rs.pbart {BART} | R Documentation |

## BART for dichotomous outcomes with parallel computation and stratified random sampling

### Description

BART is a Bayesian “sum-of-trees” model.

For numeric response `y`

, we have
`y = f(x) + \epsilon`

,
where `\epsilon \sim N(0,\sigma^2)`

.

For a binary response `y`

, `P(Y=1 | x) = F(f(x))`

, where `F`

denotes the standard normal cdf (probit link).

In both cases, `f`

is the sum of many tree models.
The goal is to have very flexible inference for the uknown
function `f`

.

In the spirit of “ensemble models”, each tree is constrained by a prior to be a weak learner so that it contributes a small amount to the overall fit.

### Usage

```
rs.pbart(
x.train, y.train, x.test=matrix(0.0,0,0),
C=floor(length(y.train)/2000),
k=2.0, power=2.0, base=.95,
binaryOffset=0,
ntree=50L, numcut=100L,
ndpost=1000L, nskip=100L,
keepevery=1L, printevery=100,
keeptrainfits=FALSE, transposed=FALSE,
mc.cores = 2L, nice = 19L,
seed = 99L
)
```

### Arguments

`x.train` |
Explanatory variables for training (in sample) data. |

`y.train` |
Dependent variable for training (in sample) data. |

`x.test` |
Explanatory variables for test (out of sample) data. |

`C` |
The number of shards to break the data into and analyze separately. |

`k` |
For binary y,
k is the number of prior standard deviations |

`power` |
Power parameter for tree prior. |

`base` |
Base parameter for tree prior. |

`binaryOffset` |
Used for binary |

`ntree` |
The number of trees in the sum. |

`numcut` |
The number of possible values of c (see usequants).
If a single number if given, this is used for all variables.
Otherwise a vector with length equal to ncol(x.train) is required,
where the |

`ndpost` |
The number of posterior draws returned. |

`nskip` |
Number of MCMC iterations to be treated as burn in. |

`keepevery` |
Every keepevery draw is kept to be returned to the user. |

`printevery` |
As the MCMC runs, a message is printed every printevery draws. |

`keeptrainfits` |
Whether to keep |

`transposed` |
When running |

`seed` |
Setting the seed required for reproducible MCMC. |

`mc.cores` |
Number of cores to employ in parallel. |

`nice` |
Set the job niceness. The default niceness is 19: niceness goes from 0 (highest) to 19 (lowest). |

### Details

BART is an Bayesian MCMC method.
At each MCMC interation, we produce a draw from the joint posterior
`(f,\sigma) | (x,y)`

in the numeric `y`

case
and just `f`

in the binary `y`

case.

Thus, unlike a lot of other modelling methods in R, we do not produce a single model object
from which fits and summaries may be extracted. The output consists of values
`f^*(x)`

(and `\sigma^*`

in the numeric case) where * denotes a particular draw.
The `x`

is either a row from the training data (x.train) or the test data (x.test).

### Value

`rs.pbart`

returns an object of type `pbart`

which is
essentially a list.

`yhat.shard` |
Estimates generated from the individual shards rather than from the whole. This object is only useful for assessing convergence. A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw |

`yhat.train` |
Estimates generated from the whole if A matrix with ndpost rows and nrow(x.train) columns.
Each row corresponds to a draw |

`yhat.test` |
Estimates generated from the whole if Same as yhat.train but now the x's are the rows of the test data. |

`varcount` |
a matrix with ndpost rows and nrow(x.train) columns. Each row is for a draw. For each variable (corresponding to the columns), the total count of the number of times that variable is used in a tree decision rule (over all trees) is given. |

In addition the list has a binaryOffset component giving the value used.

Note that in the binary `y`

, case yhat.train and yhat.test are
`f(x)`

+ binaryOffset. If you want draws of the probability
`P(Y=1 | x)`

you need to apply the normal cdf (`pnorm`

)
to these values.

### See Also

### Examples

```
##simulate from Friedman's five-dimensional test function
##Friedman JH. Multivariate adaptive regression splines
##(with discussion and a rejoinder by the author).
##Annals of Statistics 1991; 19:1-67.
f = function(x) #only the first 5 matter
sin(pi*x[ , 1]*x[ , 2]) + 2*(x[ , 3]-.5)^2+x[ , 4]+0.5*x[ , 5]-1.5
sigma = 1.0 #y = f(x) + sigma*z where z~N(0, 1)
k = 50 #number of covariates
thin = 25
ndpost = 2500
nskip = 100
C = 10
m = 10
n = 10000
set.seed(12)
x.train=matrix(runif(n*k), n, k)
Ey.train = f(x.train)
y.train=(Ey.train+sigma*rnorm(n)>0)*1
table(y.train)/n
x <- x.train
x4 <- seq(0, 1, length.out=m)
for(i in 1:m) {
x[ , 4] <- x4[i]
if(i==1) x.test <- x
else x.test <- rbind(x.test, x)
}
## parallel::mcparallel/mccollect do not exist on windows
if(.Platform$OS.type=='unix') {
##test BART with token run to ensure installation works
post = rs.pbart(x.train, y.train,
C=C, mc.cores=4, keepevery=1,
seed=99, ndpost=1, nskip=1)
}
## Not run:
post = rs.pbart(x.train, y.train, x.test=x.test,
C=C, mc.cores=8, keepevery=thin,
seed=99, ndpost=ndpost, nskip=nskip)
str(post)
par(mfrow=c(2, 2))
M <- nrow(post$yhat.test)
pred <- matrix(nrow=M, ncol=10)
for(i in 1:m) {
h <- (i-1)*n+1:n
pred[ , i] <- apply(pnorm(post$yhat.test[ , h]), 1, mean)
}
pred <- apply(pred, 2, mean)
plot(x4, qnorm(pred), xlab=expression(x[4]),
ylab='partial dependence function', type='l')
i <- floor(seq(1, n, length.out=10))
j <- seq(-0.5, 0.4, length.out=10)
for(h in 1:10) {
auto.corr <- acf(post$yhat.shard[ , i[h]], plot=FALSE)
if(h==1) {
max.lag <- max(auto.corr$lag[ , 1, 1])
plot(1:max.lag+j[h], auto.corr$acf[1+(1:max.lag), 1, 1],
type='h', xlim=c(0, max.lag+1), ylim=c(-1, 1),
ylab='auto-correlation', xlab='lag')
}
else
lines(1:max.lag+j[h], auto.corr$acf[1+(1:max.lag), 1, 1],
type='h', col=h)
}
for(j in 1:10) {
if(j==1)
plot(pnorm(post$yhat.shard[ , i[j]]),
type='l', ylim=c(0, 1),
sub=paste0('N:', n, ', k:', k),
ylab=expression(Phi(f(x))), xlab='m')
else
lines(pnorm(post$yhat.shard[ , i[j]]),
type='l', col=j)
}
geweke <- gewekediag(post$yhat.shard)
j <- -10^(log10(n)-1)
plot(geweke$z, pch='.', cex=2, ylab='z', xlab='i',
sub=paste0('N:', n, ', k:', k),
xlim=c(j, n), ylim=c(-5, 5))
lines(1:n, rep(-1.96, n), type='l', col=6)
lines(1:n, rep(+1.96, n), type='l', col=6)
lines(1:n, rep(-2.576, n), type='l', col=5)
lines(1:n, rep(+2.576, n), type='l', col=5)
lines(1:n, rep(-3.291, n), type='l', col=4)
lines(1:n, rep(+3.291, n), type='l', col=4)
lines(1:n, rep(-3.891, n), type='l', col=3)
lines(1:n, rep(+3.891, n), type='l', col=3)
lines(1:n, rep(-4.417, n), type='l', col=2)
lines(1:n, rep(+4.417, n), type='l', col=2)
text(c(1, 1), c(-1.96, 1.96), pos=2, cex=0.6, labels='0.95')
text(c(1, 1), c(-2.576, 2.576), pos=2, cex=0.6, labels='0.99')
text(c(1, 1), c(-3.291, 3.291), pos=2, cex=0.6, labels='0.999')
text(c(1, 1), c(-3.891, 3.891), pos=2, cex=0.6, labels='0.9999')
text(c(1, 1), c(-4.417, 4.417), pos=2, cex=0.6, labels='0.99999')
par(mfrow=c(1, 1))
##dev.copy2pdf(file='geweke.rs.pbart.pdf')
## End(Not run)
```

*BART*version 2.9.7 Index]