Bayesian Regression Models using 'Stan'

Fit Bayesian generalized (non-)linear multivariate multilevel models using 'Stan' for full Bayesian inference. A wide range of distributions and link functions are supported, allowing users to fit -- among others -- linear, robust linear, count data, survival, response times, ordinal, zero-inflated, hurdle, and even self-defined mixture models all in a multilevel context. Further modeling options include both theory-driven and data-driven non-linear terms, auto-correlation structures, censoring and truncation, meta-analytic standard errors, and quite a few more. In addition, all parameters of the response distribution can be predicted in order to perform distributional regression. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their prior knowledge. Models can easily be evaluated and compared using several methods assessing posterior or prior predictions. References: Bürkner (2017) ; Bürkner (2018) ; Bürkner (2021) ; Carpenter et al. (2017) .

Linear and Nonlinear Mixed Effects Models

Fit and compare Gaussian linear and nonlinear mixed-effects models.

Generate Postestimation Quantities for Bayesian MCMC Estimation

An implementation of functions to generate and plot postestimation quantities after estimating Bayesian regression models using Markov chain Monte Carlo (MCMC). Functionality includes the estimation of the Precision-Recall curves (see Beger, 2016 ), the implementation of the observed values method of calculating predicted probabilities by Hanmer and Kalkan (2013) , the implementation of the average value method of calculating predicted probabilities (see King, Tomz, and Wittenberg, 2000 ), and the generation and plotting of first differences to summarize typical effects across covariates (see Long 1997, ISBN:9780803973749; King, Tomz, and Wittenberg, 2000 ). This package can be used with MCMC output generated by any Bayesian estimation tool including 'JAGS', 'BUGS', 'MCMCpack', and 'Stan'.

Predictive Probability for a Continuous Response with an ANOVA Structure

A Bayesian approach to using predictive probability in an ANOVA construct with a continuous normal response, when threshold values must be obtained for the question of interest to be evaluated as successful (Sieck and Christensen (2021) ). The Bayesian Mission Mean (BMM) is used to evaluate a question of interest (that is, a mean that randomly selects combination of factor levels based on their probability of occurring instead of averaging over the factor levels, as in the grand mean). Under this construct, in contrast to a Gibbs sampler (or Metropolis-within-Gibbs sampler), a two-stage sampling method is required. The nested sampler determines the conditional posterior distribution of the model parameters, given Y, and the outside sampler determines the marginal posterior distribution of Y (also commonly called the predictive distribution for Y). This approach provides a sample from the joint posterior distribution of Y and the model parameters, while also accounting for the threshold value that must be obtained in order for the question of interest to be evaluated as successful.

Lasso and Elastic-Net Regularized Generalized Linear Models

Extremely efficient procedures for fitting the entire lasso or elastic-net regularization path for linear regression, logistic and multinomial regression models, Poisson regression, Cox model, multiple-response Gaussian, and the grouped multinomial regression; see and . There are two new and important additions. The family argument can be a GLM family object, which opens the door to any programmed family (). This comes with a modest computational cost, so when the built-in families suffice, they should be used instead. The other novelty is the relax option, which refits each of the active sets in the path unpenalized. The algorithm uses cyclical coordinate descent in a path-wise fashion, as described in the papers cited.

Bayesian Applied Regression Modeling via Stan

Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to the Stan C++ library for Bayesian estimation. Users specify models via the customary R syntax with a formula and data.frame plus some additional arguments for priors.

R Interface to Stan

User-facing R functions are provided to parse, compile, test, estimate, and analyze Stan models by accessing the header-only Stan library provided by the 'StanHeaders' package. The Stan project develops a probabilistic programming language that implements full Bayesian statistical inference via Markov Chain Monte Carlo, rough Bayesian inference via 'variational' approximation, and (optionally penalized) maximum likelihood estimation via optimization. In all three cases, automatic differentiation is used to quickly and accurately evaluate gradients without burdening the user with the need to derive the partial derivatives.

Geographic Data Analysis and Modeling

Reading, writing, manipulating, analyzing and modeling of spatial data. This package has been superseded by the "terra" package < https://CRAN.R-project.org/package=terra>.

MCMC, Particle Filtering, and Programmable Hierarchical Modeling

A system for writing hierarchical statistical models largely compatible with 'BUGS' and 'JAGS', writing nimbleFunctions to operate models and do basic R-style math, and compiling both models and nimbleFunctions via custom-generated C++. 'NIMBLE' includes default methods for MCMC, Laplace Approximation, Monte Carlo Expectation Maximization, and some other tools. The nimbleFunction system makes it easy to do things like implement new MCMC samplers from R, customize the assignment of samplers to different parts of a model from R, and compile the new samplers automatically via C++ alongside the samplers 'NIMBLE' provides. 'NIMBLE' extends the 'BUGS'/'JAGS' language by making it extensible: New distributions and functions can be added, including as calls to external compiled code. Although most people think of MCMC as the main goal of the 'BUGS'/'JAGS' language for writing models, one can use 'NIMBLE' for writing arbitrary other kinds of model-generic algorithms as well. A full User Manual is available at < https://r-nimble.org>.

Survival Analysis

Contains the core survival analysis routines, including definition of Surv objects, Kaplan-Meier and Aalen-Johansen (multi-state) curves, Cox models, and parametric accelerated failure time models.