init_params_additive: Initialize the parameters for an additive model

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

Initialize the parameters for an additive model

Description

Initialize the parameters for an additive model, which may contain both linear and nonlinear predictors. The nonlinear terms are modeled using orthogonalized splines.

Usage

init_params_additive(y, X_lin, X_nonlin, B_all = 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
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

Value

a named list params containing

1. mu: vector of conditional means (fitted values)

2. sigma: the conditional standard deviation

3. coefficients: a named list of parameters that determine 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)
names(params)
names(params$coefficients)

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