summary.qrjoint: Summary Method for qrjoint Model Fit

Description

Summarize model fit, including MCMC details, for qrjoint.

Usage

# S3 method for qrjoint
summary(object, ntrace = 1000, burn.perc = 0.5,
        plot.dev = TRUE, more.details = FALSE, ...)

Value

Displays the trace of the deviance statistic. More details include trace plots of of the proximity parameter of each GP, a plot of Geweke p-values for (from geweke.diag) convergence of each model parameter and an image plot of parameter correlation. Also prints two versions of Watanabe AIC.

The following quantities are returned invisibly.

deviance: vector deviance statistic of the samples parameter draws
pg: a matrix with nsamp number of columns, each columns could be coerced into a matrix of dimension ngrid * (p+1), where the columns gives the conditional posterior weights on the lambda grid values for the corresponding GP function.
prox: posterior draws of proximity in the form of a (p+1)*nsamp matrix.
ll: a matrix of n*nsamp containing observation-level log-likelihood contributions. Used to calculate waic, and could be used for other AIC calculations.
ql: a matrix of n*nsamp containing observation-level estimated quantile levels (i.e. t such that \(y = Q(t|x)\)) at each posterior draw. These may be used in lieu of residuals to assess model fit and assumption of linearity.
waic: Two versions of Watanabe AIC from Gelman, Hwang and Vehtari (2014).

Arguments

object: a fitted model of the class 'qrjoint'.
ntrace: number of draws to be included in trace plots
burn.perc: fraction of MCMC draws to be discarded as burn-in.
plot.dev: logical indicator of whether to show trace plot of deviance
more.details: logical indicating whether other details from MCMC are to be plotted
...: a limited number of plotting controls that are passed onto the deviance plot

References

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

Examples

Run this code

# 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)

# Model fitting with 40 posterior samples from 80 iterations (thin = 2) is for
# illustration only. For practical model fitting, increase iterations, 
# e.g. nsamp = 500, thin = 20
fit.qrj <- qrjoint(BetaPlasma ~ Age + Sex + SmokStat + Quetelet + VitUse + Calories + 
        Fat + Fiber + Alcohol + Cholesterol + BetaDiet, plasma, nsamp = 40, thin = 2)
summ <- summary(fit.qrj, more = TRUE)

if (FALSE) {
# Visually assess uniformity of quantile levels with histogram and qqplot
# Notes: Can assess across all MCMC draws (as below) or for single iteration;
# adjustments to quantile levels will be needed for censored observations
hist(summ$ql, breaks=40, freq=F)
curve(dunif(x),add=T)
qqplot(summ$ql, qunif(ppoints(length(summ$ql))),xlab="actual", ylab="theoretical")
abline(0,1)

# Visually assess linearity assumption using quantile levels
# Notes: Can assess across all MCMC draws or for single iteration (as below)

# Loess gives visual of center of quantile levels across covariate;
# trend line should be near 0.5
library(ggplot2)
use <- sample(1:ncol(summ$ql),1)
plasma$qlsamp <- summ$ql[,use]
ggplot(data=plasma, aes(x=Age, y=qlsamp)) + geom_point() + geom_smooth(se=F,
method="loess")

# Violin plot allows for assessment of entire distribution across covariate;
# densities within decile bins should be blocky-uniform 
cut_dec <- function(x) factor(cut(x, quantile(x,0:10/10),inc=TRUE),labels=1:10)
ggplot(data=plasma, aes(x=cut_dec(Age), y=qlsamp)) + geom_violin() +
xlab("Age Decile Bins")
}