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.

Linear Mixed Models with Sparse Matrix Methods and Smoothing

Provides tools for fitting linear mixed models using sparse matrix methods and variance component estimation. Applications include spline-based modeling of spatial and temporal trends using penalized splines (Boer, 2023) .

Functional Linear Mixed Models for Irregularly or Sparsely Sampled Data

Estimation of functional linear mixed models for irregularly or sparsely sampled data based on functional principal component analysis.

Estimated Marginal Means, aka Least-Squares Means

Obtain estimated marginal means (EMMs) for many linear, generalized linear, and mixed models. Compute contrasts or linear functions of EMMs, trends, and comparisons of slopes. Plots and other displays. Least-squares means are discussed, and the term "estimated marginal means" is suggested, in Searle, Speed, and Milliken (1980) Population marginal means in the linear model: An alternative to least squares means, The American Statistician 34(4), 216-221 .

Linear Mixed Models for Complex Survey Data

Linear mixed models for complex survey data, by pairwise composite likelihood, as described in Lumley & Huang (2023) . Supports nested and crossed random effects, and correlated random effects as in genetic models. Allows for multistage sampling and for other designs where pairwise sampling probabilities are specified or can be calculated.

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.

Multivariate Normal Mixture Models and Mixtures of Generalized Linear Mixed Models Including Model Based Clustering

Contains a mixture of statistical methods including the MCMC methods to analyze normal mixtures. Additionally, model based clustering methods are implemented to perform classification based on (multivariate) longitudinal (or otherwise correlated) data. The basis for such clustering is a mixture of multivariate generalized linear mixed models. The package is primarily related to the publications Komárek (2009, Comp. Stat. and Data Anal.) and Komárek and Komárková (2014, J. of Stat. Soft.) . It also implements methods published in Komárek and Komárková (2013, Ann. of Appl. Stat.) , Hughes, Komárek, Bonnett, Czanner, García-Fiñana (2017, Stat. in Med.) , Jaspers, Komárek, Aerts (2018, Biom. J.) and Hughes, Komárek, Czanner, García-Fiñana (2018, Stat. Meth. in Med. Res) .

Inference of Linear Mixed Models Through MM Algorithm

The main function MMEst() performs (Restricted) Maximum Likelihood in a variance component mixed models using a Min-Max (MM) algorithm (Laporte, F., Charcosset, A. & Mary-Huard, T. (2022) ).

Monte Carlo Maximum Likelihood and Analysis of Generalised Linear Mixed Models

Specification, analysis, simulation, and fitting of generalised linear mixed models. Monte Carlo Maximum likelihood model fitting for a range of models, non-linear fixed effect specifications, a wide range of flexible covariance functions including Gaussian Process approximations. Methods described in Watson, Wang, and Giorgi (2026) .

Fitting Mixed Models with Known Covariance Structures

The main functions are 'emmreml', and 'emmremlMultiKernel'. 'emmreml' solves a mixed model with known covariance structure using the 'EMMA' algorithm. 'emmremlMultiKernel' is a wrapper for 'emmreml' to handle multiple random components with known covariance structures. The function 'emmremlMultivariate' solves a multivariate gaussian mixed model with known covariance structure using the 'ECM' algorithm.