holiglm-package

Holistic Generalized Linear Models Package

The holistic generalized linear models package simplifies estimating generalized linear models under constraints. The constraints can be used to,

• bound the domains of specific covariates,
• impose linear constraints on the covariates,
• induce sparsity via best subset selection,
• impose sparsity on groups of variables,
• restrict the pairwise correlation between the selected coefficients,
• impose sign coherence constraints on selected covariates and
• force all predictors within a group either to be selected or not.

This sophisticated constraints are internally implemented via conic optimization. However, the package is designed such that the user, is not required to be familiar with conic optimization but is only required to have basic knowledge. package

References

Holistic regression

Schwendinger, B., Schwendinger, F., & Vana, L. (2024). Holistic Generalized Linear Models. tools:::Rd_expr_doi("10.18637/jss.v108.i07") .

Bertsimas, D., & King, A. (2016). OR Forum-An Algorithmic Approach to Linear Regression Operations Research 64(1):2-16. tools:::Rd_expr_doi("10.1287/opre.2015.1436")

Bertsimas, D., & Li, M. L. (2020). Scalable Holistic Linear Regression. Operations Research Letters 48 (3): 203–8. tools:::Rd_expr_doi("10.1016/j.orl.2020.02.008") .

Constrained regression

McDonald, J. W., & Diamond, I. D. (1990). On the Fitting of Generalized Linear Models with Nonnegativity Parameter Constraints. Biometrics, 46 (1): 201–206. tools:::Rd_expr_doi("10.2307/2531643")

Slawski, M., & Hein, M. (2013). Non-negative least squares for high-dimensional linear models: Consistency and sparse recovery without regularization. Electronic Journal of Statistics, 7: 3004-3056. tools:::Rd_expr_doi("10.1214/13-EJS868")

Carrizosa, E., Olivares-Nadal, A. V., & Ramírez-Cobo, P. (2020). Integer Constraints for Enhancing Interpretability in Linear Regression. SORT. Statistics and Operations Research Transactions, 44: 67-98. tools:::Rd_expr_doi("10.2436/20.8080.02.95") .

Lawson, C. L., & Hanson, R. J. (1995). Solving least squares problems. Society for Industrial and Applied Mathematics. Society for Industrial and Applied Mathematics. tools:::Rd_expr_doi("10.1137/1.9781611971217")

Generalized Linear Models

McCullagh, P., & Nelder, J. A. (2019). Generalized Linear Models (2nd ed.) Routledge. tools:::Rd_expr_doi("10.1201/9780203753736") .

Conic Optimization

Boyd, S., & Vandenberghe, L. (2004). Convex Optimization (1st ed.) Cambridge University Press. https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf. tools:::Rd_expr_doi("10.1017/cbo9780511804441")

Theußl, S., Schwendinger, F., & Hornik, K. (2020). ROI: An Extensible R Optimization Infrastructure. Journal of Statistical Software 94 (15): 1–64. tools:::Rd_expr_doi("10.18637/jss.v094.i15") .

See Also

hglm, holiglm

Author(s)

• Benjamin Schwendinger (Maintainer benjaminschwe@gmail.com )
• Florian Schwendinger
• Laura Vana