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.

Tidy Data and 'Geoms' for Bayesian Models

Compose data for and extract, manipulate, and visualize posterior draws from Bayesian models ('JAGS', 'Stan', 'rstanarm', 'brms', 'MCMCglmm', 'coda', ...) in a tidy data format. Functions are provided to help extract tidy data frames of draws from Bayesian models and that generate point summaries and intervals in a tidy format. In addition, 'ggplot2' 'geoms' and 'stats' are provided for common visualization primitives like points with multiple uncertainty intervals, eye plots (intervals plus densities), and fit curves with multiple, arbitrary uncertainty bands.

Regression Modeling Strategies

Regression modeling, testing, estimation, validation, graphics, prediction, and typesetting by storing enhanced model design attributes in the fit. 'rms' is a collection of functions that assist with and streamline modeling. It also contains functions for binary and ordinal logistic regression models, ordinal models for continuous Y with a variety of distribution families, and the Buckley-James multiple regression model for right-censored responses, and implements penalized maximum likelihood estimation for logistic and ordinary linear models. 'rms' works with almost any regression model, but it was especially written to work with binary or ordinal regression models, Cox regression, accelerated failure time models, ordinary linear models, the Buckley-James model, generalized least squares for serially or spatially correlated observations, generalized linear models, and quantile regression.

Bindings for Bayesian TidyModels

Fit Bayesian models using 'brms'/'Stan' with 'parsnip'/'tidymodels' via 'bayesian' . 'tidymodels' is a collection of packages for machine learning; see Kuhn and Wickham (2020) < https://www.tidymodels.org>). The technical details of 'brms' and 'Stan' are described in Bürkner (2017) , Bürkner (2018) , and Carpenter et al. (2017) .

Markov Chain Monte Carlo (MCMC) Package

Contains functions to perform Bayesian inference using posterior simulation for a number of statistical models. Most simulation is done in compiled C++ written in the Scythe Statistical Library Version 1.0.3. All models return 'coda' mcmc objects that can then be summarized using the 'coda' package. Some useful utility functions such as density functions, pseudo-random number generators for statistical distributions, a general purpose Metropolis sampling algorithm, and tools for visualization are provided.

Mixed-Effects Models with Autocorrelation Structures

Fits longitudinal mixed-effects models through a registered 'C++' numerical backend. Supported serial covariance structures include first-order autoregressive (AR(1)), exponential or Ornstein-Uhlenbeck, higher-order autoregressive (AR(p)), first-order autoregressive moving-average (ARMA(1,1)), compound symmetry, Toeplitz, and unstructured covariance. Serial processes can be unified or attached independently to numeric predictor loadings. Candidate temporal structures can be ranked on a common sample by dependence-component grouped cross-validation, the Akaike information criterion, the Bayesian information criterion, or log-likelihood. Clustered, crossed, and nested random intercepts and slopes are assembled jointly with diagonal or term-specific unstructured covariance. Available approximation methods include Laplace, saddlepoint likelihood with latent Laplace integration, adaptive Gaussian quadrature, full-covariance Gaussian variational inference, and penalized quasi-likelihood. Penalized smooth mean terms include ordinary and cyclic P-splines, factor-by and varying-coefficient terms, tensor products, shrinkage smooths, and whole-term selection. Term-specific penalties, grouped fold-local smoothing selection, null-space constraints, and smooth effective degrees of freedom remain separate from elastic-net coefficient shrinkage while the smooth mean and serial covariance are fitted jointly. Bootstrap resampling preserves the declared dependence components. The mixed-effects framework is inspired by Laird and Ware (1982) ; generalized-model approximations are inspired by Breslow and Clayton (1993) ; and serial covariance formulations are inspired by Pinheiro and Bates (2000) . The run-time fitting interface imports no third-party 'R' packages.

Political Science Computational Laboratory

Bayesian analysis of item-response theory (IRT) models, roll call analysis; computing highest density regions; maximum likelihood estimation of zero-inflated and hurdle models for count data; goodness-of-fit measures for GLMs; data sets used in writing and teaching; seats-votes curves.

A General Framework for Latent Class and Profile Analysis

Provides a unified framework for finite-mixture latent variable models, including latent class analysis (LCA), latent profile analysis (LPA), latent class/profile analysis with covariates, and latent transition analysis (LTA), within one consistent interface. Estimation methods include the expectation-maximization (EM) algorithm; neural network estimation, which requires 'Python' and its dependent libraries; integration with 'Mplus', which requires an installed copy of 'Mplus'; and stochastic EM (SEM) through the optional 'flexmix', 'Rmixmod', and 'RMixtComp' backends. 'flexmix' and the default 'Rmixmod' path perform configurable warm-up trajectories and promote the best candidates to full SEM replications. 'Rmixmod' additionally exposes its native strategy interface, including chained SEM-to-EM estimation, whereas 'RMixtComp' exposes its native SEM and Gibbs controls without the external warm-up stage. Model assessment includes the Akaike information criterion (AIC), Bayesian information criterion (BIC), Schwarz information criterion (SIC), consistent AIC (CAIC), approximate weight of evidence (AWE), sample-size-adjusted BIC (SABIC), entropy, and average posterior probabilities. Model-comparison procedures include the ordinary likelihood-ratio test, the Mplus TECH11 Vuong-Lo-Mendell-Rubin and adjusted Lo-Mendell-Rubin tests, and fixed-replicate or sequential parametric bootstrap likelihood-ratio tests. Standard errors can be estimated by nonparametric bootstrap, numerical observed information, or analytic observed information based on Louis' identity. Classification-error-adjusted maximum-likelihood and Bolck-Croon-Hagenaars three-step methods support covariates predicting latent membership, initial-status and transition regressions, and latent classes or states predicting continuous and categorical external observed dependent variables. Simulation, posterior-probability, classification-error, extraction, summary, plotting, model-adjustment, and update utilities are also provided for reproducible workflows.

Bayesian Additive Regression Trees

Bayesian Additive Regression Trees (BART) provide flexible nonparametric modeling of covariates for continuous, binary, categorical and time-to-event outcomes. For more information see Sparapani, Spanbauer and McCulloch .

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.