Provides functions for the estimation, plotting, predicting and cross-validation of hierarchical feature regression models as described in Pfitzinger (2024). Cluster Regularization via a Hierarchical Feature Regression. Econometrics and Statistics (in press). <doi:10.1016/j.ecosta.2024.01.003>.

Implements the hub graphical lasso and hub covariance graph proposal by Tan, KM., London, P., Mohan, K., Lee, S-I., Fazel, M., and Witten, D. (2014). Learning graphical models with hubs. Journal of Machine Learning Research 15(Oct):3297-3331.

Implemented here are procedures for fitting hierarchical generalized linear models (HGLM). It can be used for linear mixed models and generalized linear mixed models with random effects for a variety of links and a variety of distributions for both the outcomes and the random effects. Fixed effects can also be fitted in the dispersion part of the mean model. As statistical models, HGLMs were initially developed by Lee and Nelder (1996) <https://www.jstor.org/stable/2346105?seq=1>. We provide an implementation (Ronnegard, Alam and Shen 2010) <https://journal.r-project.org/archive/2010-2/RJournal_2010-2_Roennegaard~et~al.pdf> following Lee, Nelder and Pawitan (2006) <ISBN: 9781420011340> with algorithms extended for spatial modeling (Alam, Ronnegard and Shen 2015) <https://journal.r-project.org/archive/2015/RJ-2015-017/RJ-2015-017.pdf>.

This data-only package was created for distributing data used in the examples of the 'hglm' package.

The holonomic gradient method (HGM, hgm) gives a way to evaluate normalization
  constants of unnormalized probability distributions by utilizing holonomic 
  systems of differential or difference equations. The holonomic gradient descent (HGD, hgd) gives a method
  to find maximal likelihood estimates by utilizing the HGM.

Graphical model is an informative and powerful tool to explore the conditional dependence relationships among variables. The traditional Gaussian graphical model and its extensions either have a Gaussian assumption on the data distribution or assume the data are homogeneous. However, there are data with complex distributions violating these two assumptions. For example, the air pollutant concentration records are non-negative and, hence, non-Gaussian. Moreover, due to climate changes, distributions of these concentration records in different months of a year can be far different, which means it is uncertain whether datasets from different months are homogeneous. Methods with a Gaussian or homogeneous assumption may incorrectly model the conditional dependence relationships among variables. Therefore, we propose a heterogeneous graphical model for non-negative data (HGMND) to simultaneously cluster multiple datasets and estimate the conditional dependence matrix of variables from a non-Gaussian and non-negative exponential family in each cluster.