Thursday, August 12, 2010

Fun with the proto package: building an MCMC sampler for Bayesian regression

The proto package is my latest favourite R goodie. It brings prototype-based programming to the R language - a style of programming that lets you do many of the things you can do with classes, but with a lot less up-front work. Louis Kates and Thomas Petzoldt provide an excellent introduction to using proto in the package vignette.

As a learning exercise I concocted the example below involving Bayesian logistic regression. It was inspired by an article on Matt Shotwell's blog about using R environments rather than lists to store the state of a Markov Chain Monte Carlo sampler. Here I use proto to create a parent class-like object (or trait in proto-ese) to contain the regression functions and create child objects to hold both data and results for individual analyses.

First here's an example session...

# Make up some data with a continuous predictor and binary response
nrec <- 500
x <- rnorm(nrec)
y <- rbinom(nrec, 1, plogis(2 - 4*x))

# Predictor matrix with a col of 1s for intercept
pred <- matrix(c(rep(1, nrec), x), ncol=2)
colnames(pred) <- c("intercept", "X")

# Load the proto package
library(proto)

# Use the Logistic parent object to create a child object which will
# hold the data and run the regression (the $ operator references
# functions and data within a proto object)
lr <- Logistic$new(pred, y)
lr$run(5000, 1000)

# lr now contains both data and results
str(lr)

proto object
$ cov : num [1:2, 1:2] 0.05 -0.0667 -0.0667 0.1621
..- attr(*, "dimnames")=List of 2
$ prior.cov: num [1:2, 1:2] 100 0 0 100
$ prior.mu : num [1:2] 0 0
$ beta : num [1:5000, 1:2] 2.09 2.09 2.09 2.21 2.21 ...
..- attr(*, "dimnames")=List of 2
$ adapt : num 1000
$ y : num [1:500] 0 1 1 1 1 1 1 1 1 1 ...
$ x : num [1:500, 1:2] 1 1 1 1 1 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
parent: proto object

# Use the Logistic summary function to tabulate and plot results
lr$summary()

From 5000 samples after 1000 iterations burning in
intercept X
Min. :1.420 Min. :-5.296
1st Qu.:1.840 1st Qu.:-3.915
Median :2.000 Median :-3.668
Mean :1.994 Mean :-3.693
3rd Qu.:2.128 3rd Qu.:-3.455
Max. :2.744 Max. :-2.437



And here's the code for the Logistic trait...

Logistic <- proto()

Logistic$new <- function(., x, y) {
# Creates a child object to hold data and results
#
# x - a design matrix (ie. predictors
# y - a binary reponse vector

proto(., x=x, y=y)
}

Logistic$run <- function(., niter, adapt=1000) {
# Perform the regression by running the MCMC
# sampler
#
# niter - number of iterations to sample
# adapt - number of prior iterations to run
# for the 'burning in' period

require(mvtnorm)

# Set up variables used by the sampler
.$adapt <- adapt
total.iter <- niter + adapt
.$beta <- matrix(0, nrow=total.iter, ncol=ncol(.$x))
.$prior.mu <- rep(0, ncol(.$x))
.$prior.cov <- diag(100, ncol(.$x))
.$cov <- diag(ncol(.$x))

# Run the sampler
b <- rep(0, ncol(.$x))
for (i in 1:total.iter) {
b <- .$update(i, b)
.$beta[i,] <- b
}

# Trim the results matrix to remove the burn-in
# period
if (.$adapt > 0) {
.$beta <- .$beta[(.$adapt + 1):total.iter,]
}
}

Logistic$update <- function(., it, beta.old) {
# Perform a single iteration of the MCMC sampler using
# Metropolis-Hastings algorithm.
# Adapted from code by Brian Neelon published at:
# http://www.duke.edu/~neelo003/r/
#
# it - iteration number
# beta.old - vector of coefficient values from
# the previous iteration

# Update the coefficient covariance if we are far
# enough through the sampling
if (.$adapt > 0 & it > 2 * .$adapt) {
.$cov <- cov(.$beta[(it - .$adapt):(it - 1),])
}

# generate proposed new coefficient values
beta.new <- c(beta.old + rmvnorm(1, sigma=.$cov))

# calculate prior and current probabilities and log-likelihood
if (it == 1) {
.$..log.prior.old <- dmvnorm(beta.old, .$prior.mu, .$prior.cov, log=TRUE)
.$..probs.old <- plogis(.$x %*% beta.old)
.$..LL.old <- sum(log(ifelse(.$y, .$..probs.old, 1 - .$..probs.old)))
}
log.prior.new <- dmvnorm(beta.new, .$prior.mu, .$prior.cov, log=TRUE)
probs.new <- plogis(.$x %*% beta.new)
LL.new <- sum(log(ifelse(.$y, probs.new, 1-probs.new)))

# Metropolis-Hastings acceptance ratio (log scale)
ratio <- LL.new + log.prior.new - .$..LL.old - .$..log.prior.old

if (log(runif(1)) < ratio) {
.$..log.prior.old <- log.prior.new
.$..probs.old <- probs.new
.$..LL.old <- LL.new
return(beta.new)
} else {
return(beta.old)
}
}

Logistic$summary <- function(., show.plot=TRUE) {
# Summarize the results

cat("From", nrow(.$beta), "samples after", .$adapt, "iterations burning in\n")
base::print(base::summary(.$beta))

if (show.plot) {
par(mfrow=c(1, ncol(.$beta)))
for (i in 1:ncol(.$beta)) {
plot(density(.$beta[,i]), main=colnames(.$beta)[i])
}
}
}


Now that's probably not the greatest design in the world, but it only took me a few minutes to put it together and it's incredibly easy to modify or extend. Try it !

Thanks to Brian Neelon for making his MCMC logistic regression code available (http://www.duke.edu/~neelo003/r/).

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