monoreg: Bayesian monotonic regression

In monoreg: Bayesian Monotonic Regression Using a Marked Point Process Construction

Bayesian monotonic regression

Description

This function implements an extended version of the Bayesian monotonic regression procedure for continuous outcomes described in Saarela & Arjas (2011), allowing for multiple additive monotonic components. The simulated example below replicates the one in the reference.

Usage

monoreg(niter=15000, burnin=5000, adapt=5000, refresh=10, thin=5, 
        birthdeath=10, seed=1, rhoa=0.1, rhob=0.1, deltai=0.1, 
        drange=2.0, predict, include, response, offset=NULL, 
        axes, covariates, settozero, package)

Arguments

niter	Total number of MCMC iterations.
burnin	Number of iterations used for burn-in period.
adapt	Number of iterations used for adapting Metropolis-Hastings proposals.
refresh	Interval for producing summary output of the state of the MCMC sampler.
thin	Interval for saving the state of the MCMC sampler.
birthdeath	Number of birth-death proposals attempted at each iteration.
seed	Seed for the random generator.
rhoa	Shape parameter of a Gamma hyperprior for the Poisson process rate parameters.
rhob	Scale parameter of a Gamma hyperprior for the Poisson process rate parameters.
deltai	Range for a uniform proposal for the function level parameters.
drange	Allowed range for the monotonic function components.
predict	Indicator vector for the observations for which absolute risks are calculated (not included in the likelihood expression).
include	Indicator vector for the observations to be included in the likelihood expression.
response	Vector of response variable values.
offset	Vector of offset terms to be included in the linear predictor (optional).
axes	A matrix where the columns specify the covariate axes in the non-parametrically specified regression functions. Each variable here must be scaled to zero-one interval.
covariates	A matrix of additional covariates to be included in the linear predictor of the events of interest. Must include at least a vector of ones to specify an intercept term.
settozero	A zero-one matrix specifying the point process construction. Each row represents a point process, while columns correspond to the columns of the argument axes, indicating whether the column is one of the dimensions specifying the domain of the point process. (See function getcmat.)
package	An integer vector specifying the additive component into which each point process (row) specified in argument settozero is placed.

Value

A list with elements

steptotal	A sample of total number of points in the marked point process construction.
steps	A sample of the number of points used per each additive component.
rho	A sample of the Poisson process rate parameters (one per each point process specified).
loglik	A sample of log-likelihood values.
beta	A sample of regression coefficients for the variables specified in the argument covariates.
phi	A sample of non-parametric regression function levels for each observation specified in the argument predict.
pred	A sample of predicted means for each observation specified in the argument predict.
sigma	A sample of residual standard error parameters.

Author(s)

Olli Saarela <[e-mail]>

References

Saarela O., Arjas E. (2011). A method for Bayesian monotonic multiple regression. Scandinavian Journal of Statistics, 38:499–513.

Examples

## Not run: 
library(monoreg)
set.seed(1)
# nobs <- 1000
nobs <- 50
sigma <- 0.01
x1 <- runif(nobs)
x2 <- runif(nobs)

# 6 different monotonic regression surfaces:
# mu <- sqrt(x1)
mu <- 0.5 * x1 + 0.5 * x2
# mu <- pmin(x1, x2)
# mu <- 0.25 * x1 + 0.25 * x2 + 0.5 * (x1 + x2 > 1.0)
# mu <- 0.25 * x1 + 0.25 * x2 + 0.5 * (pmax(x1, x2) > 0.5)
# mu <- ifelse((x1 - 1.0)^2 + (x2 - 1.0)^2 < 1.0, sqrt(1.0 - (x1 - 1.0)^2 - (x2 - 1.0)^2), 0.0)

y <- rnorm(nobs, mu, sigma)

# results <- monoreg(niter=15000, burnin=5000, adapt=5000, refresh=10, 
results <- monoreg(niter=5000, burnin=2500, adapt=2500, refresh=10, 
                   thin=5, birthdeath=10, seed=1, rhoa=0.1, rhob=0.1, 
                   deltai=0.1, drange=2.0, predict=rep(1.0, nobs), 
                   include=rep(1.0, nobs), response=y, offset=NULL, 
                   axes=cbind(x1,x2), covariates=rep(1.0, nobs), 
                   settozero=getcmat(2), package=rep(1,3)) 

# pdf(file.path(getwd(), 'pred3d.pdf'), width=6.0, height=6.0, paper='special')
op <- par(mar=c(2,2,0,0), oma=c(0,0,0,0), mgp=c(2.5,1,0), cex=0.75)
pred <- colMeans(results$pred)
idx <- order(pred, decreasing=TRUE)

tr <- persp(z=matrix(c(NA,NA,NA,NA), 2, 2), zlim=c(0,1), 
            xlim=c(0,1), ylim=c(0,1),
            ticktype='detailed', theta=-45, phi=25, ltheta=25, 
            xlab='X1', ylab='X2', zlab='mu')
for (i in 1:nobs) {
    lines(c(trans3d(x1[idx[i]], x2[idx[i]], 0.0, tr)$x, 
            trans3d(x1[idx[i]], x2[idx[i]], pred[idx[i]], tr)$x),
          c(trans3d(x1[idx[i]], x2[idx[i]], 0.0, tr)$y, 
            trans3d(x1[idx[i]], x2[idx[i]], pred[idx[i]], tr)$y),
          col='gray70')
}
points(trans3d(x1[idx], x2[idx], pred[idx], tr), pch=21, bg='white')
par(op)
# dev.off()

## End(Not run)

monoreg documentation built on April 30, 2023, 5:12 p.m.