randomForestSRC (version 3.3.1)

plot.variable.rfsrc: Plot Marginal Effect of Variables

Description

Plot the marginal effect of an x-variable on the class probability (classification), response (regression), mortality (survival), or the expected years lost (competing risk). Users can select between marginal (unadjusted, but fast) and partial plots (adjusted, but slower).

Usage

# S3 method for rfsrc
plot.variable(x, xvar.names, target,
  m.target = NULL, time, surv.type = c("mort", "rel.freq",
  "surv", "years.lost", "cif", "chf"), class.type =
  c("prob", "bayes"), partial = FALSE, oob = TRUE,
  show.plots = TRUE, plots.per.page = 4, granule = 5, sorted = TRUE,
  nvar, npts = 25, smooth.lines = FALSE, subset, ...)

Arguments

x

An object of class (rfsrc, grow), (rfsrc, synthetic), or (rfsrc, plot.variable).

xvar.names

Names of the x-variables to be used. If not supplied all variables will be used.

target

For classification, an integer or character value specifying the class to focus on (defaults to the first class). For competing risks, an integer value between 1 and J indicating the event of interest, where J is the number of event types. The default is to use the first event type.

m.target

Character value for multivariate families specifying the target outcome to be used. If left unspecified, the algorithm will choose a default target.

time

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

surv.type

For survival, specifies the predicted value. See details below.

class.type

For classification, specifies the predicted value. See details below.

partial

Should partial plots be used?

oob

OOB (TRUE) or in-bag (FALSE) predicted values.

show.plots

Should plots be displayed?

plots.per.page

Integer value controlling page layout.

granule

Integer value controlling whether a plot for a specific variable should be treated as a factor and therefore given as a boxplot. Larger values coerce boxplots.

sorted

Should variables be sorted by importance values.

nvar

Number of variables to be plotted. Default is all.

npts

Maximum number of points used when generating partial plots for continuous variables.

smooth.lines

Use lowess to smooth partial plots.

subset

Vector indicating which rows of the x-variable matrix x$xvar to use. All rows are used if not specified. Do not define subset based on the original data (which could have been processed due to missing values or for other reasons in the previous forest call) but define subset based on the rows of x$xvar.

...

Further arguments passed to or from other methods.

Author

Hemant Ishwaran and Udaya B. Kogalur

Details

The vertical axis displays the ensemble predicted value, while x-variables are plotted on the horizontal axis.

1. For regression, the predicted response is used.

2. For classification, it is the predicted class probability specified by target, or the class of maximum probability depending on class.type is set to "prob" or "bayes".

3. For multivariate families, it is the predicted value of the outcome specified by m.target and if that is a classification outcome, by target.

4. For survival, the choices are:

   • Mortality (mort). Mortality (Ishwaran et al., 2008) represents estimated risk for an individual calibrated to the scale of number of events (as a specific example, if i has a mortality value of 100, then if all individuals had the same x-values as i, we would expect an average of 100 events).

   • Relative frequency of mortality (rel.freq).

   • Predicted survival (surv), where the predicted survival is for the time point specified using time (the default is the median follow up time).

5. For competing risks, the choices are:

   • The expected number of life years lost (years.lost).

   • The cumulative incidence function (cif).

   • The cumulative hazard function (chf).

   In all three cases, the predicted value is for the event type specified by target. For cif and chf the quantity is evaluated at the time point specified by time.

For partial plots use partial=TRUE. Their interpretation are different than marginal plots. The y-value for a variable \(X\), evaluated at \(X=x\), is $$ \tilde{f}(x) = \frac{1}{n} \sum_{i=1}^n \hat{f}(x, x_{i,o}), $$ where \(x_{i,o}\) represents the value for all other variables other than \(X\) for individual \(i\) and \(\hat{f}\) is the predicted value. Generating partial plots can be very slow. Choosing a small value for npts can speed up computational times as this restricts the number of distinct \(x\) values used in computing \(\tilde{f}\).

For continuous variables, red points are used to indicate partial values and dashed red lines indicate a smoothed error bar of +/- two standard errors. Black dashed line are the partial values. Set smooth.lines=TRUE for lowess smoothed lines. For discrete variables, partial values are indicated using boxplots with whiskers extending out approximately two standard errors from the mean. Standard errors are meant only to be a guide and should be interpreted with caution.

Partial plots can be slow. Setting npts to a smaller number can help.

For greater customization and computational speed for partial plot calls, consider using the function partial.rfsrc which provides a direct interface for calculating partial plot data.

References

Friedman J.H. (2001). Greedy function approximation: a gradient boosting machine, Ann. of Statist., 5:1189-1232.

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.

Ishwaran H., Gerds T.A., Kogalur U.B., Moore R.D., Gange S.J. and Lau B.M. (2014). Random survival forests for competing risks. Biostatistics, 15(4):757-773.

See Also

rfsrc, synthetic.rfsrc, partial.rfsrc, predict.rfsrc

Examples

# \donttest{
## ------------------------------------------------------------
## survival/competing risk
## ------------------------------------------------------------

## survival
data(veteran, package = "randomForestSRC")
v.obj <- rfsrc(Surv(time,status)~., veteran, ntree = 100)
plot.variable(v.obj, plots.per.page = 3)
plot.variable(v.obj, plots.per.page = 2, xvar.names = c("trt", "karno", "age"))
plot.variable(v.obj, surv.type = "surv", nvar = 1, time = 200)
plot.variable(v.obj, surv.type = "surv", partial = TRUE, smooth.lines = TRUE)
plot.variable(v.obj, surv.type = "rel.freq", partial = TRUE, nvar = 2)

## example of plot.variable calling a pre-processed plot.variable object
p.v <- plot.variable(v.obj, surv.type = "surv", partial = TRUE, smooth.lines = TRUE)
plot.variable(p.v)
p.v$plots.per.page <- 1
p.v$smooth.lines <- FALSE
plot.variable(p.v)

## example using a pre-processed plot.variable to define custom plots
p.v <- plot.variable(v.obj, surv.type = "surv", partial = TRUE, show.plots = FALSE)
plotthis <- p.v$plotthis
plot(plotthis[["age"]], xlab = "age", ylab = "partial effect", type = "b")
boxplot(yhat ~ x, plotthis[["trt"]], xlab = "treatment", ylab = "partial effect")


## competing risks
data(follic, package = "randomForestSRC")
follic.obj <- rfsrc(Surv(time, status) ~ ., follic, nsplit = 3, ntree = 100)
plot.variable(follic.obj, target = 2)

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

## airquality 
airq.obj <- rfsrc(Ozone ~ ., data = airquality)
plot.variable(airq.obj, partial = TRUE, smooth.lines = TRUE)
plot.variable(airq.obj, partial = TRUE, subset = airq.obj$xvar$Solar.R < 200)

## motor trend cars
mtcars.obj <- rfsrc(mpg ~ ., data = mtcars)
plot.variable(mtcars.obj, partial = TRUE, smooth.lines = TRUE)

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

## iris
iris.obj <- rfsrc(Species ~., data = iris)
plot.variable(iris.obj, partial = TRUE)

## motor trend cars: predict number of carburetors
mtcars2 <- mtcars
mtcars2$carb <- factor(mtcars2$carb,
   labels = paste("carb", sort(unique(mtcars$carb))))
mtcars2.obj <- rfsrc(carb ~ ., data = mtcars2)
plot.variable(mtcars2.obj, partial = TRUE)

## ------------------------------------------------------------
## multivariate regression
## ------------------------------------------------------------
mtcars.mreg <- rfsrc(Multivar(mpg, cyl) ~., data = mtcars)
plot.variable(mtcars.mreg, m.target = "mpg", partial = TRUE, nvar = 1)
plot.variable(mtcars.mreg, m.target = "cyl", partial = TRUE, nvar = 1)


## ------------------------------------------------------------
## multivariate mixed outcomes
## ------------------------------------------------------------
mtcars2 <- mtcars
mtcars2$carb <- factor(mtcars2$carb)
mtcars2$cyl <- factor(mtcars2$cyl)
mtcars.mix <- rfsrc(Multivar(carb, mpg, cyl) ~ ., data = mtcars2)
plot.variable(mtcars.mix, m.target = "cyl", target = "4", partial = TRUE, nvar = 1)
plot.variable(mtcars.mix, m.target = "cyl", target = 2, partial = TRUE, nvar = 1)


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