Regression, classification, contour plots, hypothesis testing and fitting of distributions for compositional data are some of the functions included.
Functions for percentages (or proportions) are also included.
{CompositionalSR} - Spatial Regression Models with Compositional Data
{heplots} - Mostly for visualizing hypothesis tests in multivariate linear models (“MLM” = {MANOVA, multivariate multiple regression, MANCOVA, and repeated measures designs}).
Also provides other tools for analysis and graphical display of MLMs.
robmlm fits a multivariate linear model by robust regression using a simple M estimator that down-weights observations with large residuals
Robust estimation for multivariate linear models (MLMs) using iteratively reweighted least squares (IRLS)
{kernreg} - Fast implementation of Nadaraya-Watson kernel regression for either univariate or multivariate responses, with one or more bandwidths. K-fold cross-validation is also performed
{randomForestSRC} - Fast Unified Random Forests for Survival, Regression, and Classification (RF-SRC)
New Mahalanobis splitting rule for correlated real-valued outcomes in multivariate regression settings
{savvySh} - Implements a suite of shrinkage estimators for multivariate linear regression to improve estimation stability and predictive accuracy
Includes the Stein estimator, Diagonal Shrinkage, the general Shrinkage estimator (solving a Sylvester equation), and Slab Regression (Simple and Generalized)
{ZIDM} (Vignette, Paper) - Model for Multivariate Compositional Count Data
Uses a Bayesian Zero-Inflated Dirichlet-Multinomial Regression model
Uses {brms} to fit a Bayesian GAM to model a compositional response. Model includes variables for elevation, slope, longitude, latitude. Includes R2 metrics for compositional modeling.
Generalized Joint Regression Modelling (GJRM)
A flexible statistical framework that generalizes classical regression models to jointly model multiple responses (or multi-response), potentially of different types, while accounting for dependencies between them.
It is particularly useful when you have multiple outcomes (e.g., continuous, binary, count data) that may influence each other.
Handles nonlinear associations between the reponse variables
Packages
{GJRM} - Routines for fitting various joint (and univariate) regression models, with several types of covariate effects, in the presence of equations’ errors association, endogeneity, non-random sample selection or partial observability.
Comparison to a Gaussian Multivariate Regression Model
Allows for more flexible marginal distributions, not limited to normal distributions.
Dependence Structure
Multivariate regression models the correlation between responses using a multivariate normal distribution, which implies a linear association.
GJRM uses copulas to model the dependence structure, allowing for more complex, non-linear associations between responses.
Flexibility
In multivariate regression with splines, the same spline structure is typically applied across all response variables..
In GJRM, each marginal can have its own unique non-linear structure, potentially using different splines or smoothing approaches for each response variable.
GJRM allows different link functions for each marginal distribution, accommodating various types of responses and not just continuous responses
GJRM can handle mixed types of responses (e.g., a combination of continuous, binary, and count data) in a single model.
Steps
First stage: Models each marginal distribution separately, allowing for different distributions and link functions for each response.
Second stage: Combines these marginals using a copula function to create the joint distribution.