mixedBayes: fit a Bayesian longitudinal regularized quantile mixed model

In mixedBayes: Bayesian Longitudinal Regularized Quantile Mixed Model

fit a Bayesian longitudinal regularized quantile mixed model

Description

fit a Bayesian longitudinal regularized quantile mixed model

Usage

mixedBayes(
  y,
  e,
  X,
  g,
  w,
  k,
  iterations = 10000,
  burn.in = NULL,
  slope = TRUE,
  robust = TRUE,
  quant = 0.5,
  sparse = TRUE,
  structure = c("bi-level", "individual")
)

Arguments

y	a numeric vector of repeated-measure responses in long format. The current version only supports continuous response.
e	the long-format design matrix for environment/treatment effects. In applications, this is a set of dummy variables encoding treatment levels.
X	the long-format design matrix, including an intercept and optionally time-related covariates.
g	the long-format matrix of genetic predictors.
w	the long-format matrix of gene-environment interaction terms.
k	integer. Number of repeated measurements per subject.
iterations	the number of MCMC iterations. The default value is 10,000.
burn.in	the number of iterations for burn-in. If NULL, no burn-in is applied and all MCMC samples are retained.
slope	logical flag. If TRUE, random intercept-and-slope model will be used. Otherwise, random intercept model will be used. The default value is TRUE.
robust	logical flag. If TRUE, robust methods will be used. Otherwise, non-robust methods will be used. The default value is TRUE.
quant	the quantile level specified by users. The default value is 0.5.
sparse	logical flag. If TRUE, spike-and-slab priors will be adopted to impose exact sparsity on regression coefficients. Otherwise, Laplacian shrinkage will be adopted. The default value is TRUE.
structure	two choices are available. "bi-level" for selection on both the main and interaction effects corresponding to individual and group levels. "individual" for selections on individual-level only.

Details

Data layout

Consider a longitudinal study with repeated measurements per subject. The response vector y and the design matrices X, e, g, and w must all be provided in long format and share the same row ordering. In practice, each row corresponds to one observation from a particular subject at a particular time point.

Model

Consider the data model described in "data":

Y_{ij} = X_{ij}^\top\gamma_{0}+E_{ij}^\top\gamma_{1}+\sum_{l=1}^{p}G_{ijl}\gamma_{2l}+\sum_{l=1}^{p}W_{ijl}^\top\gamma_{3l}+Z_{ij}^\top\alpha_{i}+\epsilon_{ij}.

, with W_{ij} = G_{ij}\bigotimes E_{ij}.

where \gamma_{0} is the coefficient vector for X_{ij}, \gamma_{1} is the coefficient vector for E_{ij}, \gamma_{2l} is the coefficient for the main effect of the lth genetic variant, and \gamma_{3l} is the coefficient vector for the interaction effect of the lth genetic variant with environment factors.

The subject-specific random effects \alpha_i capture within-subject correlation. For random intercept-and-slope model, Z_{ij}^\top = (1,j) and \alpha_{i} = (\alpha_{i1},\alpha_{i2})^\top. For random intercept model, Z_{ij}^\top = 1 and \alpha_{i} = \alpha_{i1}.

When 'structure="bi-level"', bi-level selection will be conducted. If 'structure="individual"', individual-level selection will be conducted.

When 'slope=TRUE' (default), random intercept-and-slope model will be used as the mixed effects model.

When 'sparse=TRUE' (default), spike-and-slab priors are imposed to identify important main and interaction effects. Otherwise, Laplacian shrinkage will be used.

When 'robust=TRUE' (default), the distribution of \epsilon_{ij} is defined as an asymmetric Laplace distribution with density.

f(\epsilon_{ij}|\theta,\tau) = \theta(1-\theta)\exp\left\{-\tau\rho_{\theta}(\epsilon_{ij})\right\} , (i=1,\dots,n,j=1,\dots,k ), which leads to a Bayesian formulation of quantile regression. If 'robust=FALSE', \epsilon_{ij} follows a normal distribution.

Please check the references for more details about the prior distributions.

Value

an object of class ‘mixedBayes’ is returned, which is a list with component:

posterior	posterior samples for fixed effects and random effects.
coefficient	posterior median estimates of coefficients for fixed effects and random effects.

See Also

data

Examples

data(data)

## 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"))
fit$coefficient

## Compute TP and FP
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)

## alternative: robust sparse individual level selections under random intercept-and-slope model
fit = mixedBayes(y,e,X,g,w,k,structure=c("individual"))
fit$coefficient

## 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"))
fit$coefficient

## alternative: robust sparse bi-level selection under random intercept model
fit = mixedBayes(y,e,X,g,w,k,slope=FALSE, structure=c("bi-level"))
fit$coefficient

mixedBayes documentation built on Jan. 13, 2026, 9:07 a.m.