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) .

Bayesian Estimation for Quantile Regression Mixed Models

Using a Bayesian estimation procedure, this package fits linear quantile regression models such as linear quantile models, linear quantile mixed models, quantile regression joint models for time-to-event and longitudinal data. The estimation procedure is based on the asymmetric Laplace distribution and the 'JAGS' software is used to get posterior samples (Yang, Luo, DeSantis (2019) ).

Temporal Contributions on Trends using Mixed Models

Method to estimate the effect of the trend in predictor variables on the observed trend of the response variable using mixed models with temporal autocorrelation. See Fernández-Martínez et al. (2017 and 2019) .

Data Transforming Augmentation for Linear Mixed Models

We provide a toolbox to fit univariate and multivariate linear mixed models via data transforming augmentation. Users can also fit these models via typical data augmentation for a comparison. It returns either maximum likelihood estimates of unknown model parameters (hyper-parameters) via an EM algorithm or posterior samples of those parameters via MCMC. Also see Tak et al. (2019) .

Gradient Boosting for Generalized Additive Mixed Models

Provides a novel framework to estimate mixed models via gradient boosting. The implemented functions are based on the 'mboost' and 'lme4' packages, and the family range is therefore determined by 'lme4'. A correction mechanism for cluster-constant covariates is implemented, as well as estimation of the covariance of random effects. These methods are described in the accompanying publication; see for details.

Generalized Linear Mixed Model Association Tests

Perform association tests using generalized linear mixed models (GLMMs) in genome-wide association studies (GWAS) and sequencing association studies. First, GMMAT fits a GLMM with covariate adjustment and random effects to account for population structure and familial or cryptic relatedness. For GWAS, GMMAT performs score tests for each genetic variant as proposed in Chen et al. (2016) . For candidate gene studies, GMMAT can also perform Wald tests to get the effect size estimate for each genetic variant. For rare variant analysis from sequencing association studies, GMMAT performs the variant Set Mixed Model Association Tests (SMMAT) as proposed in Chen et al. (2019) , including the burden test, the sequence kernel association test (SKAT), SKAT-O and an efficient hybrid test of the burden test and SKAT, based on user-defined variant sets.