# A Software Tool For Sparse Estimation Of A General Class Of High-dimensional GLMs

Generalized linear models are the workhorse of many inferential problems. Also in the modern era with high-dimensional settings, such models have been proven to be effective exploratory tools. Most attention has been paid to Gaussian, binomial and Poisson settings, which have efficient computational implementations and where either the dispersion parameter is largely irrelevant or absent. However, general GLMs have dispersion parameters $$\phi$$ that affect the value of the log-likelihood. This in turn, affects the value of various information criteria such as AIC and BIC, and has a considerable impact on the computation and selection of the optimal model. The R-package dglars is one of the standard packages to perform high-dimensional analyses for GLMs. Being based on fundamental likelihood considerations, rather than arbitrary penalization, it naturally extends to the general GLM setting. In this paper, we present an improved predictor-corrector (IPC) algorithm for computing the differential geometric least angle regression (dgLARS) solution curve, proposed in and . We describe the implementation of a stable estimator of the dispersion parameter proposed in for high-dimensional exponential dispersion models. A simulation study is conducted to test the performance of the proposed methods and algorithms. We illustrate the methods using an example. The described improvements have been implemented in a new version of the R-package dglars.

Hassan Pazira (Epidemiology and Biostatistics) , Luigi Augugliaro (Department of Economics, Business and Statistics) , Ernst C. Wit (Institute of Computational Science)
2022-06-21

## Supplementary materials

Supplementary materials are available in addition to this article. It can be downloaded at RJ-2022-008.zip

L. Augugliaro, A. M. Mineo and E. C. Wit. Differential geometric least angle regression: A differential geometric approach to sparse generalized linear models. Journal of the Royal Statistical Society: Series B, 75(3): 471–498, 2013.
H. Pazira, L. Augugliaro and E. C. Wit. Extended differential geometric LARS for high-dimensional GLMs with general dispersion parameter. Statistics and Computing, 28(4): 753–774, 2018. URL http://dx.doi.org/10.1007/s11222-017-9761-7.

### Reuse

Text and figures are licensed under Creative Commons Attribution CC BY 4.0. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".

### Citation

For attribution, please cite this work as

Pazira, et al., "The R Journal: A Software Tool For Sparse Estimation Of A General Class Of High-dimensional GLMs", The R Journal, 2022

BibTeX citation

@article{RJ-2022-008,
author = {Pazira, Hassan and Augugliaro, Luigi and Wit, Ernst C.},
title = {The R Journal: A Software Tool For Sparse Estimation Of A General Class Of High-dimensional GLMs},
journal = {The R Journal},
year = {2022},
note = {https://doi.org/10.32614/RJ-2022-008},
doi = {10.32614/RJ-2022-008},
volume = {14},
issue = {1},
issn = {2073-4859},
pages = {34-53}
}