An Implementation of the Bayesian Markov (Renewal) Mixed Models

The Bayesian Markov renewal mixed models take sequentially observed categorical data with continuous duration times, being either state duration or inter-state duration. These models comprehensively analyze the stochastic dynamics of both state transitions and duration times under the influence of multiple exogenous factors and random individual effect. The default setting flexibly models the transition probabilities using Dirichlet mixtures and the duration times using gamma mixtures. It also provides the flexibility of modeling the categorical sequences using Bayesian Markov mixed models alone, either ignoring the duration times altogether or dividing duration time into multiples of an additional category in the sequence by a user-specific unit. The package allows extensive inference of the state transition probabilities and the duration times as well as relevant plots and graphs. It also includes a synthetic data set to demonstrate the desired format of input data set and the utility of various functions. Methods for Bayesian Markov renewal mixed models are as described in: Abhra Sarkar et al., (2018) and Yutong Wu et al., (2022) .

Robust Bayesian T-Test

An implementation of Bayesian model-averaged t-tests that allows users to draw inferences about the presence versus absence of an effect, variance heterogeneity, and potential outliers. The 'RoBTT' package estimates ensembles of models created by combining competing hypotheses and applies Bayesian model averaging using posterior model probabilities. Users can obtain model-averaged posterior distributions and inclusion Bayes factors, accounting for uncertainty in the data-generating process (Maier et al., 2024, ). The package also provides a truncated likelihood version of the model-averaged t-test, enabling users to exclude potential outliers without introducing bias (Godmann et al., 2024, ). Users can specify a wide range of informative priors for all parameters of interest. The package offers convenient functions for summary, visualization, and fit diagnostics.

Robust Bayesian Survival Analysis

A framework for estimating ensembles of parametric survival models with different parametric families. The RoBSA framework uses Bayesian model-averaging to combine the competing parametric survival models into a model ensemble, weights the posterior parameter distributions based on posterior model probabilities and uses Bayes factors to test for the presence or absence of the individual predictors or preference for a parametric family (Bartoš, Aust & Haaf, 2022, ). The user can define a wide range of informative priors for all parameters of interest. The package provides convenient functions for summary, visualizations, fit diagnostics, and prior distribution calibration.

Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

Generalized additive (mixed) models, some of their extensions and other generalized ridge regression with multiple smoothing parameter estimation by (Restricted) Marginal Likelihood, Generalized Cross Validation and similar, or using iterated nested Laplace approximation for fully Bayesian inference. See Wood (2017) for an overview. Includes a gam() function, a wide variety of smoothers, 'JAGS' support and distributions beyond the exponential family.

Continuous Time Structural Equation Modelling

Hierarchical continuous (and discrete) time state space modelling, for linear and nonlinear systems measured by continuous variables, with limited support for binary data. The subject specific dynamic system is modelled as a stochastic differential equation (SDE) or difference equation, measurement models are typically multivariate normal factor models. Linear mixed effects SDE's estimated via maximum likelihood and optimization are the default. Nonlinearities, (state dependent parameters) and random effects on all parameters are possible, using either max likelihood / max a posteriori optimization (with optional importance sampling) or Stan's Hamiltonian Monte Carlo sampling. See < https://github.com/cdriveraus/ctsem/raw/master/vignettes/hierarchicalmanual.pdf> for details. See < https://osf.io/preprints/psyarxiv/4q9ex_v2> for a detailed tutorial. Priors may be used. For the conceptual overview of the hierarchical Bayesian linear SDE approach, see < https://www.researchgate.net/publication/324093594_Hierarchical_Bayesian_Continuous_Time_Dynamic_Modeling>. Exogenous inputs may also be included, for an overview of such possibilities see < https://www.researchgate.net/publication/328221807_Understanding_the_Time_Course_of_Interventions_with_Continuous_Time_Dynamic_Models> . < https://cdriver.netlify.app/> contains some tutorial blog posts.

Bayesian Quantile Regression for Ordinal Models

Package provides functions for estimation and inference in Bayesian quantile regression with ordinal outcomes. An ordinal model with 3 or more outcomes (labeled OR1 model) is estimated by a combination of Gibbs sampling and Metropolis-Hastings (MH) algorithm. Whereas an ordinal model with exactly 3 outcomes (labeled OR2 model) is estimated using a Gibbs sampling algorithm. The summary output presents the posterior mean, posterior standard deviation, 95% credible intervals, and the inefficiency factors along with the two model comparison measures – logarithm of marginal likelihood and the deviance information criterion (DIC). The package also provides functions for computing the covariate effects and other functions that aids either the estimation or inference in quantile ordinal models. Rahman, M. A. (2016).“Bayesian Quantile Regression for Ordinal Models.” Bayesian Analysis, 11(1): 1-24 . Yu, K., and Moyeed, R. A. (2001). “Bayesian Quantile Regression.” Statistics and Probability Letters, 54(4): 437–447 . Koenker, R., and Bassett, G. (1978).“Regression Quantiles.” Econometrica, 46(1): 33-50 . Chib, S. (1995). “Marginal likelihood from the Gibbs output.” Journal of the American Statistical Association, 90(432):1313–1321, 1995. . Chib, S., and Jeliazkov, I. (2001). “Marginal likelihood from the Metropolis-Hastings output.” Journal of the American Statistical Association, 96(453):270–281, 2001. .

Utility Functions for Multilevel Mediation Analysis

The ultimate goal is to support 2-2-1, 2-1-1, and 1-1-1 models for multilevel mediation, the option of a moderating variable for either the a, b, or both paths, and covariates. Currently the 1-1-1 model is supported and several options of random effects; the initial code for bootstrapping was evaluated in simulations by Falk, Vogel, Hammami, and Miočević (2024) . Support for Bayesian estimation using 'brms' comprises ongoing work. Currently only continuous mediators and outcomes are supported. Factors for any predictors must be numerically represented.

Latent Space Item Response Model

Analysis of dichotomous and continuous response data using latent factor by both 1PL LSIRM and 2PL LSIRM as described in Jeon et al. (2021) . It includes original 1PL LSIRM and 2PL LSIRM provided for binary response data and its extension for continuous response data. Bayesian model selection with spike-and-slab prior and method for dealing data with missing value under missing at random, missing completely at random are also supported. Various diagnostic plots are available to inspect the latent space and summary of estimated parameters.

Bayesian Mortality Modelling

Fit Bayesian graduation mortality using the Heligman-Pollard model, as seen in Heligman, L., & Pollard, J. H. (1980) and Dellaportas, Petros, et al. (2001) , and dynamic linear model (Campagnoli, P., Petris, G., and Petrone, S. (2009) ). While Heligman-Pollard has parameters with a straightforward interpretation yielding some rich analysis, the dynamic linear model provides a very flexible adjustment of the mortality curves by controlling the discount factor value. Closing methods for both Heligman-Pollard and dynamic linear model were also implemented according to Dodd, Erengul, et al. (2018) < https://www.jstor.org/stable/48547511>. The Bayesian Lee-Carter model is also implemented to fit historical mortality tables time series to predict the mortality in the following years and to do improvement analysis, as seen in Lee, R. D., & Carter, L. R. (1992) and Pedroza, C. (2006) .

Complete Environment for Bayesian Inference

Provides a complete environment for Bayesian inference using a variety of different samplers (see ?LaplacesDemon for an overview).