Mixed Model Association Test for GEne-Environment Interaction

Use a 'glmmkin' class object (GMMAT package) from the null model to perform generalized linear mixed model-based single-variant and variant set main effect tests, gene-environment interaction tests, and joint tests for association, as proposed in Wang et al. (2020) .

Estimate (Generalized) Linear Mixed Models with Factor Structures

Utilizes the 'lme4' and 'optimx' packages (previously the optim() function from 'stats') to estimate (generalized) linear mixed models (GLMM) with factor structures using a profile likelihood approach, as outlined in Jeon and Rabe-Hesketh (2012) and Rockwood and Jeon (2019) . Factor analysis and item response models can be extended to allow for an arbitrary number of nested and crossed random effects, making it useful for multilevel and cross-classified models.

Robust Bayesian Longitudinal Regularized Semiparametric Mixed Models

Our recently developed fully robust Bayesian semiparametric mixed-effect model for high-dimensional longitudinal studies with heterogeneous observations can be implemented through this package. This model can distinguish between time-varying interactions and constant-effect-only cases to avoid model misspecifications. Facilitated by spike-and-slab priors, this model leads to superior performance in estimation, identification and statistical inference. In particular, robust Bayesian inferences in terms of valid Bayesian credible intervals on both parametric and nonparametric effects can be validated on finite samples. The Markov chain Monte Carlo algorithms of the proposed and alternative models are efficiently implemented in 'C++'.

Generalized Fiducial Inference for Normal Linear Mixed Models

Simulation of the generalized fiducial distribution for normal linear mixed models with interval data. Fiducial inference is somehow similar to Bayesian inference, in the sense that it is based on a distribution that represents the uncertainty about the parameters, like the posterior distribution in Bayesian statistics. It does not require a prior distribution, and it yields results close to frequentist results. Reference: Cisewski and Hannig (2012) .

Variable Selection in Linear Mixed Models for SNP Data

Fit penalized multivariable linear mixed models with a single random effect to control for population structure in genetic association studies. The goal is to simultaneously fit many genetic variants at the same time, in order to select markers that are independently associated with the response. Can also handle prior annotation information, for example, rare variants, in the form of variable weights. For more information, see the website below and the accompanying paper: Bhatnagar et al., "Simultaneous SNP selection and adjustment for population structure in high dimensional prediction models", 2020, .

Tables and Graphs for Mixed Models for Repeated Measures (MMRM)

Mixed models for repeated measures (MMRM) are a popular choice for analyzing longitudinal continuous outcomes in randomized clinical trials and beyond; see for example Cnaan, Laird and Slasor (1997) . This package provides an interface for fitting MMRM within the 'tern' < https://cran.r-project.org/package=tern> framework by Zhu et al. (2023) and tabulate results easily using 'rtables' < https://cran.r-project.org/package=rtables> by Becker et al. (2023). It builds on 'mmrm' < https://cran.r-project.org/package=mmrm> by Sabanés Bové et al. (2023) for the actual MMRM computations.

Bayesian Spatial and Space-Time Linear Mixed Models

Fits Bayesian linear mixed models for spatial and space-time data with fixed effects, independent and identically distributed (iid) grouped random effects, and structured latent processes. The formula interface supports first-order autoregressive (AR(1)) effects, dense Gaussian processes, nearest-neighbor Gaussian processes, proper and Leroux conditional autoregressive (CAR) effects, ordered directed acyclic graph autoregressive (DAGAR) effects, separable CAR-time and DAGAR-time effects, and spatially varying coefficients. The sampler uses sparse precision matrix calculations when available and includes post-fitting tools for latent process recovery, fitted values, prediction, pointwise log likelihoods, and posterior sample extraction. Method details include Datta et al. (2016) , Finley et al. (2019) , Datta et al. (2019) , and May and Finley (2025) .

Bayesian Robust Generalized Mixed Models for Longitudinal Data

To perform model estimation using MCMC algorithms with Bayesian methods for incomplete longitudinal studies on binary and ordinal outcomes that are measured repeatedly on subjects over time with drop-outs. Details about the method can be found in the vignette or < https://sites.google.com/view/kuojunglee/r-packages/bayesrgmm>.

Fit a Cosinor Model Using a Generalized Mixed Modeling Framework

Allows users to fit a cosinor model using the 'glmmTMB' framework. This extends on existing cosinor modeling packages, including 'cosinor' and 'circacompare', by including a wide range of available link functions and the capability to fit mixed models. The cosinor model is described by Cornelissen (2014) .

Partial Eta-Squared for Crossed, Nested, and Mixed Linear Mixed Models

Computes partial eta-squared effect sizes for fixed effects in linear mixed models fitted with the 'lme4' package. Supports crossed, nested, and mixed (crossed-and-nested) random effects structures with any number of grouping factors. Mixed designs handle cases where grouping factors are simultaneously crossed with some variables and nested within others (e.g., photos nested within models, but both crossed with participants). Factor predictors are supported directly, and a single factor-level (omnibus) effect size can be obtained for a multi-level factor or multi-df interaction. Random slope variances are translated to the outcome scale using a variance decomposition approach, correctly accounting for predictor scaling and interaction terms. Both general and operative effect sizes are provided, with optional parametric bootstrap confidence intervals. For correlated predictors, per-predictor effect sizes use unique (semipartial) variance by default. Methods are based on Correll, Mellinger, McClelland, and Judd (2020) , Correll, Mellinger, and Pedersen (2022) , and Rights and Sterba (2019) .