hierNest: Fit Hierarchical Nested Regularization Model (hierNest)

In hierNest: Penalized Regression with Hierarchical Nested Parameterization Structure

Fit Hierarchical Nested Regularization Model (hierNest)

Description

Fits a hierarchical nested penalized regression model for subgroup-specific effects using overlapping group lasso penalties. This function encodes the hierarchical structure (e.g., MDC and DRG) via a reparameterized design matrix and enables information borrowing across related subgroups.

Usage

hierNest(
  x,
  y,
  group = NULL,
  family = c("gaussian", "binomial"),
  nlambda = 100,
  lambda.factor = NULL,
  lambda = NULL,
  pf_group = NULL,
  pf_sparse = NULL,
  intercept = FALSE,
  asparse1 = 1,
  asparse2 = 0.05,
  standardize = TRUE,
  lower_bnd = -Inf,
  upper_bnd = Inf,
  eps = 1e-08,
  maxit = 3e+06,
  hier_info = NULL,
  random_asparse = FALSE,
  method = "overlapping"
)

Arguments

x	Matrix of predictors (n \times p), where each row is an observation.
y	Response variable (numeric for "gaussian", binary or factor for "binomial").
group	Optional grouping vector (not required for "overlapping" method).
family	Model family; either "gaussian" for least squares or "binomial" for logistic regression.
nlambda	Number of lambda values in the regularization path (default: 100).
lambda.factor	Factor for minimal value of lambda in the sequence.
lambda	Optional user-supplied lambda sequence.
pf_group	Penalty factor(s) for each group; defaults to sqrt(group size).
pf_sparse	Penalty factors for individual predictors (L1 penalty).
intercept	Logical; should an intercept be included? Default is FALSE.
asparse1	Relative weight for group-level penalty (default: 1).
asparse2	Relative weight for subgroup-level penalty (default: 0.05).
standardize	Logical; standardize predictors? Default is TRUE.
lower_bnd	Lower bound for coefficients (default: -Inf).
upper_bnd	Upper bound for coefficients (default: Inf).
eps	Convergence tolerance (default: 1e-8).
maxit	Maximum number of optimization iterations (default: 3e6).
hier_info	Required. Matrix encoding the hierarchical structure (see Details).
random_asparse	Logical; use random sparse penalty? Default: FALSE.
method	Type of hierarchical regularization ("overlapping" [default], "sparsegl", or "general").

Details

This function builds a hierarchical design matrix reflecting group/subgroup structure (e.g., Major Diagnostic Categories [MDCs] and Diagnosis Related Groups [DRGs]), encoding overall, group-specific, and subgroup-specific effects. It fits a penalized model using overlapping group lasso, as described in Jiang et al. (2024, submitted). The main computational engine is hierNest::overlapping_gl.

Value

Returns a model fit object as produced by hierNest::overlapping_gl, including selected coefficients, cross-validation results, and tuning parameters.

References

Jiang, Z., Huo, L., Hou, J., Vaughan-Sarrazin, M., Smith, M. A., & Huling, J. D. (2024). Heterogeneous readmission prediction with hierarchical effect decomposition and regularization.

hierNest documentation built on March 24, 2026, 5:07 p.m.