var.select.rfsrc {randomForestSRC} | R Documentation

## Variable Selection

### Description

Variable selection using minimal depth.

### Usage

    ## S3 method for class 'rfsrc'
    var.select(formula,
      data,
      object,
      cause,
      m.target,
      method = c("md", "vh", "vh.vimp"),
      conservative = c("medium", "low", "high"),
      ntree = (if (method == "md") 1000 else 500),
      mvars = (if (method != "md") ceiling(ncol(data)/5) else NULL),
      mtry = (if (method == "md") ceiling(ncol(data)/3) else NULL),
      nodesize = 2, splitrule = NULL, nsplit = 10, xvar.wt = NULL,
      refit = (method != "md"), fast = FALSE,
      na.action = c("na.omit", "na.impute"),
      always.use = NULL, nrep = 50, K = 5, nstep = 1,
      prefit =  list(action = (method != "md"), ntree = 100,
      mtry = 500, nodesize = 3, nsplit = 1),
      verbose = TRUE, ...)

### Arguments

`formula` | A symbolic description of the model to be fit. Must be specified unless `object` is given.
`data` | Data frame containing the y-outcome and x-variables in the model. Must be specified unless `object` is given.
`object` | An object of class `(rfsrc, grow)`. Not required when `formula` and `data` are supplied.
`cause` | Integer value between 1 and `J` indicating the event of interest for competing risks, where `J` is the number of event types (this option applies only to competing risk families). 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.

`method`

Variable selection method:

`md`:

  minimal depth (default).

`vh`:

  variable hunting.

`vh.vimp`:

  variable hunting with VIMP (variable importance).

`conservative`

Level of conservativeness of the thresholding rule used in minimal depth selection:

`high`:

  Use the most conservative threshold.

`medium`:

  Use the default less conservative tree-averaged threshold.

`low`:

  Use the more liberal one standard error rule.

`ntree` | Number of trees to grow.
`mvars` | Number of randomly selected variables used in the variable hunting algorithm (ignored when method="md").
`mtry` | The mtry value used.
`nodesize` | Forest average terminal node size.
`splitrule` | Splitting rule used.
`nsplit` | If non-zero, the specified tree splitting rule is randomized which significantly increases speed.
`xvar.wt` | Vector of non-negative weights specifying the probability of selecting a variable for splitting a node. Must be of dimension equal to the number of variables. Default (`NULL`) invokes uniform weighting or a data-adaptive method depending on `prefit$action`.
`refit` | Should a forest be refit using the selected variables?
`fast` | Speeds up the cross-validation used for variable hunting for a faster analysis. See miscellanea below.
`na.action` | Action to be taken if the data contains `NA` values.
`always.use` | Character vector of variable names to always be included in the model selection procedure and in the final selected model.
`nrep` | Number of Monte Carlo iterations of the variable hunting algorithm.
`K` | Integer value specifying the `K`-fold size used in the variable hunting algorithm.
`nstep` | Integer value controlling the step size used in the forward selection process of the variable hunting algorithm. Increasing this will encourage more variables to be selected.

`prefit`

List containing parameters used in preliminary forest analysis for determining weight selection of variables. Users can set all or some of the following parameters:

`action`:

  Determines how (or if) the preliminary forest is fit. See details below.

`ntree`:

  Number of trees used in the preliminary analysis.

`mtry`:

  mtry used in the preliminary analysis.

`nodesize`:

  nodesize used in the preliminary analysis.

`nsplit`:

  nsplit value used in the preliminary analysis.

`verbose` | Set to `TRUE` for verbose output.
`...` | Further arguments passed to forest grow call.

### Details

This function implements random forest variable selection using tree minimal depth methodology (Ishwaran et al., 2010). The option method allows for two different approaches:

1. method="md"

   Invokes minimal depth variable selection. Variables are selected using minimal depth variable selection. Uses all data and all variables simultaneously. This is basically a front-end to the `max.subtree` wrapper. Users should consult the `max.subtree` help file for details.

   Set mtry to larger values in high-dimensional problems.

2. method="vh" or method="vh.vimp"

   Invokes variable hunting. Variable hunting is used for problems where the number of variables is substantially larger than the sample size (e.g., p/n is greater than 10). It is always prefered to use method="md", but to find more variables, or when computations are high, variable hunting may be preferred.

   When method="vh": Using training data from a stratified K-fold subsampling (stratification based on the y-outcomes), a forest is fit using `mvars` randomly selected variables (variables are chosen with probability proportional to weights determined using an initial forest fit; see below for more details). The `mvars` variables are ordered by increasing minimal depth and added sequentially (starting from an initial model determined using minimal depth selection) until joint VIMP no longer increases (signifying the final model). A forest is refit to the final model and applied to test data to estimate prediction error. The process is repeated `nrep` times. Final selected variables are the top P ranked variables, where P is the average model size (rounded up to the nearest integer) and variables are ranked by frequency of occurrence.

   The same algorithm is used when method="vh.vimp", but variables are ordered using VIMP. This is faster, but not as accurate.

Miscellanea

1. When variable hunting is used, a preliminary forest is run and its VIMP is used to define the probability of selecting a variable for splitting a node. Thus, instead of randomly selecting `mvars` at random, variables are selected with probability proportional to their VIMP (the probability is zero if VIMP is negative). A preliminary forest is run once prior to the analysis if `prefit$action=TRUE`, otherwise it is run prior to each iteration (this latter scenario can be slow). When method="md", a preliminary forest is fit only if `prefit$action=TRUE`. Then instead of randomly selecting `mtry` variables at random, `mtry` variables are selected with probability proportional to their VIMP. In all cases, the entire option is overridden if `xvar.wt` is non-null.

2. If `object` is supplied and method="md", the grow forest from `object` is parsed for minimal depth information. While this avoids fitting another forest, thus saving computational time, certain options no longer apply. In particular, the value of `cause` plays no role in the final selected variables as minimal depth is extracted from the grow forest, which has already been grown under a preselected `cause` specification. Users wishing to specify `cause` should instead use the formula and data interface. Also, if the user requests a prefitted forest via `prefit$action=TRUE`, then `object` is not used and a refitted forest is used in its place for variable selection. Thus, the effort spent to construct the original grow forest is not used in this case.

3. If fast=TRUE, and variable hunting is used, the training data is chosen to be of size n/K, where n=sample size (i.e., the size of the training data is swapped with the test data). This speeds up the algorithm. Increasing K also helps.

4. Can be used for competing risk data. When method="vh.vimp", variable selection based on VIMP is confined to an event specific cause specified by `cause`. However, this can be unreliable as not all y-outcomes can be guaranteed when subsampling (this is true even when stratifed subsampling is used as done here).

### Value

Invisibly, a list with the following components:

`err.rate` | Prediction error for the forest (a vector of length `nrep` if variable hunting is used).
`modelsize` | Number of variables selected.
`topvars` | Character vector of names of the final selected variables.
`varselect` | Useful output summarizing the final selected variables.
`rfsrc.refit.obj` | Refitted forest using the final set of selected variables (requires refit=TRUE).
`md.obj` | Minimal depth object. `NULL` unless method="md".

### Author(s)

Hemant Ishwaran and Udaya B. Kogalur

### References

Ishwaran H., Kogalur U.B., Gorodeski E.Z, Minn A.J. and Lauer M.S. (2010). High-dimensional variable selection for survival data. J. Amer. Statist. Assoc., 105:205-217.

Ishwaran H., Kogalur U.B., Chen X. and Minn A.J. (2011). Random survival forests for high-dimensional data. Statist. Anal. Data Mining, 4:115-132.

### See Also

`find.interaction.rfsrc`, `holdout.vimp.rfsrc`, `max.subtree.rfsrc`, `vimp.rfsrc`

### Examples

    ## ------------------------------------------------------------
    ## Minimal depth variable selection
    ## survival analysis
    ## use larger node size which is better for minimal depth
    ## ------------------------------------------------------------

    data(pbc, package = "randomForestSRC")
    pbc.obj <- rfsrc(Surv(days, status) ~ ., pbc, nodesize = 20, importance = TRUE)

    # default call corresponds to minimal depth selection
    vs.pbc <- var.select(object = pbc.obj)
    topvars <- vs.pbc$topvars

    # the above is equivalent to
    max.subtree(pbc.obj)$topvars

    # different levels of conservativeness
    var.select(object = pbc.obj, conservative = "low")
    var.select(object = pbc.obj, conservative = "medium")
    var.select(object = pbc.obj, conservative = "high")

    ## ------------------------------------------------------------
    ## Minimal depth variable selection
    ## competing risk analysis
    ## use larger node size which is better for minimal depth
    ## ------------------------------------------------------------

    ## competing risk data set involving AIDS in women
    data(wihs, package = "randomForestSRC")
    vs.wihs <- var.select(Surv(time, status) ~ ., wihs, nsplit = 3,
                          nodesize = 20, ntree = 100, importance = TRUE)

    ## competing risk analysis of pbc data from survival package
    ## implement cause-specific variable selection
    if (library("survival", logical.return = TRUE)) {
      data(pbc, package = "survival")
      pbc$id <- NULL
      var.select(Surv(time, status) ~ ., pbc, cause = 1)
      var.select(Surv(time, status) ~ ., pbc, cause = 2)
    }

    ## ------------------------------------------------------------
    ## Minimal depth variable selection
    ## classification analysis
    ## ------------------------------------------------------------

    vs.iris <- var.select(Species ~ ., iris)

    ## ------------------------------------------------------------
    ## Variable hunting high-dimensional example
    ## van de Vijver microarray breast cancer survival data
    ## nrep is small for illustration; typical values are nrep = 100
    ## ------------------------------------------------------------

    data(vdv, package = "randomForestSRC")
    vh.breast <- var.select(Surv(Time, Censoring) ~ ., vdv,
          method = "vh", nrep = 10, nstep = 5)

    # plot top 10 variables
    plot.variable(vh.breast$rfsrc.refit.obj,
      xvar.names = vh.breast$topvars[1:10])
    plot.variable(vh.breast$rfsrc.refit.obj,
      xvar.names = vh.breast$topvars[1:10], partial = TRUE)

    ## similar analysis, but using weights from univarate cox p-values
    if (library("survival", logical.return = TRUE))
    {
      cox.weights <- function(rfsrc.f, rfsrc.data) {
        event.names <- all.vars(rfsrc.f)[1:2]
        p <- ncol(rfsrc.data) - 2
        event.pt <- match(event.names, names(rfsrc.data))
        xvar.pt <- setdiff(1:ncol(rfsrc.data), event.pt)
        sapply(1:p, function(j) {
          cox.out <- coxph(rfsrc.f, rfsrc.data[, c(event.pt, xvar.pt[j])])
          pvalue <- summary(cox.out)$coef[5]
          if (is.na(pvalue)) 1.0 else 1/(pvalue + 1e-100)
        })
      }
      data(vdv, package = "randomForestSRC")
      rfsrc.f <- as.formula(Surv(Time, Censoring) ~ .)
      cox.wts <- cox.weights(rfsrc.f, vdv)
      vh.breast.cox <- var.select(rfsrc.f, vdv, method = "vh", nstep = 5,
        nrep = 10, xvar.wt = cox.wts)
    }

[Package randomForestSRC version 2.9.3 Index]