Robust Bayesian Longitudinal Regularized Semiparametric Mixed Models

Our recently developed fully robust Bayesian semiparametric mixed-effect model for high-dimensional longitudinal studies with heterogeneous observations can be implemented through this package. This model can distinguish between time-varying interactions and constant-effect-only cases to avoid model misspecifications. Facilitated by spike-and-slab priors, this model leads to superior performance in estimation, identification and statistical inference. In particular, robust Bayesian inferences in terms of valid Bayesian credible intervals on both parametric and nonparametric effects can be validated on finite samples. The Markov chain Monte Carlo algorithms of the proposed and alternative models are efficiently implemented in 'C++'.

Blend

Robust Bayesian Longitudinal Regularized Semiparametric Mixed Models

Our recently developed fully robust Bayesian semiparametric mixed-effect model for high-dimensional longitudinal studies with heterogeneous observations can be implemented through this package. This model can distinguish between time-varying interactions and constant-effect-only cases to avoid model misspecifications. Facilitated by spike-and-slab priors, this model leads to superior performance in estimation, identification and statistical inference. In particular, robust Bayesian inferences in terms of valid Bayesian credible intervals on both parametric and nonparametric effects can be validated on finite samples. The Markov chain Monte Carlo algorithms of the proposed and alternative models are efficiently implemented in 'C++'.

How to install

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

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

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

install.packages("Blend")

Examples

Example.1 (default method)

library(Blend)
data(dat)

fit = Blend(y,x,t,J,kn,degree) 
fit$coefficient 
Coverage(fit)
plot_Blend(fit,sparse=TRUE)

Example.2 (alternative: robust non-structural)

fit = Blend(y,x,t,J,kn,degree,structural=FALSE) 

Example.3 (alternative: non-robust structural)

fit = Blend(y,x,t,J,kn,degree, robust=FALSE)

Example.4 (alternative: non-robust non-structural)

fit = Blend(y,x,t,J,kn,degree, robust=FALSE, structural=FALSE) 

News

Blend 0.1.3 [2026-09-28]

• Minor updates.

Blend 0.1.2 [2026-02-16]

• Minor updates.

Blend 0.1.1.1 [2025-01-29]

• Updated README file.

Blend 0.1.1 [2025-01-21]

• Fixed minor bugs.

Methods

This package provides implementation for methods proposed in

-Fan, K., Ren, J., Ma, Shuangge and Wu, C. (2026+). Robust Bayesian variable selection and inference under misspecified nonparametric mixed models in longitudinal studies. (Under Review)