Check if folds result from subsampling with p = 0.5.

Description

(Internal) function that checks if folds result from subsampling with p = 0.5 and adds complementary pairs if needed.

Usage

check_folds(folds, B, n, sampling.type)

Arguments

Details

This is an internal function used to check if folds are specified correctly. For details (e.g. on arguments) see stabsel.

Value

A matrix containing the folds, possibly after adding the complementary pairs.

References

B. Hofner, L. Boccuto and M. Goeker (2015), Controlling false discoveries in high-dimensional situations: Boosting with stability selection. BMC Bioinformatics, 16:144.
doi: 10.1186/s12859-015-0575-3.

See Also

For details see stabsel.

Fit Functions for Stability Selection

Description

Functions that fit a model until q variables are selected and that returns the indices (and names) of the selected variables.

Usage

## package lars:
lars.lasso(x, y, q, ...)
lars.stepwise(x, y, q, ...)

## package glmnet:
glmnet.lasso(x, y, q, type = c("conservative", "anticonservative"), ...)
glmnet.lasso_maxCoef(x, y, q, ...)

Arguments

Details

All fitting functions are named after the package and the type of model that is fitted: package_name.model, e.g., glmnet.lasso stands for a lasso model that is fitted using the package glmnet.

glmnet.lasso_maxCoef fits a lasso model with a given penalty parameter and returns the q largest coefficients. If one wants to use glmnet.lasso_maxCoef, one must specify the penalty parameter lambda (via the ... argument) or in stabsel via args.fitfun(lambda = ). Note that usually, the penalty parameter cannot be specified but is chosen such that q variables are selected. For an example on how to use glmnet.lasso_maxCoef see stabsel.

Value

A named list with elements

See Also

stabsel for stability selection itself.

Examples

  if (require("TH.data")) {
      ## make data set available
      data("bodyfat", package = "TH.data")
  } else {
      ## simulate some data if TH.data not available. 
      ## Note that results are non-sense with this data.
      bodyfat <- matrix(rnorm(720), nrow = 72, ncol = 10)
  }
  
  if (require("lars")) {
      ## selected variables
      lars.lasso(bodyfat[, -2], bodyfat[,2], q = 3)$selected
      lars.stepwise(bodyfat[, -2], bodyfat[,2], q = 3)$selected
  }
  
  if (require("glmnet")) {
      glmnet.lasso(bodyfat[, -2], bodyfat[,2], q = 3)$selected
      ## selection path
      glmnet.lasso(bodyfat[, -2], bodyfat[,2], q = 3)$path
  
      ## Using the anticonservative glmnet.lasso (see args.fitfun):
      stab.glmnet <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                             fitfun = glmnet.lasso, 
                             args.fitfun = list(type = "anticonservative"), 
                             cutoff = 0.75, PFER = 1)
  }

Method to Extract Parameters

Description

Extract stability selection parameters, i.e., tuning parameters, from a stabsel object.

Usage

parameters(object)

## extract parameters from a stabsel model
## (same as parameters(p) )
## S3 method for class 'stabsel'
stabsel_parameters(p, ...)

Arguments

Value

An object of class stabsel_parameters with a special print method. See there for details.

See Also

stabsel to run stability selection and stabsel_parameters for details on the parameters.

Plot and Print Methods for Stability Selection

Description

Display results of stability selection.

Usage

## S3 method for class 'stabsel'
plot(x, main = deparse(x$call), type = c("maxsel", "paths"),
     xlab = NULL, ylab = NULL, col = NULL, ymargin = 10, np = sum(x$max > 0),
     labels = NULL, ...)
## S3 method for class 'stabsel'
print(x, decreasing = FALSE, print.all = TRUE, ...)

Arguments

Details

This function implements the stability selection procedure by Meinshausen and Buehlmann (2010) and the improved error bounds by Shah and Samworth (2013).

Two of the three arguments cutoff, q and PFER must be specified. The per-family error rate (PFER), i.e., the expected number of false positives E(V), where V is the number of false positives, is bounded by the argument PFER.

As controlling the PFER is more conservative as controlling the family-wise error rate (FWER), the procedure also controlls the FWER, i.e., the probability of selecting at least one non-influential variable (or model component) is less than PFER.

Value

An object of class stabsel with a special print method. The object has the following elements:

References

B. Hofner, L. Boccuto and M. Goeker (2015), Controlling false discoveries in high-dimensional situations: Boosting with stability selection. BMC Bioinformatics, 16:144.
doi: 10.1186/s12859-015-0575-3.

N. Meinshausen and P. Buehlmann (2010), Stability selection. Journal of the Royal Statistical Society, Series B, 72, 417–473.

R.D. Shah and R.J. Samworth (2013), Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society, Series B, 75, 55–80.

See Also

stabsel

Examples

  if (require("TH.data")) {
      ## make data set available
      data("bodyfat", package = "TH.data")
  } else {
      ## simulate some data if TH.data not available. 
      ## Note that results are non-sense with this data.
      bodyfat <- matrix(rnorm(720), nrow = 72, ncol = 10)
  }
  
  ## set seed
  set.seed(1234)

  ####################################################################
  ### using stability selection with Lasso methods:

  if (require("lars")) {
      (stab.lasso <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                             fitfun = lars.lasso, cutoff = 0.75,
                             PFER = 1))
      par(mfrow = c(2, 1))
      plot(stab.lasso, ymargin = 6)
      opar <- par(mai = par("mai") * c(1, 1, 1, 2.7))
      plot(stab.lasso, type = "paths")
  }

Run Stability Selection

Description

(Internal) function that is used to run stability selection (i.e. to apply the fit-function to the subsamples. This function is not intended to be directly called.

Usage

run_stabsel(fitter, args.fitter, n, p, cutoff, q, PFER, folds, B, assumption,
            sampling.type, papply, verbose, FWER, eval, names,
            mc.preschedule = FALSE, ...)

Arguments

Details

This is an internal function that fits the actual models to the subsamples, i.e., this is the work horse that runs stability selection. Usually, one should use stabsel, which internally calls run_stabsel.

run_stabsel can be used by expert users to implement stability selection methods for new model types.

For details (e.g. on arguments) see stabsel.

Value

An object of class stabsel with the following elements:

References

B. Hofner, L. Boccuto and M. Goeker (2015), Controlling false discoveries in high-dimensional situations: Boosting with stability selection. BMC Bioinformatics, 16:144.
doi: 10.1186/s12859-015-0575-3.

See Also

For details see stabsel.

Method to Extract Selected Variables

Description

Extract selected variables from a stabsel object.

Usage

selected(object, ...)
## S3 method for class 'stabsel'
selected(object, ...)

Arguments

Details

The ids of variables selected during the stability selection process can be extracted using selected().

Stability Selection

Description

Selection of influential variables or model components with error control.

Usage

## generic stability selection funcion
stabsel(x, ...)

## a method to fit models with stability selection
## S3 method for class 'matrix'
stabsel(x, y, fitfun = lars.lasso,
        args.fitfun = list(), cutoff, q, PFER,
        folds = subsample(rep(1, nrow(x)), B = B),
        B = ifelse(sampling.type == "MB", 100, 50),
        assumption = c("unimodal", "r-concave", "none"),
        sampling.type = c("SS", "MB"),
        papply = mclapply, mc.preschedule = FALSE,
        verbose = TRUE, FWER, eval = TRUE, ...)

## essentially a wrapper for data.frames (see details)
## S3 method for class 'data.frame'
stabsel(x,  y, intercept = FALSE, ...)

Arguments

Details

This function implements the stability selection procedure by Meinshausen and Buehlmann (2010) and the improved error bounds by Shah and Samworth (2013). For details see also Hofner et al. (2014). The error bounds are implemented in the function stabsel_parameters. Two of the three arguments cutoff, q and PFER must be specified. The per-family error rate (PFER), i.e., the expected number of false positives E(V), where V is the number of false positives, is bounded by the argument PFER.

As controlling the PFER is more conservative as controlling the family-wise error rate (FWER), the procedure also controlls the FWER, i.e., the probability of selecting at least one non-influential variable (or model component) is less than PFER.

Predefined fitfuns functions exist but more can be easily implemented. Note that stepwise regression methods are usually not advised as they tend to be relatively unstable. See example below.

The function stabsel for data.frames is essentially just a wrapper to the matrix function with the same argments. The only difference is that in a pre-processing step, the data set is converted to a model matrix using the function model.matrix. The additional argument intercept determines if an explicit intercept should be added to the model matrix. This is often not neccessary but depends on the fitfun.

Value

An object of class stabsel with a special print method. The object has the following elements:

References

B. Hofner, L. Boccuto and M. Goeker (2015), Controlling false discoveries in high-dimensional situations: Boosting with stability selection. BMC Bioinformatics, 16:144.
doi: 10.1186/s12859-015-0575-3.

N. Meinshausen and P. Buehlmann (2010), Stability selection. Journal of the Royal Statistical Society, Series B, 72, 417–473.

R.D. Shah and R.J. Samworth (2013), Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society, Series B, 75, 55–80.

See Also

stabsel_parameters for the computation of error bounds, stabsel.stabsel for the fast re-computation of parameters of a fitted stabsel object, fitfun for available fitting functions and plot.stabsel for available plot functions

Examples

  
  if (require("TH.data")) {
      ## make data set available
      data("bodyfat", package = "TH.data")
  } else {
      ## simulate some data if TH.data not available. 
      ## Note that results are non-sense with this data.
      bodyfat <- matrix(rnorm(720), nrow = 72, ncol = 10)
  }
  
  ## set seed
  set.seed(1234)
  
  ####################################################################
  ### using stability selection with Lasso methods:

  if (require("lars")) {
      (stab.lasso <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                             fitfun = lars.lasso, cutoff = 0.75,
                             PFER = 1))
      (stab.stepwise <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                                fitfun = lars.stepwise, cutoff = 0.75,
                                PFER = 1))
      par(mfrow = c(2, 1))
      plot(stab.lasso, main = "Lasso")
      plot(stab.stepwise, main = "Stepwise Selection")
      ## --> stepwise selection seems to be quite unstable even in this low
      ##     dimensional example!
  }

  ## set seed (again to make results comparable)
  set.seed(1234)
  if (require("glmnet")) {
      (stab.glmnet <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                              fitfun = glmnet.lasso, cutoff = 0.75,
                              PFER = 1))
      par(mfrow = c(2, 1))
      plot(stab.glmnet, main = "Lasso (glmnet)")
      if (exists("stab.lasso"))
          plot(stab.lasso, main = "Lasso (lars)")    
  }
  
  
  ## Select variables with maximum coefficients based on lasso estimate
  
  set.seed(1234) # reset seed
  if (require("glmnet")) {
      ## use cross-validated lambda 
      lambda.min <- cv.glmnet(x = as.matrix(bodyfat[, -2]), y = bodyfat[,2])$lambda.min
      (stab.maxCoef <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                               fitfun = glmnet.lasso_maxCoef, 
                               # specify additional parameters to fitfun
                               args.fitfun = list(lambda = lambda.min),
                               cutoff = 0.75, PFER = 1))
                               
      ## WARNING: Using a fixed penalty (lambda) is usually not permitted and 
      ##          not sensible. See ?fitfun for details.
      
      ## now compare standard lasso with "maximal parameter estimates" from lasso
      par(mfrow = c(2, 1))
      plot(stab.maxCoef, main = "Lasso (glmnet; Maximum Coefficients)")
      plot(stab.glmnet, main = "Lasso (glmnet)")
      ## --> very different results.
  }

  ####################################################################
  ### using stability selection directly on computed boosting models
  ### from mboost


  if (require("mboost")) {
      ### low-dimensional example
      mod <- glmboost(DEXfat ~ ., data = bodyfat)

      ## compute cutoff ahead of running stabsel to see if it is a sensible
      ## parameter choice.
      ##   p = ncol(bodyfat) - 1 (= Outcome) + 1 ( = Intercept)
      stabsel_parameters(q = 3, PFER = 1, p = ncol(bodyfat) - 1 + 1,
                         sampling.type = "MB")
      ## the same:
      stabsel(mod, q = 3, PFER = 1, sampling.type = "MB", eval = FALSE)

      ### Do not test the following code per default on CRAN as it takes some time to run:
      ## now run stability selection
      (sbody <- stabsel(mod, q = 3, PFER = 1, sampling.type = "MB"))
      opar <- par(mai = par("mai") * c(1, 1, 1, 2.7))
      plot(sbody)
      par(opar)
      plot(sbody, type = "maxsel", ymargin = 6)
      
  }

Compute Error Bounds for Stability Selection

Description

Compute the missing parameter from the two given parameters in order to assess suitability of the parameter constellation

Usage

stabsel_parameters(p, ...)

## Default S3 method:
stabsel_parameters(p, cutoff, q, PFER,
                   B = ifelse(sampling.type == "MB", 100, 50),
                   assumption = c("unimodal", "r-concave", "none"),
                   sampling.type = c("SS", "MB"),
                   verbose = FALSE, FWER, ...)

## S3 method for class 'stabsel_parameters'
print(x, heading = TRUE, ...)

Arguments

Details

This function implements the error bounds for stability selection by Meinshausen and Buehlmann (2010) and the improved error bounds by Shah and Samworth (2013). For details see also Hofner et al. (2014).

Two of the three arguments cutoff, q and PFER must be specified. The per-family error rate (PFER), i.e., the expected number of false positives E(V), where V is the number of false positives, is bounded by the argument PFER.

For more details see also stabsel.

Value

An object of class stabsel_parameters with a special print method. The object has the following elements:

References

B. Hofner, L. Boccuto and M. Goeker (2015), Controlling false discoveries in high-dimensional situations: Boosting with stability selection. BMC Bioinformatics, 16:144.
doi: 10.1186/s12859-015-0575-3.

N. Meinshausen and P. Buehlmann (2010), Stability selection. Journal of the Royal Statistical Society, Series B, 72, 417–473.

R.D. Shah and R.J. Samworth (2013), Variable selection with error control: another look at stability selection. Journal of the Royal Statistical Society, Series B, 75, 55–80.

See Also

For more details see also stabsel.

Change Parameters of Stability Selection

Description

Method to change the parameters cutoff, PFER and assumption of stability selection that can be altered without the need to re-run the subsampling process.

Usage

## S3 method for class 'stabsel'
stabsel(x, cutoff, PFER, assumption = x$assumption, ...)

Arguments

Details

This function allows to alter the parameters cutoff, PFER and assumption of a fitted stability selection result. All other parameters are re-used from the original stability selection results. The missing paramter is computed and the selected variables are updated accordingly.

Value

An object of class stabsel. For details see there.

See Also

stabsel for the generic function, stabsel_parameters for the computation of error bounds, fitfun for available fitting functions and plot.stabsel for available plot functions

Examples

  if (require("TH.data")) {
      ## make data set available
      data("bodyfat", package = "TH.data")
  } else {
      ## simulate some data if TH.data not available. 
      ## Note that results are non-sense with this data.
      bodyfat <- matrix(rnorm(720), nrow = 72, ncol = 10)
  }
  
  ## set seed
  set.seed(1234)

  ####################################################################
  ### using stability selection with Lasso methods:

  if (require("lars")) {
      (stab.lasso <- stabsel(x = bodyfat[, -2], y = bodyfat[,2],
                             fitfun = lars.lasso, cutoff = 0.75,
                             PFER = 1))

      par(mfrow = c(2, 1))
      plot(stab.lasso)

      ## now change the PFER and the assumption:
      (stab.lasso_cf0.93_rconc <- stabsel(stab.lasso, cutoff = 0.93,
                                          assumption = "r-concave"))
      plot(stab.lasso_cf0.93_rconc)
      ## the cutoff did change and hence the PFER and the selected
      ## variables
  }

Draw Random Subsamples

Description

Set up weight matrix for subsampling with sample proportion 1/2 to be used with stabsel.

Usage

subsample(weights, B = 100, strata = NULL)

Arguments

Details

The function subsample can be used to build an appropriate weight matrix to be used with stabsel. See there for more details.

If strata is defined sampling is performed in each stratum separately thus preserving the distribution of the strata variable in each fold.

See Also

stabsel

Examples

  ## just a low-dimensional example
  subsample(weights = rep(1, 10), B = 50)