Multivariate Functional Principal Component Analysis for Data Observed on Different Dimensional Domains

Calculate a multivariate functional principal component analysis for data observed on different dimensional domains. The estimation algorithm relies on univariate basis expansions for each element of the multivariate functional data (Happ & Greven, 2018) . Multivariate and univariate functional data objects are represented by S4 classes for this type of data implemented in the package 'funData'. For more details on the general concepts of both packages and a case study, see Happ-Kurz (2020) .

Tools for Post-Processing Predicted Values

Models can be improved by post-processing class probabilities, by: recalibration, conversion to hard probabilities, assessment of equivocal zones, and other activities. 'probably' contains tools for conducting these operations as well as calibration tools and conformal inference techniques for regression models.

Multidimensional Item Response Theory

Analysis of discrete response data using unidimensional and multidimensional item analysis models under the Item Response Theory paradigm (Chalmers (2012) ). Exploratory and confirmatory item factor analysis models are estimated with quadrature (EM) or stochastic (MHRM) methods. Confirmatory bi-factor and two-tier models are available for modeling item testlets using dimension reduction EM algorithms, while multiple group analyses and mixed effects designs are included for detecting differential item, bundle, and test functioning, and for modeling item and person covariates. Finally, latent class models such as the DINA, DINO, multidimensional latent class, mixture IRT models, and zero-inflated response models are supported, as well as a wide family of probabilistic unfolding models.

Tools for the Analysis of Air Pollution Data

Tools to analyse, interpret and understand air pollution data. Data are typically regular time series and air quality measurement, meteorological data and dispersion model output can be analysed. The package is described in Carslaw and Ropkins (2012, ) and subsequent papers.

Time-Varying Effect Models

Fits time-varying effect models (TVEM). These are a kind of application of varying-coefficient models in the context of longitudinal data, allowing the strength of linear, logistic, or Poisson regression relationships to change over time. These models are described further in Tan, Shiyko, Li, Li & Dierker (2012) . We thank Kaylee Litson, Patricia Berglund, Yajnaseni Chakraborti, and Hanjoo Kim for their valuable help with testing the package and the documentation. The development of this package was part of a research project supported by National Institutes of Health grants P50 DA039838 from the National Institute of Drug Abuse and 1R01 CA229542-01 from the National Cancer Institute and the NIH Office of Behavioral and Social Science Research. Content is solely the responsibility of the authors and does not necessarily represent the official views of the funding institutions mentioned above. This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

Gradient-Based Coenospace Vegetation Simulator

Simulates the composition of samples of vegetation according to gradient-based vegetation theory. Features a flexible algorithm incorporating competition and complex multi-gradient interaction.

A Multi-Process 'dplyr' Backend

Partition a data frame across multiple worker processes to provide simple multicore parallelism.

Bayesian Cost Effectiveness Analysis

Produces an economic evaluation of a sample of suitable variables of cost and effectiveness / utility for two or more interventions, e.g. from a Bayesian model in the form of MCMC simulations. This package computes the most cost-effective alternative and produces graphical summaries and probabilistic sensitivity analysis, see Baio et al (2017) .

Generalised Additive Extreme Value Models

Methods for fitting various extreme value distributions with parameters of generalised additive model (GAM) form are provided. For details of distributions see Coles, S.G. (2001) , GAMs see Wood, S.N. (2017) , and the fitting approach see Wood, S.N., Pya, N. & Safken, B. (2016) . Details of how evgam works and various examples are given in Youngman, B.D. (2022) .

Nonlinear Time Series Models with Regime Switching

Implements nonlinear autoregressive (AR) time series models. For univariate series, a non-parametric approach is available through additive nonlinear AR. Parametric modeling and testing for regime switching dynamics is available when the transition is either direct (TAR: threshold AR) or smooth (STAR: smooth transition AR, LSTAR). For multivariate series, one can estimate a range of TVAR or threshold cointegration TVECM models with two or three regimes. Tests can be conducted for TVAR as well as for TVECM (Hansen and Seo 2002 and Seo 2006).