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 .

Linear Mixed Model Solver

An efficient and flexible system to solve sparse mixed model equations. Important applications are the use of splines to model spatial or temporal trends as described in Boer (2023). ().

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.

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; ).

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.

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.

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.

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.

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, Generalized Cross Validation and similar, or using iterated nested Laplace approximation for fully Bayesian inference. See Wood (2017) for an overview. Includes a gam() function, a wide variety of smoothers, 'JAGS' support and distributions beyond the exponential family.