Acquire Partial Effect of a Variable

Direct, fast inferface for partial effect of a variable. Works for all families.

partial.rfsrc(object, oob = TRUE, 
  partial.type = NULL, partial.xvar = NULL, partial.values = NULL,
  partial.xvar2 = NULL, partial.values2 = NULL,
  partial.time = NULL, get.tree = NULL, seed = NULL, do.trace = FALSE, ...)

Arguments

object

An object of class (rfsrc, grow).

oob

By default out-of-bag values are returned, but inbag values can be requested by setting this option to FALSE.

partial.type

Character vector specifying type of predicted value requested. See details below.

partial.xvar

Character value specifying the single primary partial x-variable to be used.

partial.values

Vector of values that the primary partialy x-variable will assume.

partial.xvar2

Vector of character values specifying the second order x-variables to be used.

partial.values2

Vector of values that the second order x-variables will assume. Each second order x-variable can only assume a single value. This the length of partial.xvar2 and partial.values2 will be the same. In addition, the user must do the appropriate conversion for factors, and represent a value as a numeric element.

partial.time

For survival families, the time at which the predicted survival value is evaluated at (depends on partial.type).

get.tree

Vector of integer(s) identifying trees over which the partial values are calculated over. By default, uses all trees in the forest.

seed

Negative integer specifying seed for the random number generator.

do.trace

Number of seconds between updates to the user on approximate time to completion.

...

Further arguments passed to or from other methods.

Details

Used for direct, efficient call to obtain partial plot effects. This function is intended primarily for experts.

Out-of-bag (OOB) values are returned by default.

For factors, the partial value should be encoded as a positive integer reflecting the level number of the factor. The actual label of the factor should not be used.

The utility function get.partial.plot.data is supplied for processing returned raw partial effects in a format more convenient for plotting. Options are specified as in plot.variable. See examples for illustration.

Raw partial plot effects data is returned either as an array or a list of length equal to the number of outcomes (length is one for univariate families) with entries depending on the underlying family:

  1. For regression, partial plot data is returned as a list in regrOutput with dim [n] x [length(partial.values)].

  2. For classification, partial plot data is returned as a list in classOutput of dim [n] x [1 + yvar.nlevels[.]] x [length(partial.values)].

  3. For mixed multivariate regression, values are returned in list format both in regrOutput and classOutput

  4. For survival, values are returned as either a matrix or array in survOutput. Depending on partial type specified this can be:

    • For partial type surv returns the survival function of dim [n] x [length(partial.time)] x [length(partial.values)].

    • For partial type mort returns mortality of dim [n] x [length(partial.values)].

    • For partial type chf returns the cumulative hazard function of dim [n] x [length(partial.time)] x [length(partial.values)].

  5. For competing risks, values are returned as either a matrix or array in survOutput. Depending on the options specified this can be:

    • For partial type years.lost returns the expected number of life years lost of dim [n] x [length(event.info$event.type)] x [length(partial.values)].

    • For partial type cif returns the cumulative incidence function of dim [n] x [length(partial.time)] x [length(event.info$event.type)] x [length(partial.values)].

    • For partial type chf returns the cumulative hazard function of dim [n] x [length(partial.time)] x [length(event.info$event.type)] x [length(partial.values)].

Author

Hemant Ishwaran and Udaya B. Kogalur

References

Ishwaran H., Kogalur U.B. (2007). Random survival forests for R, Rnews, 7(2):25-31.

Ishwaran H., Kogalur U.B., Blackstone E.H. and Lauer M.S. (2008). Random survival forests, Ann. App. Statist., 2:841-860.

Examples

# \donttest{

## ------------------------------------------------------------
##
## regression
##
## ------------------------------------------------------------

airq.obj <- rfsrc(Ozone ~ ., data = airquality)

## partial effect for wind
partial.obj <- partial(airq.obj,
                  partial.xvar = "Wind",
                  partial.values = airq.obj$xvar$Wind)
pdta <- get.partial.plot.data(partial.obj)

## plot partial values
plot(pdta$x, pdta$yhat, type = "b", pch = 16,
      xlab = "wind", ylab = "partial effect of wind")


## example where we display all the partial effects
## instead of averaging - use the granule=TRUE option
pdta <- get.partial.plot.data(partial.obj, granule = TRUE)
boxplot(pdta$yhat ~ pdta$x, xlab = "Wind", ylab = "partial effect")

## ------------------------------------------------------------
##
## regression: partial effects for two variables simultaneously
##
## ------------------------------------------------------------

airq.obj <- rfsrc(Ozone ~ ., data = airquality)

## specify wind and temperature values of interest
wind <- sort(unique(airq.obj$xvar$Wind))
temp <- sort(unique(airq.obj$xvar$Temp))

## partial effect for wind, for a given temp
pdta <- do.call(rbind, lapply(temp, function(x2) {
  o <- partial(airq.obj,
         partial.xvar = "Wind", partial.xvar2 = "Temp",
         partial.values = wind, partial.values2 = x2)
  cbind(wind, x2, get.partial.plot.data(o)$yhat)
}))
pdta <- data.frame(pdta)
colnames(pdta) <- c("wind", "temp", "effectSize")

## coplot of partial effect of wind and temp 
coplot(effectSize ~ wind|temp, pdta, pch = 16, overlap = 0)


## ------------------------------------------------------------
##
## regression: partial effects for three variables simultaneously
## (can be slow, so modify accordingly)
##
## ------------------------------------------------------------

n <- 1000
x <- matrix(rnorm(n * 3), ncol = 3)
y <- x[, 1] + x[, 1] * x[, 2] + x[, 1] * x[, 2] * x[, 3]
o <- rfsrc(y ~ ., data = data.frame(y = y, x))

## define target x values
x1 <- seq(-3, 3, length = 40)
x2 <- x3 <- seq(-3, 3, length = 10)

## extract second order partial effects
pdta <- do.call(rbind,
          lapply(x3, function(x3v) {
            cat("outer loop x3 = ", x3v, "\n")
            do.call(rbind,lapply(x2, function(x2v) {
              o <- partial(o,
                      partial.xvar = "X1",
                      partial.values = x1,
                      partial.xvar2 = c("X2", "X3"),
                      partial.values2 = c(x2v, x3v))
              cbind(x1, x2v, x3v, get.partial.plot.data(o)$yhat)
            }))
          }))
pdta <- data.frame(pdta)
colnames(pdta) <- c("x1", "x2", "x3", "effectSize")

## coplot of partial effects
coplot(effectSize ~ x1|x2*x3, pdta, pch = 16, overlap = 0)


## ------------------------------------------------------------
##
## classification
##
## ------------------------------------------------------------

iris.obj <- rfsrc(Species ~., data = iris)

## partial effect for sepal length
partial.obj <- partial(iris.obj,
                  partial.xvar = "Sepal.Length",
                  partial.values = iris.obj$xvar$Sepal.Length)

## extract partial effects for each species outcome
pdta1 <- get.partial.plot.data(partial.obj, target = "setosa")
pdta2 <- get.partial.plot.data(partial.obj, target = "versicolor")
pdta3 <- get.partial.plot.data(partial.obj, target = "virginica")

## plot the results
par(mfrow=c(1,1))
plot(pdta1$x, pdta1$yhat, type="b", pch = 16,
     xlab = "sepal length", ylab = "adjusted probability", 
     ylim = range(pdta1$yhat,pdta2$yhat,pdta3$yhat))
points(pdta2$x, pdta2$yhat, col = 2, type = "b", pch = 16)
points(pdta3$x, pdta3$yhat, col = 4, type = "b", pch = 16)
legend("topleft", legend=levels(iris.obj$yvar), fill = c(1, 2, 4))

## ------------------------------------------------------------
##
## survival
##
## ------------------------------------------------------------

data(veteran, package = "randomForestSRC")
v.obj <- rfsrc(Surv(time,status)~., veteran, nsplit = 10, ntree = 100)

## partial effect of age on mortality
partial.obj <- partial(v.obj,
  partial.type = "mort",
  partial.xvar = "age",
  partial.values = v.obj$xvar$age,
  partial.time = v.obj$time.interest)
pdta <- get.partial.plot.data(partial.obj)

plot(lowess(pdta$x, pdta$yhat, f = 1/3),
   type = "l", xlab = "age", ylab = "adjusted mortality")

## example where x is discrete - partial effect of age on mortality
## we use the granule=TRUE option
partial.obj <- partial(v.obj,
       partial.type = "mort",
       partial.xvar = "trt",
       partial.values = v.obj$xvar$trt,
       partial.time = v.obj$time.interest)
pdta <- get.partial.plot.data(partial.obj, granule = TRUE)
boxplot(pdta$yhat ~ pdta$x, xlab = "treatment", ylab = "partial effect")


## partial effects of karnofsky score on survival
karno <- quantile(v.obj$xvar$karno)
partial.obj <- partial(v.obj,
  partial.type = "surv",
  partial.xvar = "karno",
  partial.values = karno,
  partial.time = v.obj$time.interest)
pdta <- get.partial.plot.data(partial.obj)

matplot(pdta$partial.time, t(pdta$yhat), type = "l", lty = 1,
     xlab = "time", ylab = "karnofsky adjusted survival")
legend("topright", legend = paste0("karnofsky = ", karno), fill = 1:5)


## ------------------------------------------------------------
##
## competing risk
##
## ------------------------------------------------------------

data(follic, package = "randomForestSRC")
follic.obj <- rfsrc(Surv(time, status) ~ ., follic, nsplit = 3, ntree = 100)

## partial effect of age on years lost
partial.obj <- partial(follic.obj,
  partial.type = "years.lost",
  partial.xvar = "age",
  partial.values = follic.obj$xvar$age,
  partial.time = follic.obj$time.interest)
pdta1 <- get.partial.plot.data(partial.obj, target = 1)
pdta2 <- get.partial.plot.data(partial.obj, target = 2)

par(mfrow=c(2,2))
plot(lowess(pdta1$x, pdta1$yhat),
   type = "l", xlab = "age", ylab = "adjusted years lost relapse")
plot(lowess(pdta2$x, pdta2$yhat),
   type = "l", xlab = "age", ylab = "adjusted years lost death")

## partial effect of age on cif
partial.obj <- partial(follic.obj,
  partial.type = "cif",
  partial.xvar = "age",
  partial.values = quantile(follic.obj$xvar$age),
  partial.time = follic.obj$time.interest)
pdta1 <- get.partial.plot.data(partial.obj, target = 1)
pdta2 <- get.partial.plot.data(partial.obj, target = 2)

matplot(pdta1$partial.time, t(pdta1$yhat), type = "l", lty = 1,
     xlab = "time", ylab = "age adjusted cif for relapse")
matplot(pdta2$partial.time, t(pdta2$yhat), type = "l", lty = 1,
     xlab = "time", ylab = "age adjusted cif for death")


## ------------------------------------------------------------
##
## multivariate mixed outcomes
##
## ------------------------------------------------------------

mtcars2 <- mtcars
mtcars2$carb <- factor(mtcars2$carb)
mtcars2$cyl <- factor(mtcars2$cyl)
mtcars.mix <- rfsrc(Multivar(carb, mpg, cyl) ~ ., data = mtcars2)

## partial effect of displacement for each the three-outcomes
partial.obj <- partial(mtcars.mix,
                  partial.xvar = "disp",
                  partial.values = mtcars.mix$xvar$disp)
pdta1 <- get.partial.plot.data(partial.obj, m.target = "carb")
pdta2 <- get.partial.plot.data(partial.obj, m.target = "mpg")
pdta3 <- get.partial.plot.data(partial.obj, m.target = "cyl")

par(mfrow=c(2,2))
plot(lowess(pdta1$x, pdta1$yhat), type = "l", xlab="displacement", ylab="carb")
plot(lowess(pdta2$x, pdta2$yhat), type = "l", xlab="displacement", ylab="mpg")
plot(lowess(pdta3$x, pdta3$yhat), type = "l", xlab="displacement", ylab="cyl")


# }