GEMMA Multivariate Linear Mixed Model

Fits a multivariate linear mixed effects model that uses a polygenic term, after Zhou & Stephens (2014) (< https://www.nature.com/articles/nmeth.2848>). Of particular interest is the estimation of variance components with restricted maximum likelihood (REML) methods. Genome-wide efficient mixed-model association (GEMMA), as implemented in the package 'gemma2', uses an expectation-maximization algorithm for variance components inference for use in quantitative trait locus studies.

Various Linear Mixed Model Analyses

This package offers three important components: (1) to construct a use-defined linear mixed model, (2) to employ one of linear mixed model approaches: minimum norm quadratic unbiased estimation (MINQUE) (Rao, 1971) for variance component estimation and random effect prediction; and (3) to employ a jackknife resampling technique to conduct various statistical tests. In addition, this package provides the function for model or data evaluations.This R package offers fast computations for large data sets analyses for various irregular data structures.

Generalized Additive Latent and Mixed Models

Estimates generalized additive latent and mixed models using maximum marginal likelihood, as defined in Sorensen et al. (2023) , which is an extension of Rabe-Hesketh and Skrondal (2004)'s unifying framework for multilevel latent variable modeling . Efficient computation is done using sparse matrix methods, Laplace approximation, and automatic differentiation. The framework includes generalized multilevel models with heteroscedastic residuals, mixed response types, factor loadings, smoothing splines, crossed random effects, and combinations thereof. Syntax for model formulation is close to 'lme4' (Bates et al. (2015) ) and 'PLmixed' (Rockwood and Jeon (2019) ).

Generalised Linear Mixed Models in R

Specification, analysis, simulation, and fitting of generalised linear mixed models. Includes Markov Chain Monte Carlo Maximum likelihood and Laplace approximation model fitting for a range of models, non-linear fixed effect specifications, a wide range of flexible covariance functions that can be combined arbitrarily, robust and bias-corrected standard error estimation, power calculation, data simulation, and more. See < https://samuel-watson.github.io/glmmr-web/> for a detailed manual.

Multivariate Functional Additive Mixed Models

An implementation for multivariate functional additive mixed models (multiFAMM), see Volkmann et al. (2021, ). It builds on developed methods for univariate sparse functional regression models and multivariate functional principal component analysis. This package contains the function to run a multiFAMM and some convenience functions useful when working with large models. An additional package on GitHub contains more convenience functions to reproduce the analyses of the corresponding paper (< https://github.com/alexvolkmann/multifammPaper>).

Dyadic Mixed Model for Pedigree Data

Mixed model analysis for quantitative genetics with multi-trait responses and pedigree-based partitioning of individual variation into a range of environmental and genetic variance components for individual and maternal effects. Method documented in dmmOverview.pdf; dmm is an implementation of dispersion mean model described by Searle et al. (1992) "Variance Components", Wiley, NY. 'DMM' can do 'MINQUE', 'bias-corrected-ML', and 'REML' variance component estimates.

Generalized Additive Mixed Model Interface

An interface for fitting generalized additive models (GAMs) and generalized additive mixed models (GAMMs) using the 'lme4' package as the computational engine, as described in Helwig (2024) . Supports default and formula methods for model specification, additive and tensor product splines for capturing nonlinear effects, and automatic determination of spline type based on the class of each predictor. Includes an S3 plot method for visualizing the (nonlinear) model terms, an S3 predict method for forming predictions from a fit model, and an S3 summary method for conducting significance testing using the Bayesian interpretation of a smoothing spline.

The Phylogenetic Ornstein-Uhlenbeck Mixed Model

The Phylogenetic Ornstein-Uhlenbeck Mixed Model (POUMM) allows to estimate the phylogenetic heritability of continuous traits, to test hypotheses of neutral evolution versus stabilizing selection, to quantify the strength of stabilizing selection, to estimate measurement error and to make predictions about the evolution of a phenotype and phenotypic variation in a population. The package implements combined maximum likelihood and Bayesian inference of the univariate Phylogenetic Ornstein-Uhlenbeck Mixed Model, fast parallel likelihood calculation, maximum likelihood inference of the genotypic values at the tips, functions for summarizing and plotting traces and posterior samples, functions for simulation of a univariate continuous trait evolution model along a phylogenetic tree. So far, the package has been used for estimating the heritability of quantitative traits in macroevolutionary and epidemiological studies, see e.g. Bertels et al. (2017) and Mitov and Stadler (2018) . The algorithm for parallel POUMM likelihood calculation has been published in Mitov and Stadler (2019) .

Bias Diagnostic for Linear Mixed Models

Provides a function to perform bias diagnostics on linear mixed models fitted with lmer() from the 'lme4' package. Implements permutation tests for assessing the bias of fixed effects, as described in Karl and Zimmerman (2021) . Karl and Zimmerman (2020) provide R code for implementing the test using 'mvglmmRank' output. Development of this package was assisted by 'GPT o1-preview' for code structure and documentation.

Multilevel/Mixed Model Helper Functions

A collection of miscellaneous helper function for running multilevel/mixed models in 'lme4'. This package aims to provide functions to compute common tasks when estimating multilevel models such as computing the intraclass correlation and design effect, centering variables, estimating the proportion of variance explained at each level, pseudo-R squared, random intercept and slope reliabilities, tests for homogeneity of variance at level-1, and cluster robust and bootstrap standard errors. The tests and statistics reported in the package are from Raudenbush & Bryk (2002, ISBN:9780761919049), Hox et al. (2018, ISBN:9781138121362), and Snijders & Bosker (2012, ISBN:9781849202015).