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

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

data: A data.frame (n x p) with variables in columns. Variables may be numeric, integer, logical, or factors. Character and Date/POSIXt variables are not supported and must be converted prior to model fitting. Variable types are internally mapped to MGM types as follows: continuous numeric (double) variables are treated as Gaussian; integer variables are treated as Poisson unless they take only values in {0,1}, in which case they are treated as binary categorical; factors and logical variables are treated as categorical. Binary categorical variables (two-level factors and logical variables) are internally recoded to {0,1} for model fitting. The original input data are not modified.
layers: A named vector (names = variable names) assigning each node to a layer (character or factor). Must cover all columns of data except variables listed in covariates (treated as adjustment covariates).
layer_rules: A square matrix (L × L), where L is the number of layers. Row and column names must match the layer names. Entries equal to TRUE or 1 allow cross-layer edges between the corresponding pair of layers, while FALSE or 0 disallow them. The matrix is symmetrized internally. Diagonal entries are ignored (intralayer edges are always permitted).
scale: Logical; if TRUE (default) Gaussian variables (type == "g") are z-standardized internally by mgm(). Use scale = FALSE if your data are already standardized.
reps: Integer (>= 0). Number of bootstrap replications (row resampling with replacement). If reps = 0, no bootstrap is performed.
lambdaSel: Method for lambda selection in mgm: "CV" or "EBIC".
lambdaFolds: Number of folds for CV (if lambdaSel = "CV").
lambdaGam: EBIC gamma parameter (if lambdaSel = "EBIC").
alphaSeq: Alpha parameters of the elastic net penalty (values between 0 and 1).
alphaSel: Method for selecting the alpha parameter: "CV" or "EBIC".
alphaFolds: Number of folds for CV (if alphaSel = "CV").
alphaGam: EBIC gamma parameter (if alphaSel = "EBIC").
k: Integer (>= 1). Order of modeled interactions.
ruleReg: Rule to combine neighborhood estimates: "AND" or "OR".
threshold: Threshold below which edge-weights are set to zero: Available options are "LW", "HW", or "none". "LW" applies the threshold proposed by Loh & Wainwright; "HW" applies the threshold proposed by Haslbeck & Waldorp; "none" disables thresholding. Defaults to "LW".
overparameterize: Logical; controls how categorical interactions are parameterized in the neighborhood regressions. If TRUE, categorical interactions are represented using a fully over-parameterized design matrix (i.e., all category combinations are explicitly modeled). If FALSE, the standard glmnet parameterization is used, where one category serves as reference. For continuous variables, both parameterizations are equivalent. The default is FALSE. The over-parameterized option may be advantageous when distinguishing pairwise from higher-order interactions.
thresholdCat: Logical; if FALSE thresholds of categorical variables are set to zero.
quantile_level: Level of the central bootstrap quantile region (default 0.95). Must be a single number between 0 and 1.
covariates: Character vector. Variables used as adjustment covariates in model estimation.
exclude_from_cluster: Character vector of node names. Nodes in this set are excluded from community detection in addition to covariates.
seed_model: Optional integer seed for reproducibility of the initial MGM fit.
seed_boot: Optional integer seed passed to future.apply for reproducibility of bootstrap replications.
treat_singletons_as_excluded: Logical; if TRUE, singleton communities (size 1) are treated as "excluded" when computing bridge metrics and related summaries.
cluster_method: Community detection algorithm applied within each layer. One of "louvain", "fast_greedy", "infomap", "walktrap", or "edge_betweenness".
compute_loadings: Logical; if TRUE (default), compute community loadings (EGAnet::net.loads). Only supported for Gaussian, Poisson, and binary categorical nodes; otherwise loadings are skipped and the reason is stored in community_loadings$reason.
boot_what: Character vector specifying which quantities to bootstrap. Valid options are: "general_index" (intralayer centrality indices), "interlayer_index" (interlayer-only node metrics), "bridge_index" (bridge metrics for nodes in communities), "excluded_index" (bridge metrics for nodes treated as excluded), "community" (community memberships), "loadings" (within-layer community loadings, only if compute_loadings = TRUE), and "none" (skip all node-level bootstrap: only edge-weight bootstrap is performed if reps > 0).
save_data: Logical; if TRUE, store the original data in the output object.
progress: Logical; if TRUE (default), show a bootstrap progress bar.

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.

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.

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