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 dataset

Description

Example dataset used in MixMashNet examples. 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. (2025). networktools: Tools for identifying important nodes in networks. R package version 1.6.1. https://github.com/paytonjjones/networktools

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. 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.

Value

A list with class c("mixmashnet","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 c("mixmashnet","community_scores") object. If fit is a multimixMN_fit and layer = NULL, returns a named list of community_scores objects (one per layer).

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.

Usage

find_bridge_communities(fit, node)

Arguments

Details

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

Notes:

• 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.

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).

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. This function is used internally by mixMN() and multimixMN(). Stability is expressed as the proportion of bootstrap replications that assign each node to its empirical (original) community.

Usage

membershipStab(fit, IS.plot = FALSE)

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.

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", "fast_greedy", "infomap", "walktrap", "edge_betweenness"),
  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 c("mixmashnet", "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, 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,
  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,
  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", "fast_greedy", "infomap", "walktrap", "edge_betweenness"),
  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 c("mixmashnet", "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, 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 dataset

Description

Example dataset used in MixMashNet examples. 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/

NHGH dataset

Description

Example dataset used in MixMashNet examples. This dataset contains 15 variables derived from the National Health and Nutrition Examination Survey (NHANES)

Usage

data(nhgh_data)

Format

A data frame with 5621 rows and 15 variables:

wt

Weight (numeric).

ht

Height (numeric).

bmi

Body mass index (numeric).

leg

Leg length (numeric).

arml

Arm length (numeric).

armc

Arm circumference (numeric).

tri

Triceps skinfold (numeric).

sub

Subscapular skinfold (numeric).

gh

Glychohemoglobin (numeric).

albumin

Albumin (numeric).

bun

Blood urea nitrogen (numeric).

SCr

Serum creatinine (numeric).

age

Age (numeric).

sex

Sex with 0=woman and 1=man.

re

Race with 1=Mexican American, 2=Other Hispanic, 3=Non-Hispanic White, 4=Non-Hispanic Black, 5=Other Race Including Multi-Racial.

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 MixMashNet objects

Description

Unified plotting interface for objects returned by mixMN() and multimixMN(). Depending on what, it can:

• what = "network": plot the estimated network (single layer or multilayer);

• what = "intra": plot intralayer node/edge statistics with bootstrap quantile regions at the level stored in the object (centrality and bridge metrics);

• what = "inter": plot interlayer node metrics or interlayer edge weights with bootstrap quantile regions at the level stored in the object (multilayer only), and the chosen statistics;

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

Usage

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

Arguments

Details

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

color_by

Node coloring. Single layer: c("community","none"). Multilayer: 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. For multilayer objects:

• if layer is provided, plots that layer only;

• if layer is NULL, plots all layers (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". Note: 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. In multilayer mode, if not provided a layer-specific title is added automatically.

Interlayer summaries (what = "inter"; multilayer only): 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. For multilayer objects, layer selects a specific layer; if layer is NULL, 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.

Print method for MixMashNet objects

Description

Compact textual summary for objects returned by mixMN() and multimixMN(). The method reports:

• whether the fit is single layer (mixMN) or multilayer (multimixMN);

• number of subjects (if available) and variables;

• for multilayer fits, the number of nodes and non-zero edges per layer and, if present, per interlayer pair;

• size of the global graph (nodes and edges);

• number of communities (single layer) or communities per layer (multilayer);

• covariates used for adjustment and nodes excluded from the graph and/or clustering;

• main settings for community detection and bootstrap;

• data info.

Usage

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

Arguments

Value

The input object x, returned invisibly.

See Also

mixMN, multimixMN

Summarize MixMashNet fits (single and multilayer) in long format

Description

Summarizes fitted MixMashNet objects (single and multilayer). The summary includes the original estimates and, when available, bootstrap means, standard errors, and quantile regions.

Usage

## S3 method for class 'mixmashnet'
summary(
  object,
  what = c("intra", "inter"),
  statistics = NULL,
  layer = NULL,
  pairs = NULL,
  digits = 3,
  ...
)

Arguments

Value

A list (class "summary.mixmashnet") with up to four data frames ($index, $edges, $interlayer_index, $interlayer_edges) and the quantile region used to compute the bootstrap quantile regions ($quantile_level).

Depending on what and statistics, some of these elements may be NULL.

Update community and layer color palettes in MixMashNet objects

Description

Updates the color palettes associated with communities and/or layers in mixMN_fit and multimixMN_fit objects. The function replaces only the colors corresponding to the provided names, leaving all other colors unchanged.

If colors are provided for names that do not exist in the object (e.g., unknown community labels or layer names), a warning is issued and those entries are ignored. If some communities or layers are not specified, their original colors are preserved.

Usage

update_palette(fit, community_colors = NULL, layer_colors = NULL)

Arguments

Details

For mixMN_fit objects, community colors are updated in fit$communities$palette.

For multimixMN_fit objects, community colors are updated separately within each layer (i.e., in fit$layer_fits[[L]]$communities$palette), while layer colors are updated in fit$layers$palette.

The function performs in-place modification of the palettes and returns the updated object.

Value

The input object fit, 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
)

# View original community palette
fit$communities$palette

# Update colors for communities 1 and 2
fit2 <- update_palette(
  fit,
  community_colors = c("1" = "red", "2" = "blue")
)

fit2$communities$palette

set.seed(1)
plot(fit2)