Blend: fit a robust Bayesian longitudinal regularized...

In Blend: Robust Bayesian Longitudinal Regularized Semiparametric Mixed Models

fit a robust Bayesian longitudinal regularized semi-parametric mixed model

Description

fit a robust Bayesian longitudinal regularized semi-parametric mixed model

Usage

Blend(
  y,
  x,
  t,
  J,
  kn,
  degree,
  iterations = 10000,
  burn.in = NULL,
  robust = TRUE,
  sparse = "TRUE",
  structural = TRUE
)

Arguments

y	the vector of repeated - measured response variable. The current version of mixed only supports continuous response.
x	the matrix of repeated - measured predictors (genetic factors) with intercept. Each row should be an observation vector for each measurement.
t	the vector of scheduled time points.
J	the vector of number of repeated measurement for each subject.
kn	the number of interior knots for B-spline.
degree	the degree of B spline basis.
iterations	the number of MCMC iterations.
burn.in	the number of iterations for burn-in.
robust	logical flag. If TRUE, robust methods will be used.
sparse	logical flag. If TRUE, spike-and-slab priors will be used to shrink coefficients of irrelevant covariates to zero exactly.
structural	logical flag. If TRUE, the coefficient functions with varying effects and constant effects will be penalized separately.

Details

Consider the data model described in "data":

Y_{ij} = \alpha_0(t_{ij})+\sum_{k=1}^{m}\beta_{k}(t_{ij})X_{ijk}+\boldsymbol{Z^\top_{ij}}\boldsymbol{\zeta_{i}}+\epsilon_{ij}.

The basis expansion and changing of basis with B splines will be done automatically:

\beta_{k}(\cdot)\approx \gamma_{k1} + \sum_{u=2}^{q}{B}_{ku}(\cdot)\gamma_{ku}

where B_{ku}(\cdot) represents B spline basis. \gamma_{k1} and (\gamma_{k2}, \ldots, \gamma_{kq})^\top correspond to the constant and varying parts of the coefficient functional, respectively. q=kn+degree+1 is the number of basis functions. By default, kn=degree=2. User can change the values of kn and degree to any other positive integers. When 'structural=TRUE'(default), the coefficient functions with varying effects and constant effects will be penalized separately. Otherwise, the coefficient functions with varying effects and constant effects will be penalized together.

When 'sparse="TRUE"' (default), spike-and-slab priors are imposed on individual and/or group levels to identify important constant and varying effects. Otherwise, Laplacian shrinkage will be used.

When 'robust=TRUE' (default), the distribution of \epsilon_{ij} is defined as a 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,J_{i} ), where \theta = 0.5. 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 ‘Blend’ is returned, which is a list with component:

posterior	the posteriors of coefficients.
coefficient	the estimated coefficients.
burn.in	the total number of burn-ins.
iterations	the total number of iterations.

See Also

data

Examples

data(dat)

## default method
fit = Blend(y,x,t,J,kn,degree)
fit$coefficient


## alternative: robust non-structural
fit = Blend(y,x,t,J,kn,degree, structural=FALSE)
fit$coefficient

## alternative: non-robust structural
fit = Blend(y,x,t,J,kn,degree, robust=FALSE)
fit$coefficient

## alternative: non-robust non-structural
fit = Blend(y,x,t,J,kn,degree, robust=FALSE, structural=FALSE)
fit$coefficient

Blend documentation built on April 3, 2025, 10:36 p.m.