Mixed graphical model

Estimates a mixed graphical model by nodewise L1-penalized regression – a gaussian (linear) lasso for continuous nodes and a logistic lasso for binary nodes – with per-node EBIC selection, combined by the AND rule. Equivalent in purpose to mgm::mgm(), but pure base R and self-certified: each node's regression reports its stationarity (KKT) residual (see glm_lasso_kkt()).

Usage

mgm_fit(
  data,
  gamma = 0.25,
  types = NULL,
  nlambda = 100L,
  lambda_min_ratio = 0.01,
  threshold = c("LW", "HW", "none"),
  rule = c("AND", "OR"),
  moderators = NULL,
  weights = NULL,
  na_method = c("pairwise", "listwise"),
  native = TRUE,
  labels = NULL
)

Arguments

data

Data frame or matrix (rows = observations). Columns are continuous, binary, or – with native = FALSE – multi-level categorical (a factor/character column, or a numeric one caught by the detection rule below). A column with fewer than two distinct observed values carries no information and is dropped, as in every other estimator. A character column with more than 10 distinct values is refused as an identifier (convert it with factor() if it really is a categorical node), and a column declared "c" via types with more than 10 distinct values is refused as a mislabelled continuous variable.

gamma

EBIC hyperparameter. Default 0.25.

types

Optional character vector of node types ("g" gaussian, "c" categorical); auto-detected if NULL. Detection follows mgm::mgm()'s own rule: a factor/character column is categorical, and so is a numeric column with 10 or fewer distinct integer values. A numeric column promoted by that integer rule is warned about by name, because it switches the node from gaussian to categorical – a different model, not a different encoding. Likert and count items hit this rule routinely.

nlambda

Number of penalties per nodewise path. Default 100.

lambda_min_ratio

Smallest penalty as a fraction of the largest. With native = FALSE, omitting the argument retains glmnet's reference default for compatibility; an explicitly supplied value is honored.

threshold

Post-selection coefficient threshold: "LW" (default), "HW", or "none", matching mgm::mgm().

rule

Edge-combination rule: "AND" (default) or "OR".

moderators

Optional single column index of a moderator variable. When supplied, fits a moderated MGM (that variable moderates every pairwise edge) and returns a psychnet_moderated object to be read with condition(). Honours native like the unmoderated path: the default base kernel is pure R and KKT-certified, and covers gaussian and binary nodes; native = FALSE uses glmnet and additionally allows multi-level categorical nodes. weights are not supported in this mode.

weights

Optional non-negative observation weights, one per row of the (NA-prepared) data. NULL (default) is unweighted.

na_method

Missing-data handling: "pairwise" (default) single-imputes each column over its observed values (mean for continuous, modal level for binary and multi-level categorical), keeping the full sample; "listwise" drops incomplete rows. Applies identically on both engines.

native

Solver switch. TRUE (default) uses psychnet's own pure-R, dependency-free, self-certified L1 path (KKT ~1e-9). FALSE delegates each per-node fit to the glmnet package with mgm's exact EBIC/LW path (gaussian lasso for continuous nodes, multinomial lasso for categorical ones), so the returned edge magnitudes byte-match abs(mgm::mgm()$pairwise$wadj) (to ~1e-6) at the cost of glmnet's looser self-certificate. native = FALSE needs the optional glmnet package (Suggests); weights are supported with native = TRUE only.

Only native = FALSE supports multi-level categorical nodes: the base kernel is a binomial solver, so a node with more than two levels errors there by name. One-hot encoding is not an equivalent workaround – it turns one k-level node into k separate nodes, which is a different model. A network containing a multi-level node cannot be passed to net_predict(), because a k-level predictor occupies k-1 design columns and so has no one-coefficient-per-variable representation.

labels

Optional node labels.

Value

A psychnet object whose $weights is the symmetric standardized weight matrix, with $types, $levels (number of levels per node, 1 for gaussian) and $kkt (the worst nodewise residual). Node order in $weights and $nodes is always the column order of the input data, never sorted, and a k-level categorical stays ONE node. A binary-binary edge carries the sign of its nodewise-logistic coefficient; mgm::mgm() reports the same edge as a magnitude only (its sign is undefined for a categorical-categorical interaction), so compare such edges on abs(). Continuous columns are standardized internally, binary predictors enter the graph on their 0/1 dummy scale, and binary-response logit coefficients are converted to mgm's two-class multinomial scale before edge aggregation. With these conventions the edge magnitudes match mgm::mgm closely for gaussian-gaussian, gaussian-binary, and binary-binary edges alike; weak edges near the EBIC/threshold boundary can still differ in support because the penalty is selected on an independent base-R path.

Examples

set.seed(1)
f <- stats::rnorm(400)
g1 <- f + stats::rnorm(400); g2 <- f + stats::rnorm(400)
b1 <- (f + stats::rnorm(400) > 0) * 1L
d <- data.frame(g1 = g1, g2 = g2, b1 = b1, n = stats::rnorm(400))
mgm_fit(d)
#> <psychnet> mgm network
#>   nodes: 4   edges: 3   (undirected)
#>   optimality (KKT residual): 6.84e-09