sample_params_additive: Sample the parameters for an additive model

In drkowal/rSTAR: MCMC and EM algorithms for Simultaneous Transformation and Rounding (STAR) Models

Sample the parameters for an additive model

Description

Sample the parameters for an additive model, which may contain both linear and nonlinear predictors. The nonlinear terms are modeled using orthogonalized splines. The sampler draws the linear terms jointly and then samples each vector of nonlinear coefficients using Bayesian backfitting (i.e., conditional on all other nonlinear and linear terms).

Usage

sample_params_additive(
  y,
  X_lin,
  X_nonlin,
  params,
  A = 10^4,
  B_all = NULL,
  diagBtB_all = NULL,
  XtX = NULL
)

Arguments

y	n x 1 vector of data
X_lin	n x pL matrix of predictors to be modelled as linear
X_nonlin	n x pNL matrix of predictors to be modelled as nonlinear
params	the named list of parameters containing mu: vector of conditional means (fitted values) sigma: the conditional standard deviation coefficients: a named list of parameters that determine mu
A	the prior scale for sigma_beta, which we assume follows a Uniform(0, A) prior.
B_all	optional pNL-dimensional list of n x L[j] dimensional basis matrices for each nonlinear term j=1,...,pNL; if NULL, compute internally
diagBtB_all	optional pNL-dimensional list of diag(crossprod(B_all[[j]])); if NULL, compute internally
XtX	optional p x p matrix of crossprod(X) (one-time cost); if NULL, compute internally

Value

The updated named list params with draws from the full conditional distributions of sigma and coefficients (and updated mu).

Note

The parameters in coefficients are:

• beta: the p x 1 linear coefficients, including the linear terms from X_nonlin

• f_j: the n x pNL matrix of fitted values for each nonlinear function

• theta_j: the pNL-dimensional of nonlinear basis coefficients

• sigma_beta: p x 1 vector of linear regression coefficient standard deviations

• sigma_theta_j: pNL x 1 vector of nonlinear coefficient standard deviations

Examples

# Simulate data for illustration:
sim_dat = simulate_nb_friedman(n = 100, p = 5)
y = sim_dat$y; X = sim_dat$X

# Linear and nonlinear components:
X_lin = as.matrix(X[,-(1:3)])
X_nonlin = as.matrix(X[,(1:3)])

# Initialize:
params = init_params_additive(y = y, X_lin = X_lin, X_nonlin = X_nonlin)

# Sample:
params = sample_params_additive(y = y,
                                X_lin = X_lin,
                                X_nonlin = X_nonlin,
                                params = params)
names(params)
names(params$coefficients)

# And plot an example:
plot(X_nonlin[,1], params$coefficients$f_j[,1])

drkowal/rSTAR documentation built on July 5, 2023, 2:18 p.m.