mixedBayes

Bayesian Longitudinal Regularized Quantile Mixed Model

With high-dimensional omics features, repeated measure ANOVA leads to longitudinal gene-environment interaction studies that have intra-cluster correlations, outlying observations and structured sparsity arising from the ANOVA design. In this package, we have developed robust sparse Bayesian mixed effect models tailored for the above studies (Fan et al. (2025)). An efficient Gibbs sampler has been developed to facilitate fast computation. The Markov chain Monte Carlo algorithms of the proposed and alternative methods are efficiently implemented in 'C++'. The development of this software package and the associated statistical methods have been partially supported by an Innovative Research Award from Johnson Cancer Research Center, Kansas State University.

How to install

• To install from github, run these two lines of code in R

install.packages("devtools")
devtools::install_github("kunfa/mixedBayes")

• Released versions of mixedBayes are available on CRAN (link), and can be installed within R via

install.packages("mixedBayes")

Load the package

library(mixedBayes)

Data

The example data set `data` simulated under random intercept-and-slope model included in the package can be loaded by

data(data)

Examples

Example.1 (default method: robust sparse bi-level selection under random intercept -and- slope model)

fit = mixedBayes(y,e,X,g,w,k,structure=c("bi-level"))

# Estimated coefficients(posterior median)
fit$coefficient

# Identification
b = selection(fit,sparse=TRUE)
index = which(coeff!=0)
pos = which(b != 0)
tp = length(intersect(index, pos))
fp = length(pos) - tp
list(tp=tp, fp=fp)

# Prediction
prediction=predict_mixedBayes(fit,y,X,e,g,w,k,slope=TRUE,loss = "L1")
prediction

Example.2 (alternative: robust sparse individual level selection under random intercept -and- slope model)

fit = mixedBayes(y,e,X,g,w,k,structure=c("individual"))

# Estimated coefficients(posterior median)
fit$coefficient

# Identification
b = selection(fit,sparse=TRUE)
index = which(coeff!=0)
pos = which(b != 0)
tp = length(intersect(index, pos))
fp = length(pos) - tp
list(tp=tp, fp=fp)

# Prediction
prediction=predict_mixedBayes(fit,y,X,e,g,w,k,slope=TRUE,loss = "L1")
prediction

Example.3 (alternative: non-robust sparse bi-level selection under random intercept -and- slope model)

fit = mixedBayes(y,e,X,g,w,k,robust=FALSE, structure=c("bi-level"))

# Estimated coefficients(posterior median)
fit$coefficient

# Identification
b = selection(fit,sparse=TRUE)
index = which(coeff!=0)
pos = which(b != 0)
tp = length(intersect(index, pos))
fp = length(pos) - tp
list(tp=tp, fp=fp)

# Prediction
prediction=predict_mixedBayes(fit,y,X,e,g,w,k,slope=TRUE,loss = "L2")
prediction

Example.4 (alternative: robust sparse bi-level selection under random intercept model)

fit = mixedBayes(y,e,X,g,w,k,slope=FALSE, structure=c("bi-level"))

# Estimated coefficients(posterior median)
fit$coefficient

# Identification
b = selection(fit,sparse=TRUE)
index = which(coeff!=0)
pos = which(b != 0)
tp = length(intersect(index, pos))
fp = length(pos) - tp
list(tp=tp, fp=fp)

# Prediction
prediction=predict_mixedBayes(fit,y,X,e,g,w,k,slope=FALSE,loss = "L1")
prediction

Methods

This package provides implementation for methods proposed in

• Fan, K., Jiang, Y., Ma, S., Wang, W. and Wu, C. (2025). Robust Sparse Bayesian Regression for Longitudinal Gene-Environment Interactions. Journal of the Royal Statistical Society Series C: Applied Statistics, 74(5), 1372–1394.