Data Transforming Augmentation for Linear Mixed Models

We provide a toolbox to fit univariate and multivariate linear mixed models via data transforming augmentation. Users can also fit these models via typical data augmentation for a comparison. It returns either maximum likelihood estimates of unknown model parameters (hyper-parameters) via an EM algorithm or posterior samples of those parameters via MCMC. Also see Tak et al. (2019) .

Gradient Boosting for Generalized Additive Mixed Models

Provides a novel framework to estimate mixed models via gradient boosting. The implemented functions are based on the 'mboost' and 'lme4' packages, and the family range is therefore determined by 'lme4'. A correction mechanism for cluster-constant covariates is implemented, as well as estimation of the covariance of random effects. These methods are described in the accompanying publication; see for details.

Penalized Linear Mixed Models for Correlated Data

Fits penalized linear mixed models that correct for unobserved confounding factors. 'plmmr' infers and corrects for the presence of unobserved confounding effects such as population stratification and environmental heterogeneity. It then fits a linear model via penalized maximum likelihood. Originally designed for the multivariate analysis of single nucleotide polymorphisms (SNPs) measured in a genome-wide association study (GWAS), 'plmmr' eliminates the need for subpopulation-specific analyses and post-analysis p-value adjustments. Functions for the appropriate processing of 'PLINK' files are also supplied. For examples, see the package homepage. < https://pbreheny.github.io/plmmr/>.

Bayesian Mixed Models for Qualitative Individual Differences

Test whether equality and order constraints hold for all individuals simultaneously by comparing Bayesian mixed models through Bayes factors. A tutorial style vignette and a quickstart guide are available, via vignette("manual", "quid"), and vignette("quickstart", "quid") respectively. See Haaf and Rouder (2017) ; Haaf, Klaassen and Rouder (2019) ; and Rouder & Haaf (2021) .

Bayesian Longitudinal Regularized Quantile Mixed Model

With high-dimensional omics features, repeated measure ANOVA leads to longitudinal gene-environment interaction studies that have intra-cluster correlations, outlying observations and structured sparsity arising from the ANOVA design. In this package, we have developed robust sparse Bayesian mixed effect models tailored for the above studies (Fan et al. (2025) ). An efficient Gibbs sampler has been developed to facilitate fast computation. The Markov chain Monte Carlo algorithms of the proposed and alternative methods are efficiently implemented in 'C++'. The development of this software package and the associated statistical methods have been partially supported by an Innovative Research Award from Johnson Cancer Research Center, Kansas State University.

Nonlinear Mixed Effects Models in Population PK/PD, Estimation Routines

Fit and compare nonlinear mixed-effects models in differential equations with flexible dosing information commonly seen in pharmacokinetics and pharmacodynamics (Almquist, Leander, and Jirstrand 2015 ). Differential equation solving is by compiled C code provided in the 'rxode2' package (Wang, Hallow, and James 2015 ).

Multiplicative Mixed Models using the Template Model Builder

Fit multiplicative mixed models using maximum likelihood estimation via the Template Model Builder (TMB), Kristensen K, Nielsen A, Berg CW, Skaug H, Bell BM (2016) . One version of the multiplicative mixed model is applied in Piepho (1999) . The package provides functions for calculating confidence intervals for the model parameters and for performing likelihood ratio tests.

Bayesian Model Selection for Generalized Linear Mixed Models

A Bayesian model selection approach for generalized linear mixed models. Currently, 'GLMMselect' can be used for Poisson GLMM and Bernoulli GLMM. 'GLMMselect' can select fixed effects and random effects simultaneously. Covariance structures for the random effects are a product of a unknown scalar and a known semi-positive definite matrix. 'GLMMselect' can be widely used in areas such as longitudinal studies, genome-wide association studies, and spatial statistics. 'GLMMselect' is based on Xu, Ferreira, Porter, and Franck (202X), Bayesian Model Selection Method for Generalized Linear Mixed Models, Biometrics, under review.

Nonlinear Mixed Effects Models in Population PK/PD, Data

Datasets for 'nlmixr2' and 'rxode2'. 'nlmixr2' is used for fitting and comparing nonlinear mixed-effects models in differential equations with flexible dosing information commonly seen in pharmacokinetics and pharmacodynamics (Almquist, Leander, and Jirstrand 2015 ). Differential equation solving is by compiled C code provided in the 'rxode2' package (Wang, Hallow, and James 2015 ).

Analysis of Factorial Experiments

Convenience functions for analyzing factorial experiments using ANOVA or mixed models. aov_ez(), aov_car(), and aov_4() allow specification of between, within (i.e., repeated-measures), or mixed (i.e., split-plot) ANOVAs for data in long format (i.e., one observation per row), automatically aggregating multiple observations per individual and cell of the design. mixed() fits mixed models using lme4::lmer() and computes p-values for all fixed effects using either Kenward-Roger or Satterthwaite approximation for degrees of freedom (LMM only), parametric bootstrap (LMMs and GLMMs), or likelihood ratio tests (LMMs and GLMMs). afex_plot() provides a high-level interface for interaction or one-way plots using ggplot2, combining raw data and model estimates. afex uses type 3 sums of squares as default (imitating commercial statistical software).