Layer pairs to show. Either "*" (all available) or a character vector of pair keys like "bio_dis" (order-insensitive).

edges_top_n

Integer; keep the top interlayer edges by absolute weight.

ordering

Ordering within panels: c("value","alphabetical").

standardize

Logical; if TRUE, z-standardize values (node metrics by metric, edges by pair).

exclude_nodes

Optional character vector; removes nodes and incident interlayer edges.

nodes_layer

Optional layer name to restrict node metrics to nodes belonging to that layer.

title

Optional plot title.

Community membership stability (what = "stability"): Plots node stability by community. If layer is provided, only that layer is shown. Otherwise, stability plots are shown for all layers.

Supported arguments (via ...):

title

Plot title. Default: "Node Stability by Community".

cutoff

Optional numeric threshold in [0,1] shown as a dashed vertical line. Use NULL to hide the line. Default: 0.7.

The quantile region level is taken from the fitted object (x$settings$quantile_level); if missing or invalid, a default of 0.95 is used.

Value

If what != "network", the function returns a ggplot object. If what = "network", the network is plotted directly.

See Also

multimixMN

Print method for single layer MixMashNet objects

Description

Compact textual summary for objects returned by mixMN().

Usage

## S3 method for class 'mixMN_fit'
print(x, ...)

Arguments

Value

The input object x, returned invisibly.

See Also

mixMN

Print method for multilayer MixMashNet objects

Description

Compact textual summary for objects returned by multimixMN().

Usage

## S3 method for class 'multimixMN_fit'
print(x, ...)

Arguments

Value

The input object x, returned invisibly.

See Also

multimixMN

Summarize top intralayer edges for single-layer MixMashNet fits

Description

Returns the top 10 intralayer edges for fitted objects returned by mixMN(), in the same long-format structure used for edge summaries.

Usage

## S3 method for class 'mixMN_fit'
summary(object, top_n = 10L, digits = NULL, drop_na_boot = TRUE, ...)

Arguments

Value

An object of class "summary.mixMN_fit" containing the top intralayer edges.

Summarize top interlayer edges for multilayer MixMashNet fits

Description

Returns the top 10 interlayer edges for fitted objects returned by multimixMN(), in the same long-format structure used for edge summaries.

Usage

## S3 method for class 'multimixMN_fit'
summary(object, top_n = 10L, digits = NULL, drop_na_boot = TRUE, ...)

Arguments

Value

An object of class "summary.multimixMN_fit" containing the top interlayer edges.

Update community and layer color palettes in MixMashNet objects

Description

Updates the color palettes associated with communities and/or layers in fitted mixMN_fit and multimixMN_fit objects.

For mixMN_fit objects, community_colors must be a named character vector specifying colors for community labels in object$communities$palette.

For multimixMN_fit objects, community_colors must be a named list whose elements correspond to layer names. Each element must be a named character vector specifying colors for the community labels of that layer. The list may be partial, so only the specified layers are updated.

For multimixMN_fit objects, layer_colors updates the palette stored in object$layers$palette.

The function replaces only the colors corresponding to the provided names, leaving all other colors unchanged. Unknown layer names, community labels, or layer labels are ignored with a warning.

Usage

update_palette(object, ...)

## S3 method for class 'mixMN_fit'
update_palette(object, community_colors = NULL, layer_colors = NULL, ...)

## S3 method for class 'multimixMN_fit'
update_palette(object, community_colors = NULL, layer_colors = NULL, ...)

Arguments

Details

For single layer fits, only community_colors is used.

For multilayer fits:

• community_colors updates community palettes within the specified layers;

• layer_colors updates the palette of the layers themselves.

For multilayer fits, community_colors can be partial: layers not included in the list are left unchanged.

Value

The input object, with updated community and/or layer palettes.

Examples

data(bacteremia)

vars <- c("WBC", "NEU", "HGB", "PLT", "CRP")
df <- bacteremia[, vars]

fit <- mixMN(
  data = df,
  lambdaSel = "EBIC",
  reps = 0,
  seed_model = 42,
  compute_loadings = FALSE,
  progress = FALSE
)

fit$communities$palette

fit2 <- update_palette(
  fit,
  community_colors = c("1" = "red", "2" = "blue")
)

fit2$communities$palette

set.seed(1)
plot(fit2)