SDAM: Spectrally Deconfounded Additive Models
In SDModels: Spectrally Deconfounded Models

View source: R/SDAM.R

SDAM	R Documentation

Spectrally Deconfounded Additive Models

Description

Estimate high-dimensional additive models using spectral deconfounding \insertCitescheidegger2023spectralSDModels. The covariates are expanded into B-spline basis functions. A spectral transformation is used to remove bias arising from hidden confounding and a group lasso objective is minimized to enforce component-wise sparsity. Optimal number of basis functions per component and sparsity penalty are chosen by cross validation.

Usage

SDAM(
  formula = NULL,
  data = NULL,
  x = NULL,
  y = NULL,
  Q_type = "trim",
  trim_quantile = 0.5,
  q_hat = 0,
  nfolds = 5,
  cv_method = "1se",
  n_K = 4,
  n_lambda1 = 10,
  n_lambda2 = 20,
  Q_scale = TRUE,
  ind_lin = NULL,
  mc.cores = 1,
  verbose = TRUE
)

Arguments

`formula`	Object of class `formula` or describing the model to fit of the form `y ~ x1 + x2 + ...` where `y` is a numeric response and `x1, x2, ...` are vectors of covariates. Interactions are not supported.
`data`	Training data of class `data.frame` containing the variables in the model.
`x`	Matrix of covariates, alternative to `formula` and `data`.
`y`	Vector of responses, alternative to `formula` and `data`.
`Q_type`	Type of deconfounding, one of 'trim', 'pca', 'no_deconfounding'. 'trim' corresponds to the Trim transform \insertCiteCevid2020SpectralModelsSDModels as implemented in the Doubly debiased lasso \insertCiteGuo2022DoublyConfoundingSDModels, 'pca' to the PCA transformation\insertCitePaul2008PreconditioningProblemsSDModels. See `get_Q`.
`trim_quantile`	Quantile for Trim transform, only needed for trim, see `get_Q`.
`q_hat`	Assumed confounding dimension, only needed for pca, see `get_Q`.
`nfolds`	The number of folds for cross-validation. Default is 5.
`cv_method`	The method for selecting the regularization parameter during cross-validation. One of "min" (minimum cv-loss) and "1se" (one-standard-error rule) Default is "1se".
`n_K`	The number of candidate values for the number of basis functions for B-splines. Default is 4.
`n_lambda1`	The number of candidate values for the regularization parameter in the initial cross-validation step. Default is 10.
`n_lambda2`	The number of candidate values for the regularization parameter in the second stage of cross-validation (once the optimal number of basis function K is decided, a second stage of cross-validation for the regularization parameter is performed on a finer grid). Default is 20.
`Q_scale`	Should data be scaled to estimate the spectral transformation? Default is `TRUE` to not reduce the signal of high variance covariates.
`ind_lin`	A vector of indices specifying which covariates to model linearly (i.e. not expanded into basis function). Default is 'NULL'.
`mc.cores`	Number of cores to use for parallel processing, if `mc.cores > 1` the cross validation is parallelized. Default is '1'. (only supported for unix)
`verbose`	If `TRUE` fitting information is shown.

Value

An object of class 'SDAM' containing the following elements:

`X`	The original design matrix.
`p`	The number of covariates in 'X'.
`intercept`	The intercept term of the fitted model.
`K`	A vector of the number of basis functions for each covariate, where 1 corresponds to a linear term. The entries of the vector will mostly by the same, but some entries might be lower if the corresponding component of X contains only few unique values.
`breaks`	A list of breakpoints used for the B-splines. Used to reconstruct the B-spline basis functions.
`coefs`	A list of coefficients for the B-spline basis functions for each component.
`active`	A vector of active covariates that contribute to the model.

Author(s)

Cyrill Scheidegger

References

\insertAllCited

Examples

set.seed(1)
X <- matrix(rnorm(10 * 5), ncol = 5)
Y <- sin(X[, 1]) -  X[, 2] + rnorm(10)
model <- SDAM(x = X, y = Y, Q_type = "trim", trim_quantile = 0.5, nfold = 2, n_K = 1)



library(HDclassif)
data(wine)
names(wine) <- c("class", "alcohol", "malicAcid", "ash", "alcalinityAsh", "magnesium", 
                 "totPhenols", "flavanoids", "nonFlavPhenols", "proanthocyanins", 
                 "colIntens", "hue", "OD", "proline")
wine <- log(wine)

# estimate model
# do not use class in the model and restrict proline to be linear 
model <- SDAM(alcohol ~ -class + ., wine, ind_lin = "proline", nfold = 3)

# extract variable importance
varImp(model)

# most important variable
mostImp <- names(which.max(varImp(model)))
mostImp

# predict for individual Xj
predJ <- predict_individual_fj(object = model, j = mostImp)
plot(wine[, mostImp], predJ, 
     xlab = paste0("log ", mostImp), ylab = "log alcohol")

# partial dependece
plot(partDependence(model, mostImp))

# predict 
predict(model, newdata = wine[42, ])

## alternative function call
mod_none <- SDAM(x = as.matrix(wine[1:10, -c(1, 2)]), y = wine$alcohol[1:10], 
                 Q_type = "no_deconfounding", nfolds = 2, n_K = 4, 
                 n_lambda1 = 4, n_lambda2 = 8)

SDModels documentation built on April 11, 2025, 5:50 p.m.