Graphical Markov Models with Mixed Graphs

Provides functions for defining mixed graphs containing three types of edges, directed, undirected and bi-directed, with possibly multiple edges. These graphs are useful because they capture fundamental independence structures in multivariate distributions and in the induced distributions after marginalization and conditioning. The package is especially concerned with Gaussian graphical models for (i) ML estimation for directed acyclic graphs, undirected and bi-directed graphs and ancestral graph models (ii) testing several conditional independencies (iii) checking global identification of DAG Gaussian models with one latent variable (iv) testing Markov equivalences and generating Markov equivalent graphs of specific types.

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.

Likelihood-Based Boosting for Generalized Mixed Models

Likelihood-based boosting approaches for generalized mixed models are provided.

Longitudinal Drift-Diffusion Mixed Models (LDDMM)

Implementation of the drift-diffusion mixed model for category learning as described in Paulon et al. (2021) .

Power Analysis for Random Effects in Mixed Models

Simulation functions to assess or explore the power of a dataset to estimates significant random effects (intercept or slope) in a mixed model. The functions are based on the "lme4" and "lmerTest" packages.

Poisson-Tweedie Generalized Linear Mixed Model

Fits the Poisson-Tweedie generalized linear mixed model described in Signorelli et al. (2021, ). Likelihood approximation based on adaptive Gauss Hermite quadrature rule.

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) .

Functional Data Analysis in a Mixed Model Framework

Likelihood based analysis of 1-dimension functional data in a mixed-effects model framework. Matrix computation are approximated by semi-explicit operator equivalents with linear computational complexity. Markussen (2013) .

Bayesian Estimation for Quantile Regression Mixed Models

Using a Bayesian estimation procedure, this package fits linear quantile regression models such as linear quantile models, linear quantile mixed models, quantile regression joint models for time-to-event and longitudinal data. The estimation procedure is based on the asymmetric Laplace distribution and the 'JAGS' software is used to get posterior samples (Yang, Luo, DeSantis (2019) ).

Temporal Contributions on Trends using Mixed Models

Method to estimate the effect of the trend in predictor variables on the observed trend of the response variable using mixed models with temporal autocorrelation. See Fernández-Martínez et al. (2017 and 2019) .