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).

Graphical Markov Models with Mixed Graphs

Provides functions for defining mixed graphs containing three types of edges, directed, undirected and bi-directed, with possibly multiple edges. These graphs are useful because they capture fundamental independence structures in multivariate distributions and in the induced distributions after marginalization and conditioning. The package is especially concerned with Gaussian graphical models for (i) ML estimation for directed acyclic graphs, undirected and bi-directed graphs and ancestral graph models (ii) testing several conditional independencies (iii) checking global identification of DAG Gaussian models with one latent variable (iv) testing Markov equivalences and generating Markov equivalent graphs of specific types.

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) .

Power Analysis for Random Effects in Mixed Models

Simulation functions to assess or explore the power of a dataset to estimates significant random effects (intercept or slope) in a mixed model. The functions are based on the "lme4" and "lmerTest" packages.

Poisson-Tweedie Generalized Linear Mixed Model

Fits the Poisson-Tweedie generalized linear mixed model described in Signorelli et al. (2021, ). Likelihood approximation based on adaptive Gauss Hermite quadrature rule.

An Implementation of the Bayesian Markov (Renewal) Mixed Models

The Bayesian Markov renewal mixed models take sequentially observed categorical data with continuous duration times, being either state duration or inter-state duration. These models comprehensively analyze the stochastic dynamics of both state transitions and duration times under the influence of multiple exogenous factors and random individual effect. The default setting flexibly models the transition probabilities using Dirichlet mixtures and the duration times using gamma mixtures. It also provides the flexibility of modeling the categorical sequences using Bayesian Markov mixed models alone, either ignoring the duration times altogether or dividing duration time into multiples of an additional category in the sequence by a user-specific unit. The package allows extensive inference of the state transition probabilities and the duration times as well as relevant plots and graphs. It also includes a synthetic data set to demonstrate the desired format of input data set and the utility of various functions. Methods for Bayesian Markov renewal mixed models are as described in: Abhra Sarkar et al., (2018) and Yutong Wu et al., (2022) .

Functional Data Analysis in a Mixed Model Framework

Likelihood based analysis of 1-dimension functional data in a mixed-effects model framework. Matrix computation are approximated by semi-explicit operator equivalents with linear computational complexity. Markussen (2013) .