Linear and Nonlinear Mixed Effects Models

Fit and compare Gaussian linear and nonlinear mixed-effects models.

Generalized Linear Mixed Models using Template Model Builder

Fit linear and generalized linear mixed models with various extensions, including zero-inflation. The models are fitted using maximum likelihood estimation via 'TMB' (Template Model Builder). Random effects are assumed to be Gaussian on the scale of the linear predictor and are integrated out using the Laplace approximation. Gradients are calculated using automatic differentiation.

Linear Mixed-Effects Models using 'Eigen' and S4

Fit linear and generalized linear mixed-effects models. The models and their components are represented using S4 classes and methods. The core computational algorithms are implemented using the 'Eigen' C++ library for numerical linear algebra and 'RcppEigen' "glue".

MCMC Generalised Linear Mixed Models

Fits Multivariate Generalised Linear Mixed Models (and related models) using Markov chain Monte Carlo techniques (Hadfield 2010 J. Stat. Soft.).

Generalized Additive Mixed Models using 'mgcv' and 'lme4'

Estimate generalized additive mixed models via a version of function gamm() from 'mgcv', using 'lme4' for estimation.

Parametric Bootstrap, Kenward-Roger and Satterthwaite Based Methods for Test in Mixed Models

Computes p-values based on (a) Satterthwaite or Kenward-Rogers degree of freedom methods and (b) parametric bootstrap for mixed effects models as implemented in the 'lme4' package. Implements parametric bootstrap test for generalized linear mixed models as implemented in 'lme4' and generalized linear models. The package is documented in the paper by Halekoh and Højsgaard, (2012, ). Please see 'citation("pbkrtest")' for citation details.

Solving Mixed Model Equations in R

Structural multivariate-univariate linear mixed model solver for estimation of multiple random effects with unknown variance-covariance structures (e.g., heterogeneous and unstructured) and known covariance among levels of random effects (e.g., pedigree and genomic relationship matrices) (Covarrubias-Pazaran, 2016 ; Maier et al., 2015 ; Jensen et al., 1997). REML estimates can be obtained using the Direct-Inversion Newton-Raphson and Direct-Inversion Average Information algorithms for the problems r x r (r being the number of records) or using the Henderson-based average information algorithm for the problem c x c (c being the number of coefficients to estimate). Spatial models can also be fitted using the two-dimensional spline functionality available.

Mixed Models for Repeated Measures

Mixed models for repeated measures (MMRM) are a popular choice for analyzing longitudinal continuous outcomes in randomized clinical trials and beyond; see Cnaan, Laird and Slasor (1997) for a tutorial and Mallinckrodt, Lane, Schnell, Peng and Mancuso (2008) for a review. This package implements MMRM based on the marginal linear model without random effects using Template Model Builder ('TMB') which enables fast and robust model fitting. Users can specify a variety of covariance matrices, weight observations, fit models with restricted or standard maximum likelihood inference, perform hypothesis testing with Satterthwaite or Kenward-Roger adjustment, and extract least square means estimates by using 'emmeans'.

Tests in Linear Mixed Effects Models

Provides p-values in type I, II or III anova and summary tables for lmer model fits (cf. lme4) via Satterthwaite's degrees of freedom method. A Kenward-Roger method is also available via the pbkrtest package. Model selection methods include step, drop1 and anova-like tables for random effects (ranova). Methods for Least-Square means (LS-means) and tests of linear contrasts of fixed effects are also available.

Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

Generalized additive (mixed) models, some of their extensions and other generalized ridge regression with multiple smoothing parameter estimation by (Restricted) Marginal Likelihood, Cross Validation and similar, or using iterated nested Laplace approximation for fully Bayesian inference. See Wood (2025) for an overview. Includes a gam() function, a wide variety of smoothers, 'JAGS' support and distributions beyond the exponential family.