Interpreting Time Series and Autocorrelated Data Using GAMMs

GAMM (Generalized Additive Mixed Modeling; Lin & Zhang, 1999) as implemented in the R package 'mgcv' (Wood, S.N., 2006; 2011) is a nonlinear regression analysis which is particularly useful for time course data such as EEG, pupil dilation, gaze data (eye tracking), and articulography recordings, but also for behavioral data such as reaction times and response data. As time course measures are sensitive to autocorrelation problems, GAMMs implements methods to reduce the autocorrelation problems. This package includes functions for the evaluation of GAMM models (e.g., model comparisons, determining regions of significance, inspection of autocorrelational structure in residuals) and interpreting of GAMMs (e.g., visualization of complex interactions, and contrasts).

Generalized Additive Models with Flexible Response Functions

Standard generalized additive models assume a response function, which induces an assumption on the shape of the distribution of the response. However, miss-specifying the response function results in biased estimates. Therefore in Spiegel et al. (2017) we propose to estimate the response function jointly with the covariate effects. This package provides the underlying functions to estimate these generalized additive models with flexible response functions. The estimation is based on an iterative algorithm. In the outer loop the response function is estimated, while in the inner loop the covariate effects are determined. For the response function a strictly monotone P-spline is used while the covariate effects are estimated based on a modified Fisher-Scoring algorithm. Overall the estimation relies on the 'mgcv'-package.

Spline-Based Nonlinear Modeling for Multilevel and Longitudinal Data

Provides a unified framework for fitting, predicting, and interpreting nonlinear relationships in single-level, multilevel, and longitudinal regression models. Flexible functional forms are supported using natural cubic splines ('splines'), B-splines ('splines'), and GAM smooths ('mgcv'). Supports two-way and nested clustering via 'lme4', automatic knot selection by AIC or BIC, multilevel R-squared decomposition (Nakagawa-Schielzeth marginal and conditional R-squared with level-specific variance partitioning), a postestimation suite returning first and second derivatives with confidence bands, turning points and inflection regions, and a model comparison workflow contrasting linear, polynomial, and spline fits by AIC, BIC, and likelihood-ratio tests. Cluster heterogeneity in nonlinear effects is supported via random-slope spline terms.

Transformation Models with Mixed Effects

Likelihood-based estimation of mixed-effects transformation models using the Template Model Builder ('TMB', Kristensen et al., 2016) . The technical details of transformation models are given in Hothorn et al. (2018) . Likelihood contributions of exact, randomly censored (left, right, interval) and truncated observations are supported. The random effects are assumed to be normally distributed on the scale of the transformation function, the marginal likelihood is evaluated using the Laplace approximation, and the gradients are calculated with automatic differentiation (Tamasi & Hothorn, 2021) . Penalized smooth shift terms can be defined using the 'mgcv' notation. Additive mixed-effects transformation models are described in Tamasi (2025) .

Easy Graphs for Data Visualisation and Linear Models for ANOVA

Easily explore data by plotting graphs with a few lines of code. Use these ggplot() wrappers to quickly draw graphs of scatter/dots with box-whiskers, violins or SD error bars, data distributions, before-after graphs, factorial ANOVA and more. Customise graphs in many ways, for example, by choosing from colour blind-friendly palettes (12 discreet, 3 continuous and 2 divergent palettes). Use the simple code for ANOVA as ordinary (lm()) or mixed-effects linear models (lmer()), including randomised-block or repeated-measures designs, and fit non-linear outcomes as a generalised additive model (gam) using mgcv(). Obtain estimated marginal means and perform post-hoc comparisons on fitted models (via emmeans()). Also includes small datasets for practising code and teaching basics before users move on to more complex designs. See vignettes for details on usage < https://grafify.shenoylab.com/>. Citation: .

Parallelize Common Functions via One Magic Function

The futurize() function transpiles calls to sequential map-reduce functions such as base::lapply(), purrr::map(), 'foreach::foreach() %do% { ... }' into concurrent alternatives, providing you with a simple, straightforward path to scalable parallel computing via the 'future' ecosystem . By combining this function with R's native pipe operator, you have a convenient way for speeding up iterative computations with minimal refactoring, e.g. 'lapply(xs, fcn) |> futurize()', 'purrr::map(xs, fcn) |> futurize()', and 'foreach::foreach(x = xs) %do% { fcn(x) } |> futurize()'. Other map-reduce packages that can be "futurized" are 'BiocParallel', 'plyr', 'crossmap', 'pbapply' packages. There is also support for a growing set of domain-specific packages on CRAN (e.g. 'boot', 'caret', 'fgsea', 'fwb', 'gamlss', 'glmmTMB', 'glmnet', 'kernelshap', 'lme4', 'metafor', 'mgcv', 'partykit', 'riskRegression', 'seriation', 'shapr', 'SimDesign', 'strucchange', 'tm', 'TSP', and 'vegan') and on Bioconductor (e.g. 'DESeq2', 'GenomicAlignments', 'GSVA', 'Rsamtools', 'scater', 'scuttle', 'SingleCellExperiment', and 'sva').

Latent Variable Models Diagnostics

Diagnostics and visualization tools for latent variable models fitted with 'lavaan' (Rosseel, 2012 ). The package provides fast, parallel-safe factor-score prediction (lavPredict_parallel()), data augmentation with model predictions, residuals, delta-method standard errors and confidence intervals (augment()), and model-based latent grids for continuous, ordinal, or mixed indicators (prepare()). It offers item-level empirical versus model curve comparison using generalized additive models for both continuous and ordinal indicators (item_data(), item_plot()) via 'mgcv' (Wood, 2017, ISBN:9781498728331), residual diagnostics including residual correlation tables and plots (resid_cor(), resid_corrplot()) using 'corrplot' (Wei and Simko, 2021 < https://github.com/taiyun/corrplot>), and Q–Q checks of residual z-statistics (resid_qq()), optionally with non-overlapping labels from 'ggrepel' (Slowikowski, 2024 < https://CRAN.R-project.org/package=ggrepel>). Heavy computations are parallelized via 'future'/'furrr' (Bengtsson, 2021 ; Vaughan and Dancho, 2018 < https://CRAN.R-project.org/package=furrr>). Methods build on established literature and packages listed above.

Spatial and Spatiotemporal SPDE-Based GLMMs with 'TMB'

Implements spatial and spatiotemporal GLMMs (Generalized Linear Mixed Effect Models) using 'TMB', 'fmesher', and the SPDE (Stochastic Partial Differential Equation) Gaussian Markov random field approximation to Gaussian random fields. One common application is for spatially explicit species distribution models (SDMs). See Anderson et al. (2025) .

Community Ecology Package

Ordination methods, diversity analysis and other functions for community and vegetation ecologists.

Vector Generalized Linear and Additive Models

An implementation of about 6 major classes of statistical regression models. The central algorithm is Fisher scoring and iterative reweighted least squares. At the heart of this package are the vector generalized linear and additive model (VGLM/VGAM) classes. VGLMs can be loosely thought of as multivariate GLMs. VGAMs are data-driven VGLMs that use smoothing. The book "Vector Generalized Linear and Additive Models: With an Implementation in R" (Yee, 2015) gives details of the statistical framework and the package. Currently only fixed-effects models are implemented. Many (100+) models and distributions are estimated by maximum likelihood estimation (MLE) or penalized MLE. The other classes are RR-VGLMs (reduced-rank VGLMs), quadratic RR-VGLMs, doubly constrained RR-VGLMs, quadratic RR-VGLMs, reduced-rank VGAMs, RCIMs (row-column interaction models)---these classes perform constrained and unconstrained quadratic ordination (CQO/UQO) models in ecology, as well as constrained additive ordination (CAO). Hauck-Donner effect detection is implemented. Note that these functions are subject to change; see the NEWS and ChangeLog files for latest changes.