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) ).

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 and covariance 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) .

Generalised Linear Mixed Model Selection

Provides tools for fitting sparse generalised linear mixed models with l0 regularisation. Selects fixed and random effects under the hierarchy constraint that fixed effects must precede random effects. Uses coordinate descent and local search algorithms to rapidly deliver near-optimal estimates. Gaussian and binomial response families are currently supported. For more details see Thompson, Wand, and Wang (2025) .

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).

Bias Diagnostic for Linear Mixed Models

Provides a function to perform bias diagnostics on linear mixed models fitted with lmer() from the 'lme4' package. Compares an internal random-effects alignment diagnostic with a fitted permutation reference distribution, following Karl and Zimmerman (2021) . Conditional response-refit simulations separately record random-effects alignment and residual-weight contributions to estimation error. Karl and Zimmerman (2020) provide R code for implementing the test using 'mvglmmRank' output. Development and review were assisted by 'GPT o1-preview', 'GPT 5 Pro', and 'GPT6 Astra'; the author is responsible for the code and its interpretation.

Heritability Estimation from Mixed Models

Reporting heritability estimates is an important to quantitative genetics studies and breeding experiments. Here we provide functions to calculate various broad-sense heritabilities from 'asreml' and 'lme4' model objects. All methods we have implemented in this package have extensively discussed in the article by Schmidt et al. (2019) .

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).