Power Analysis for Generalised Linear Mixed Models by Simulation

Calculate power for generalised linear mixed models, using simulation. Designed to work with models fit using the 'lme4' package. Described in Green and MacLeod, 2016 .

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) .

Generalized Linear Mixed Model Trees

Recursive partitioning based on (generalized) linear mixed models (GLMMs) combining lmer()/glmer() from 'lme4' and lmtree()/glmtree() from 'partykit'. The fitting algorithm is described in more detail in Fokkema, Smits, Zeileis, Hothorn & Kelderman (2018; ). For detecting and modeling subgroups in growth curves with GLMM trees see Fokkema & Zeileis (2024; ).

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 .

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.

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) ).

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.