PRIM_paste: Pasting-Function
In ao90/PRIM: Patient Rule Induction Method (PRIM)

Description Usage Arguments Details Value References Examples

This function is an implementation of the Pasting-Algorithm as suggested by Friedman and Fisher (1999). In each iteration the fraction alpha is pasted to one edge of the current box.

1	PRIM_paste(fixbox, paste_alpha = 0.01, max_steps = 50, stop_by_dec = TRUE)

`fixbox`	an object of class `fixbox`, which was defined after the peeling function and now should be used for pasting.
`paste_alpha`	alpha-fraction that is pasted to the box at each iteration.
`max_steps`	maximum number of pasting steps the function should make.
`stop_by_dec`	logical. If `TRUE` the pasting stops if the target at one step is lower than the target of the last step.

The outcome of this function is also a "peel"-object, because it has basically the same structure as the outcome of the peeling functions. The only difference is, that pasting goes from small supports to bigger ones, while by peeling its the other way round.

PRIM_paste returns an object of class "peel", which is a list containing at least the following components:

`f`	vector of the target functions evaluated on the box at each pasting step.
`beta`	vector of the supports beta of the boxes at each pasting step.
`box`	a `data.frame` defining the borders of the boxes. Each row belongs to one pasting step. The columns with "`min.`" and "`max.`" describe the lower and upper boundaries of the at least ordinal covariates. Therefore the value taken is the last one that is not included in the current box. For the nominal variables there are columns for every category they can take. If the category is removed from the box the value `FALSE` is taken. The names of these columns are structured like: `<variable name>.<category>` For each variable with missing values (only if `use_NAs = TRUE`) there is also a column taking the value `FALSE` if the `NA`s of this variable are removed from the current box. The names of these columns are structured like: `<variable name>.NA`
`box_metric, box_nom, box_na`	easier to handle definitions of the boxes for other functions
`subsets`	`list` of logical vectors indicating the subsets at each pasting step (i.e. the observations that lie in the box)
`data_orig`	original dataset that is used (extracted from `fixbox`).

Friedman, J. H. and Fisher, N. I., 'Bump hunting in high-dimensional data', Statistics and Computing 9 (2) (1999), 123-143

Ott, A. and Hapfelmeier, A., 'Nonparametric Subgroup Identification by PRIM and CART: A Simulation and Application Study', Computational and Mathematical Methods in Medicine, vol. 2017 (2017), 17 pages, Article ID 5271091

# generating random data:
set.seed(123)
n <- 500
x1 <- runif(n = n, min = -1)
x2 <- runif(n = n, min = -1)
x3 <- runif(n = n, min = -1)
cat <- as.factor(sample(c("a","b","c", "d"), size = n, replace = TRUE))
wsk <- (1-sqrt(x1^2+x2^2)/sqrt(2))
y <- as.logical(rbinom(n = n, prob = wsk, size = 1))
dat <- cbind.data.frame(y, x1, x2, x3, cat)
#plot(dat$x1, dat$x2, col=dat$y+1, pch=16)
remove(x1, x2, x3, y, wsk, cat, n)

# apply the PRIM_peel function:
prim <- PRIM_peel(y ~ ., data = dat, beta_min = .01, peel_alpha = .1)
plot(prim)
abline(h=prim$f[17], v=prim$beta[17]) # box decided to paste
fix <- define_fixbox(prim, 17) # define fixbox

# apply the PRIM_paste function:
paste <- PRIM_paste(fix, stop_by_dec = FALSE)
head(cbind(paste$box, paste$f, paste$beta))