WAIC: Compute WAIC value

In RprobitB: Bayesian Probit Choice Modeling

Compute WAIC value

Description

This function computes the WAIC value of an RprobitB_fit object.

Usage

WAIC(x)

Arguments

x	An object of class RprobitB_fit.

Details

WAIC is short for Widely Applicable (or Watanabe-Akaike) Information Criterion. As for AIC and BIC, the smaller the WAIC value the better the model. Its definition is

WAIC = -2 \cdot lppd + 2 \cdot p_{WAIC},

where lppd stands for log pointwise predictive density and p_{WAIC} is a penalty term proportional to the variance in the posterior distribution that is sometimes called effective number of parameters. The lppd is approximated as follows. Let

p_{is} = \Pr(y_i\mid θ_s)

be the probability of observation y_i given the sth set θ_s of parameter samples from the posterior. Then

lppd = ∑_i \log S^{-1} ∑_s p_{si}.

The penalty term is computed as the sum over the variances in log-probability for each observation:

p_{WAIC} = ∑_i V_{θ} ≤ft[ \log p_{si} \right].

Value

A numeric, the WAIC value, with the following attributes:

• se_waic, the standard error of the WAIC value,

• lppd, the log pointwise predictive density,

• p_waic, the effective number of parameters,

• p_waic_vec, the vector of summands of p_waic,

• p_si, the output of compute_p_si.

RprobitB documentation built on Nov. 10, 2022, 5:12 p.m.