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.

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.

Regression Models for Ordinal Data

Implementation of cumulative link (mixed) models also known as ordered regression models, proportional odds models, proportional hazards models for grouped survival times and ordered logit/probit/... models. Estimation is via maximum likelihood and mixed models are fitted with the Laplace approximation and adaptive Gauss-Hermite quadrature. Multiple random effect terms are allowed and they may be nested, crossed or partially nested/crossed. Restrictions of symmetry and equidistance can be imposed on the thresholds (cut-points/intercepts). Standard model methods are available (summary, anova, drop-methods, step, confint, predict etc.) in addition to profile methods and slice methods for visualizing the likelihood function and checking convergence.

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) ).

Spatial Generalised Linear Mixed Models for Areal Unit Data

Implements a class of univariate and multivariate spatial generalised linear mixed models for areal unit data, with inference in a Bayesian setting using Markov chain Monte Carlo (MCMC) simulation using a single or multiple Markov chains. The response variable can be binomial, Gaussian, multinomial, Poisson or zero-inflated Poisson (ZIP), and spatial autocorrelation is modelled by a set of random effects that are assigned a conditional autoregressive (CAR) prior distribution. A number of different models are available for univariate spatial data, including models with no random effects as well as random effects modelled by different types of CAR prior, including the BYM model (Besag et al., 1991, ) and Leroux model (Leroux et al., 2000, ). Additionally, a multivariate CAR (MCAR) model for multivariate spatial data is available, as is a two-level hierarchical model for modelling data relating to individuals within areas. Full details are given in the vignette accompanying this package. The initial creation of this package was supported by the Economic and Social Research Council (ESRC) grant RES-000-22-4256, and on-going development has been supported by the Engineering and Physical Science Research Council (EPSRC) grant EP/J017442/1, ESRC grant ES/K006460/1, Innovate UK / Natural Environment Research Council (NERC) grant NE/N007352/1 and the TB Alliance.

Fitting the Centered Autologistic and Sparse Spatial Generalized Linear Mixed Models for Areal Data

Provides tools for analyzing spatial data, especially non- Gaussian areal data. The current version supports the sparse restricted spatial regression model of Hughes and Haran (2013) , the centered autologistic model of Caragea and Kaiser (2009) , and the Bayesian spatial filtering model of Hughes (2017) .

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.