multivarbayes

The goal of multivarbayes is to fit Bayesian multivariate linear regression models using conjugate priors. This package allows users to specify their own prior distributions or use default settings for natural conjugate priors. The model supports simulation-based posterior inference for both the regression coefficients and the covariance structure of the residuals.

Key features

• Supports conjugate Bayesian multivariate linear regression.
• Simulates posterior distributions for regression coefficients and covariance matrices.
• Computes analytical and simulated posterior predictive distributions.
• Includes summary and visualization functions for posterior distributions.

Installation

multivarbayes is not yet available on CRAN. You can install the development version from GitHub with:

# Install the development version from GitHub
remotes::install_github("jmartinez-minaya/multivarbayes")

Example

Here is a basic example of how to fit a multivariate linear model using multivarbayes and summarize the results:

library(multivarbayes)
set.seed(123)
n <- 1000  # number of observations
k <- 3    # number of covariates (including intercept)
m <- 2    # number of response variables
nsims <- 1000

# Covariate matrix with intercept
X <- cbind(1, matrix(rnorm(n * (k - 1)), n, k - 1))  

# True coefficients
B_true <- matrix(c(1, 0.5, -0.3, 2, -0.5, 1), ncol = m)

# Multivariate normal errors
Sigma_true <- matrix(c(1, 0.3, 0.3, 1), ncol = m)
errors <- MASS::mvrnorm(n, mu = rep(0, m), Sigma = Sigma_true)

# Response matrix
Y <- X %*% B_true + errors  

# Combine into data frame
data <- data.frame(cbind(Y, X))
colnames(data) <- c("Y1", "Y2", "Intercept", "X1", "X2")


# Fit the Bayesian multivariate linear model
formula <- as.matrix(data[, c("Y1", "Y2")]) ~  X1 + X2
model_fit <- mlvr(formula, data = data)

# Summarize the fitted model
summary(model_fit)

# Plot posterior distributions
plot(model_fit)

Additional Resources

• For a detailed tutorial on fitting a Bayesian multivariate linear regression model, check out the vignette: Link to vignette

References

The underlying methodology is based on standard Bayesian multivariate linear regression models, with posterior inference carried out using conjugate priors for both the regression coefficients and the covariance structure of the residuals.

• Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian data analysis. Chapman and Hall/CRC.

• Rossi, P. E., & Allenby, G. M. (2003). Bayesian statistics and marketing. Marketing Science, 22(3), 304-328.

Issues

If you encounter any problems or have suggestions for improvements, please open an issue.