A Fast Laplace Method for Spatial Generalized Linear Mixed Model

Fitting a fast Laplace approximation for Spatial Generalized Linear Mixed Model as described in Park and Lee (2021) < https://github.com/sangwan93/fastLaplace/blob/main/FastLaplaceMain.pdf>.

Fast Functional Mixed Models using Fast Univariate Inference

Implementation of the fast univariate inference approach (Cui et al. (2022) , Loewinger et al. (2023) ) for fitting functional mixed models.

Fitting Linear Quantile Regression Mixed Models with Relationship Matrix

Fit a quantile regression mixed model involved Relationship Matrix using a sparse implementation of the Frisch-Newton interior-point algorithm as described in Portnoy and Koenker (1977, Statistical Science) < https://www.jstor.org/stable/2246216>.

Generalized Linear Mixed Models using Adaptive Gaussian Quadrature

Fits generalized linear mixed models for a single grouping factor under maximum likelihood approximating the integrals over the random effects with an adaptive Gaussian quadrature rule; Jose C. Pinheiro and Douglas M. Bates (1995) .

High Dimensional Penalized Generalized Linear Mixed Models (pGLMM)

Fits high dimensional penalized generalized linear mixed models using the Monte Carlo Expectation Conditional Minimization (MCECM) algorithm. The purpose of the package is to perform variable selection on both the fixed and random effects simultaneously for generalized linear mixed models. The package supports fitting of Binomial, Gaussian, and Poisson data with canonical links, and supports penalization using the MCP, SCAD, or LASSO penalties. The MCECM algorithm is described in Rashid et al. (2020) . The techniques used in the minimization portion of the procedure (the M-step) are derived from the procedures of the 'ncvreg' package (Breheny and Huang (2011) ) and 'grpreg' package (Breheny and Huang (2015) ), with appropriate modifications to account for the estimation and penalization of the random effects. The 'ncvreg' and 'grpreg' packages also describe the MCP, SCAD, and LASSO penalties.

Spaghetti-Plot Fixed and Random Effects of Linear Mixed Models

Plot both fixed and random effects of linear mixed models, multilevel models in a single spaghetti plot. The package allows to visualize the effect of a predictor on a criterion between different levels of a grouping variable. Additionally, confidence intervals can be displayed for fixed effects. Calculation of predicted values of random effects allows only models with one random intercept and/or one random slope to be plotted. Confidence intervals and predicted values of fixed effects are computed using the 'ggpredict' function from the 'ggeffects' package. Lüdecke, D. (2018) .

Multivariate Generalized Linear Mixed Models for Ranking Sports Teams

Maximum likelihood estimates are obtained via an EM algorithm with either a first-order or a fully exponential Laplace approximation as documented by Broatch and Karl (2018) , Karl, Yang, and Lohr (2014) , and by Karl (2012) . Karl and Zimmerman use this package to illustrate how the home field effect estimator from a mixed model can be biased under nonrandom scheduling.

Flexible Tree Taper Curves Based on Semiparametric Mixed Models

Implementation of functions for fitting taper curves (a semiparametric linear mixed effects taper model) to diameter measurements along stems. Further functions are provided to estimate the uncertainty around the predicted curves, to calculate timber volume (also by sections) and marginal (e.g., upper) diameters. For cases where tree heights are not measured, methods for estimating additional variance in volume predictions resulting from uncertainties in tree height models (tariffs) are provided. The example data include the taper curve parameters for Norway spruce used in the 3rd German NFI fitted to 380 trees and a subset of section-wise diameter measurements of these trees. The functions implemented here are detailed in Kublin, E., Breidenbach, J., Kaendler, G. (2013) .

Confidence Intervals for Robust and Classical Linear Mixed Model Estimators

The main function calculates confidence intervals (CI) for Mixed Models, utilizing both classical estimators from the lmer() function in the 'lme4' package and robust estimators from the rlmer() function in the 'robustlmm' package, as well as the varComprob() function in the 'robustvarComp' package. Three methods are available: the classical Wald method, the wild bootstrap, and the parametric bootstrap. Bootstrap methods offer flexibility in obtaining lower and upper bounds through percentile or BCa methods. More details are given in Mason, F., Cantoni, E., & Ghisletta, P. (2021) and Mason, F., Cantoni, E., & Ghisletta, P. (2024) .

Lasso, Group Lasso, and Sparse-Group Lasso for Mixed Models

Proximal gradient descent solver for the operators lasso, (fitted) group lasso, and (fitted) sparse-group lasso. The implementation involves backtracking line search and warm starts. Input data needs to be clustered/ grouped for each group lasso variant before calling these algorithms.