Initialize linear regression parameters assuming a g-prior

Initialize the parameters for a linear regression model assuming a g-prior for the coefficients.

Usage

init_lm_gprior(y, X, X_test = NULL)

Arguments

y

n x 1 vector of data

X

n x p matrix of predictors

X_test

n0 x p matrix of predictors at test points (default is NULL)

Value

a named list params containing at least

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

2. sigma: the conditional standard deviation

3. coefficients: a named list of parameters that determine mu

Additionally, if X_test is not NULL, then the list includes an element mu_test, the vector of conditional means at the test points

Note

The parameters in coefficients are:

• beta: the p x 1 vector of regression coefficients components of beta

Examples

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

# Initialize:
params = init_lm_gprior(y = y, X = X)
names(params)
#> [1] "mu"           "sigma"        "coefficients"
names(params$coefficients)
#> [1] "beta"