quadratic effects or spline functions). Multilevel models
with missing data in predictors is also available for
Bayesian estimation. Substantive-model compatible multiple

Imports: CDM (>= 7.0-12), coda, graphics, MASS, miceadds (>= 2.13-60),

Imports: CDM (>= 7.1-2), coda, graphics, MASS, miceadds (>= 2.13-60),

Imports: CDM, coda, graphics, miceadds (>= 3.2-23), Rcpp, sirt, stats,

Luedtke, Robitzsch, & West, 2020a, 2020b;

Title: Graph-Constrained Regression with Enhanced Regularization
Authors@R: c(person("Marta", "Karas", email = "marta.karass@gmail.com", role = c("aut", "cre")),
person("Damian", "Brzyski", email = "dbrzyski@iu.edu", role = "ctb"),
person("Jaroslaw", "Harezlak", email = "harezlak@iu.edu", role = "ctb"))
Author: Marta Karas [aut, cre], Damian Brzyski [ctb], Jaroslaw Harezlak [ctb]
Description: Performs graph-constrained regularization in which regularization parameters are selected with the use of a known fact of equivalence between penalized regression and Linear Mixed Model solutions. Provides implementation of three different regression methods where graph-constraints among coefficients are accounted for. 'crPEER' (Partially Empirical Eigenvectors for Regression with Constant Ridge, Constant Ridge PEER) method utilizes additional Ridge term to handle the non-invertibility of a graph Laplacian matrix. 'vrPEER' (Variable Reduction PEER) method performs variable-reduction procedure to handle the non-invertibility of a graph Laplacian matrix. Finally, 'RidgePEER' method employs a penalty term being a linear combination of graph-originated and Ridge-originated penalty terms, whose two regularization parameters are ML estimators from corresponding Linear Mixed Model solution. Notably, in 'RidgePEER' method a graph-originated penalty term allows imposing similarity between coefficients based on graph information given whereas additional Ridge-originated penalty term facilitates parameters estimation: it reduces computational issues arising from singularity in a graph-originated penalty matrix and yields plausible results in situations when graph information is not informative or when it is unclear whether connectivities represented by a graph reflect similarities among corresponding coefficients.
Imports: MASS, glmgraph, magic, reshape2, ggplot2, scalreg, glmnet,