sparseSIR {SISIR}

sparse SIR

Description

sparseSIR performs the second step of the method (shrinkage of ridge SIR results

Usage

sparseSIR(
  object,
  inter_len,
  adaptive = FALSE,
  sel_prop = 0.05,
  parallel = FALSE,
  ncores = NULL
)

Arguments

object

an object of class ridgeRes as obtained from the function ridgeSIR

inter_len

(numeric) vector with interval lengths

adaptive

should the function returns the list of strong zeros and non strong zeros (logical). Default to FALSE

sel_prop

used only when adaptive = TRUE. Fraction of the coefficients that will be considered as strong zeros and strong non zeros. Default to 0.05

parallel

whether the computation should be performed in parallel or not. Logical. Default is FALSE

ncores

number of cores to use if parallel = TRUE. If left to NULL, all available cores minus one are used

Value

S3 object of class sparseRes: a list consisting of

• sEDR the estimated EDR space (a p x d matrix)

• alpha the estimated shrinkage coefficients (a vector having a length similar to inter_len)

• quality a vector with various qualities for the model (see Details)

• adapt_res if adaptive = TRUE, a list of two vectors:

  • nonzeros indexes of variables that are strong non zeros

  • zeros indexes of variables that are strong zeros

• parameters a list of hyper-parameters for the method:

  • inter_len lengths of intervals

  • sel_prop if adaptive = TRUE, fraction of the coefficients which are considered as strong zeros or strong non zeros

• rSIR same as the input object

• fit a list for LASSO fit with:

  • glmnet result of the glmnet function

  • lambda value of the best Lasso parameter by CV

  • x exploratory variable values as passed to fit the model

@details Different quality criteria used to select the best models among a list of models with different interval definitions. Quality criteria are: log-likelihood (loglik), cross-validation error as provided by the function glmnet, two versions of the AIC (AIC and AIC2) and of the BIC (BIC and BIC2) in which the number of parameters is either the number of non null intervals or the number of non null parameters with respect to the original variables.

Author(s)

Victor Picheny, [e-mail]
Remi Servien, [e-mail]
Nathalie Vialaneix, [e-mail]

References

Picheny, V., Servien, R., and Villa-Vialaneix, N. (2019) Interpretable sparse SIR for digitized functional data. Statistics and Computing, 29(2), 255–267.

See Also

ridgeSIR, project.sparseRes, SISIR

Examples

set.seed(1140)
tsteps <- seq(0, 1, length = 200)
nsim <- 100
simulate_bm <- function() return(c(0, cumsum(rnorm(length(tsteps)-1, sd=1))))
x <- t(replicate(nsim, simulate_bm()))
beta <- cbind(sin(tsteps*3*pi/2), sin(tsteps*5*pi/2))
beta[((tsteps < 0.2) | (tsteps > 0.5)), 1] <- 0
beta[((tsteps < 0.6) | (tsteps > 0.75)), 2] <- 0
y <- log(abs(x %*% beta[ ,1]) + 1) + sqrt(abs(x %*% beta[ ,2]))
y <- y + rnorm(nsim, sd = 0.1)
res_ridge <- ridgeSIR(x, y, H = 10, d = 2, mu2 = 10^8)
res_sparse <- sparseSIR(res_ridge, rep(10, 20))