# waic: Watanabe Information Criterion In qrjoint: Joint Estimation in Linear Quantile Regression

## Description

Calculates two versions of the Watanabe information criteria from MCMC draws.

## Usage

 ```1 2``` ``` waic(logliks, print = TRUE) ```

## Arguments

 `logliks` a matrix of observation level log-likelihood values, the columns are MCMC iterations and the rows are observations in the data `print` logical whether to print the results

## Value

Returns the two version of the WAIC

## References

Gelman, A., Hwang, J., and Vehtari, A. (2014). Understanding predictive information criterion for Bayesian models. Stat Comput, 24, 997-1016.

`summary.qrjoint`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ``` # Plasma data analysis # recoding variables data(plasma) plasma\$Sex <- as.factor(plasma\$Sex) plasma\$SmokStat <- as.factor(plasma\$SmokStat) plasma\$VitUse <- 3 - plasma\$VitUse plasma\$VitUse <- as.factor(plasma\$VitUse) # creating predictors and response (beta carotene concentration in the plasma) X <- model.matrix(BetaPlasma ~ Age + Sex + SmokStat + Quetelet + VitUse + Calories + Fat + Fiber + Alcohol + Cholesterol + BetaDiet, data = plasma)[,-1] Y <- plasma\$BetaPlasma # model fitting with 50 posterior samples from 100 iterations (thin = 2) fit.qrj <- qrjoint(X, Y, 50, 2) sm <- summary(fit.qrj, plot = FALSE) # the call to summary already shows the waic for the fitted model, it also returns # the observation level log-likelihood vales. To calculate waic from last 20 draws # we can use: ll <- sm\$ll waic(ll[,31:50]) ```