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.

Penalized Linear Mixed Models for Correlated Data

Fits penalized linear mixed models that correct for unobserved confounding factors. 'plmmr' infers and corrects for the presence of unobserved confounding effects such as population stratification and environmental heterogeneity. It then fits a linear model via penalized maximum likelihood. Originally designed for the multivariate analysis of single nucleotide polymorphisms (SNPs) measured in a genome-wide association study (GWAS), 'plmmr' eliminates the need for subpopulation-specific analyses and post-analysis p-value adjustments. Functions for the appropriate processing of 'PLINK' files are also supplied. For examples, see the package homepage. < https://pbreheny.github.io/plmmr/>.

Bayesian Mixed Models for Qualitative Individual Differences

Test whether equality and order constraints hold for all individuals simultaneously by comparing Bayesian mixed models through Bayes factors. A tutorial style vignette and a quickstart guide are available, via vignette("manual", "quid"), and vignette("quickstart", "quid") respectively. See Haaf and Rouder (2017) ; Haaf, Klaassen and Rouder (2019) ; and Rouder & Haaf (2021) .

Bayesian Longitudinal Regularized Quantile Mixed Model

With high-dimensional omics features, repeated measure ANOVA leads to longitudinal gene-environment interaction studies that have intra-cluster correlations, outlying observations and structured sparsity arising from the ANOVA design. In this package, we have developed robust sparse Bayesian mixed effect models tailored for the above studies (Fan et al. (2025) ). An efficient Gibbs sampler has been developed to facilitate fast computation. The Markov chain Monte Carlo algorithms of the proposed and alternative methods are efficiently implemented in 'C++'. The development of this software package and the associated statistical methods have been partially supported by an Innovative Research Award from Johnson Cancer Research Center, Kansas State University.

Multiplicative Mixed Models using the Template Model Builder

Fit multiplicative mixed models using maximum likelihood estimation via the Template Model Builder (TMB), Kristensen K, Nielsen A, Berg CW, Skaug H, Bell BM (2016) . One version of the multiplicative mixed model is applied in Piepho (1999) . The package provides functions for calculating confidence intervals for the model parameters and for performing likelihood ratio tests.