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) .

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).

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) .

Multivariate Normal and t Distributions

Computes multivariate normal and t probabilities, quantiles, random deviates, and densities. Log-likelihoods for multivariate Gaussian models and Gaussian copulae parameterised by Cholesky factors of covariance or precision matrices are implemented for interval-censored and exact data, or a mix thereof. Score functions for these log-likelihoods are available. A class representing multiple lower triangular matrices and corresponding methods are part of this package.

Likelihood-Based Boosting for Generalized Mixed Models

Likelihood-based boosting approaches for generalized mixed models are provided.

Longitudinal Drift-Diffusion Mixed Models (LDDMM)

Implementation of the drift-diffusion mixed model for category learning as described in Paulon et al. (2021) .