Generalized Linear Mixed Models using Adaptive Gaussian Quadrature

Fits generalized linear mixed models for a single grouping factor under maximum likelihood approximating the integrals over the random effects with an adaptive Gaussian quadrature rule; Jose C. Pinheiro and Douglas M. Bates (1995) .

Extended Mixed Models Using Latent Classes and Latent Processes

Estimation of various extensions of the mixed models including latent class mixed models, joint latent class mixed models, mixed models for curvilinear outcomes, mixed models for multivariate longitudinal outcomes using a maximum likelihood estimation method (Proust-Lima, Philipps, Liquet (2017) ).

Linear Quantile Mixed Models

Functions to fit quantile regression models for hierarchical data (2-level nested designs) as described in Geraci and Bottai (2014, Statistics and Computing) . A vignette is given in Geraci (2014, Journal of Statistical Software) and included in the package documents. The packages also provides functions to fit quantile models for independent data and for count responses.

Genetic Data Handling (QC, GRM, LD, PCA) & Linear Mixed Models

Manipulation of genetic data (SNPs). Computation of GRM and dominance matrix, LD, heritability with efficient algorithms for linear mixed model (AIREML). Dandine et al .

Mixed Model ANOVA and Statistics for Education

The main functions perform mixed models analysis by least squares or REML by adding the function r() to formulas of lm() and glm(). A collection of text-book statistics for higher education is also included, e.g. modifications of the functions lm(), glm() and associated summaries from the package 'stats'.

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; ).

Mixed Effects Cox Models

Fit Cox proportional hazards models containing both fixed and random effects. The random effects can have a general form, of which familial interactions (a "kinship" matrix) is a particular special case. Note that the simplest case of a mixed effects Cox model, i.e. a single random per-group intercept, is also called a "frailty" model. The approach is based on Ripatti and Palmgren, Biometrics 2002.

Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models

The 'DHARMa' package uses a simulation-based approach to create readily interpretable scaled (quantile) residuals for fitted (generalized) linear mixed models. Currently supported are linear and generalized linear (mixed) models from 'lme4' (classes 'lmerMod', 'glmerMod'), 'glmmTMB', 'GLMMadaptive', and 'spaMM'; phylogenetic linear models from 'phylolm' (classes 'phylolm' and 'phyloglm'); generalized additive models ('gam' from 'mgcv'); 'glm' (including 'negbin' from 'MASS', but excluding quasi-distributions) and 'lm' model classes. Moreover, externally created simulations, e.g. posterior predictive simulations from Bayesian software such as 'JAGS', 'STAN', or 'BUGS' can be processed as well. The resulting residuals are standardized to values between 0 and 1 and can be interpreted as intuitively as residuals from a linear regression. The package also provides a number of plot and test functions for typical model misspecification problems, such as over/underdispersion, zero-inflation, and residual spatial, phylogenetic and temporal autocorrelation.

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) .