Distributional Stochastic Frontier Analysis

Framework to fit distributional stochastic frontier models. Casts the stochastic frontier model into the flexible framework of distributional regression or otherwise known as General Additive Models of Location, Scale and Shape (GAMLSS). Allows for linear, non-linear, random and spatial effects on all the parameters of the distribution of the output, e.g. effects on the production or cost function, heterogeneity of the noise and inefficiency. Available distributions are the normal-halfnormal and normal-exponential distribution. Estimation via the fast and reliable routines of the 'mgcv' package. For more details see .

Asymmetric Smoothed-Association Matrices via GAM Fits

Render a pairwise, asymmetric smoothed-association matrix of continuous variables. Each cell shows the fitted spline from an 'mgcv' generalised additive model, with the upper triangle displaying 'gam(x_j ~ s(x_i))' and the lower triangle 'gam(x_i ~ s(x_j))'. Unlike Pearson's correlation matrix, the visualisation is intentionally asymmetric, revealing heteroscedasticity, leverage, and directional non-linearity that a single scalar correlation hides. An asymmetry index and a 24-category shape taxonomy quantify the directional difference and qualitative form of each fitted smooth.

Shape Constrained Additive Models

Generalized additive models under shape constraints on the component functions of the linear predictor. Models can include multiple shape-constrained (univariate and bivariate) and unconstrained terms. Routines of the package 'mgcv' are used to set up the model matrix, print, and plot the results. Multiple smoothing parameter estimation by the Generalized Cross Validation or similar. See Pya and Wood (2015) for an overview. A broad selection of shape-constrained smoothers, linear functionals of smooths with shape constraints, and Gaussian models with AR1 residuals.

Predict and Visualize Population-Level Changes in Allele Frequencies in Response to Climate Change

Methods () are provided of calibrating and predicting shifts in allele frequencies through redundancy analysis ('vegan::rda()') and generalized additive models ('mgcv::gam()'). Visualization functions for predicted changes in allele frequencies include 'shift.dot.ggplot()', 'shift.pie.ggplot()', 'shift.moon.ggplot()', 'shift.waffle.ggplot()' and 'shift.surf.ggplot()' that are made with input data sets that are prepared by helper functions for each visualization method. Examples in the documentation show how to prepare animated climate change graphics through a time series with the 'gganimate' package. Function 'amova.rda()' shows how Analysis of Molecular Variance can be directly conducted with the results from redundancy analysis.

Gradient Boosting for Nonlinear Spatial Autoregressive Models

Flexible nonlinear extension of spatial autoregressive (SAR), spatial error (SEM), and spatial autoregressive with autoregressive disturbances (SARAR) models with multiple regression engines (generalized additive models ('mgcv'), gradient boosting ('mboost'), multivariate adaptive regression splines ('earth'), and 'xgboost') and two families of spatial-parameter estimators: maximum likelihood and the determinant-free Closed-Form Estimator of Smirnov (2020) . See Geniaux G. (2026). "Flexible nonlinear spatial autoregressive models: a gradient boosting approach with closed-form estimation." Presented at Spatial Econometrics World Congress (SEA/SEW 2026, Paris), unpublished.

Meta-Analysis of Generalized Additive Models

Meta-analysis of generalized additive models and generalized additive mixed models. A typical use case is when data cannot be shared across locations, and an overall meta-analytic fit is sought. 'metagam' provides functionality for removing individual participant data from models computed using the 'mgcv' and 'gamm4' packages such that the model objects can be shared without exposing individual data. Furthermore, methods for meta-analysing these fits are provided. The implemented methods are described in Sorensen et al. (2020), , extending previous works by Schwartz and Zanobetti (2000) and Crippa et al. (2018) .

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.

Debiased Score Tests for Goodness of Fit and Model Comparison

Debiased (Neyman-orthogonalized) score tests for assessing whether a semiparametric or parametric regression model is well-specified and for comparing nested models. The test employs a hunt-and-test strategy: on a held-out hunt sample, it fits the null model and uses machine learning to find a direction in which the null model's score seems positive; on an independent test sample, it assesses the significance of the score in the hunted direction. The test employs orthogonalization to eliminate the bias from estimating the null model, yielding a test statistic that is asymptotically standard normal under the null without requiring a parametric form for the alternative. Methods are provided for 'glm', 'lm' and 'mgcv::gam' fits as well as for detecting heterogeneous treatment effects. The methodology is described in Dhawan, Guo and Shah (2026) .

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) .