crch.stabsel

Auxiliary Functions for Stability Selection Using Boosting

Description

Auxilirary function which allows to do stability selection on heteroscedastic crch models based on crch.boost.

Usage

crch.stabsel(formula, data, ..., nu = 0.1, q, B = 100, thr = 0.9, 
  maxit = 2000, data_percentage = 0.5)

Arguments

`formula`	a formula expression of the form `y ~ x \| z` where `y` is the response and `x` and `z` are regressor variables for the location and the scale of the fitted distribution respectively.
`data`	an optional data frame containing the variables occurring in the formulas.
`…`	Additional attributes to control the `crch` model. Note that `control` is not allowed; `crch.stabsel` uses `crch.boost` by default.
`nu`	Boosting step size (see `crch.boost`) default is `0.1` as for `crch.boost` while lower values might yield better results frequently and should be considered.
`q`	Positive `numeric`. Maximum number of parameters to be selected during each iteration (not including intercepts).
`B`	`numeric`, total number of iterations.
`thr`	`numeric` threshold (`(0.5-1.0)`). Used to generate the new formula and the computation of the per-family error rate.
`maxit`	Positive `numeric` value. Maximum number for the boosting algorithm. If `q` is not reached before `maxit` the algorithm will stop.
`data_percentage`	Percentage of data which should be sampled in each of the iterations. Default (and suggested) is `0.5`.

Details

crch.boost allows to perform gradient boosting on heteroscedastic additive models. crch.stabsel is a wrapper around the core crch.boost algorithm to perform stability selection (see references).

Half of the data set (data) is sampled B times to perform boosting (based on crch.boost). Rather than perform the boosting iterations until a certain stopping criterion is reached (e.g., maximum number of iterations maxit) the algorithm stops as soon as q parameters have been selected. The number of parameters is computed across both parameters location and scale. Intercepts are not counted.

Value

Returns an object of class “stabsel.crch” containing the stability selection summary and the new formula based on the stability selection.

`table`	A table object containing the parameters which have been selected and the corresponding frequency of selection.
`formula.org`	Original formula used to perform the stability selection.
`formula.new`	New formula based including the coefficients selected during stability selection.
`family`	A list object which contains the distribution-specification from the `crch.stabsel` call including: `dist`, `cens`, and `truncated`.
`parameter`	List with the parameters used to perform the stability selection including `q`, `B`, `thr`, `p`, and `PFER` (per-family error rate).

References

Meinhausen N, Buehlmann P (2010). Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(4), 417–473. doi:10.1111/j.1467-9868.2010.00740.x.

Examples

library("crch")

# generate data
suppressWarnings(RNGversion("3.5.0"))
set.seed(5)
x <- matrix(rnorm(1000*20),1000,20)
y <- rnorm(1000, 1 + x[,1] - 1.5 * x[,2], exp(-1 + 0.3*x[,3]))
y <- pmax(0, y)
data <- data.frame(cbind(y, x))

# fit model with maximum likelihood
CRCH1 <- crch(y ~ .|., data = data, dist = "gaussian", left = 0)

# Perform stability selection
stabsel <- crch.stabsel(y ~ .|.,  data = data, dist = "gaussian", left = 0,
           q = 8, B = 5)

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# Show stability selection summary
print(stabsel); plot(stabsel)


  crch Stability Selection Info

  Family information
   Distribution:       gaussian
   Truncated:          FALSE
   Left-censoring:     0
   Right-censoring:    Inf

  Selection parameters
   Number of parameters (q):         8
   Number of iterations (B):         5
   Selection threshold (thr):     0.90
   Total number of parameter (p):   40

  Per family error rate
   Given p/q/thr the expected value of falsely
   chosen parameters is:          2.00

  Selected formula:
   y ~ V2 + V3 | V4
<environment: 0x55cd7697fd90>

CRCH2 <- crch(stabsel$formula.new, data = data, dist = "gaussian", left = 0 )
BOOST <- crch(stabsel$formula.new, data = data, dist = "gaussian", left = 0,
              control = crch.boost() )

### AIC comparison
sapply( list(CRCH1,CRCH2,BOOST), logLik )

[1] -367.6337 -384.2485 -385.0090