Type:	Package
Title:	Sparse Projected Averaged Regression
Version:	1.1.0
Description:	A flexible framework combining variable screening and random projection techniques for fitting ensembles of predictive generalized linear models to high-dimensional data. Designed for extensibility, the package implements key techniques as S3 classes with user-friendly constructors, enabling easy integration and development of new procedures for high-dimensional applications. For more details see Parzer et al (2024a) <doi:10.48550/arXiv.2312.00130> and Parzer et al (2024b) <doi:10.48550/arXiv.2410.00971>.
License:	GPL-3
Imports:	Matrix, ROCR, Rdpack, ggplot2, rlang, glmnet, methods
RdMacros:	Rdpack
Encoding:	UTF-8
RoxygenNote:	7.3.2
URL:	https://github.com/lauravana/spareg
BugReports:	https://github.com/lauravana/spareg/issues
Suggests:	testthat (≥ 3.0.0), foreach, doParallel, doRNG, robustbase, cellWise, VariableScreening, ggpubr, R.matlab
Config/testthat/edition:	3
Depends:	R (≥ 4.0.0)
NeedsCompilation:	no
Packaged:	2025-07-18 13:53:45 UTC; lauravanagur
Author:	Laura Vana-Gür [aut, cre], Roman Parzer [aut], Peter Filzmoser [aut]
Maintainer:	Laura Vana-Gür <laura.vana.guer@tuwien.ac.at>
Repository:	CRAN
Date/Publication:	2025-07-18 15:20:02 UTC

coef.spar

Description

Extract coefficients from 'spar' object

Usage

## S3 method for class 'spar'
coef(
  object,
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median", "none"),
  ...
)

Arguments

Value

object of class 'coefspar' which is a list with elements

• intercept intercept value

• beta vector of length p of averaged coefficients

• nummod number of models based on which the coefficient is computed

• nu threshold based on which the coefficient is computed

See Also

print.coefspar, summary.coefspar

coef.spar.cv

Description

Extract coefficients from 'spar.cv' object

Usage

## S3 method for class 'spar.cv'
coef(
  object,
  nummod = NULL,
  nu = NULL,
  opt_par = c("best", "1se"),
  aggregate = c("mean", "median", "none"),
  ...
)

Arguments

Value

List with elements

• intercept intercept value

• beta vector of length p of averaged coefficients

• nummod number of models based on which the coefficient is computed

• nu threshold based on which the coefficient is computed

Constructor function for building 'randomprojection' objects

Description

Creates an object class 'randomprojection' using arguments passed by user.

Usage

constructor_randomprojection(
  name,
  generate_fun,
  update_fun = NULL,
  update_rpm_w_data = NULL,
  control = list()
)

Arguments

Value

a function which in turn creates an object of class 'randomprojection'

Constructor function for building 'screencoef' objects

Description

The created function will return a object of class 'screencoef' which constitutes of a list. The attributes of the generating object will include by default type, which can take one of two values "prob" (indicating probabilistic screening should be employed), "fixed" (indicating that the top nscreen variables should be employed).

Usage

constructor_screencoef(name, generate_fun)

Arguments

Details

Creates an object class 'screencoef' using arguments passed by user.

Value

a function which in turn creates an object of class 'screencoef'

Constructor function for building 'sparmodel' objects

Description

The created function will return a object of class 'sparmodel' which constitutes of a list.

Usage

constructor_sparmodel(name, model_fun, update_fun = NULL)

Arguments

Details

Creates an object of class 'sparmodel' using arguments passed by user.

Value

a function which in turn creates an object of class 'sparmodel'.

Sparse embedding matrix

Description

Sparse embedding matrix

Usage

generate_cw(rp, m, included_vector, x = NULL, y = NULL)

Arguments

Value

(possibly sparse) matrix with m rows and length(included_vector) columns.

Gaussian random projection matrix

Description

Gaussian random projection matrix

Usage

generate_gaussian(rp, m, included_vector, x = NULL, y = NULL)

Arguments

Value

matrix with m rows and length(included_vector) columns sampled from the normal distribution.

Generate screening coefficient based on correlation

Description

Generate screening coefficient based on correlation

Usage

generate_scrcoef_cor(y, x, object)

Arguments

Value

vector of screening coefficients of length p

Screening coefficient based on glmnet coefficients

Description

Screening coefficient based on glmnet coefficients

Usage

generate_scrcoef_glmnet(y, x, object)

Arguments

Value

vector of screening coefficients of length p

Generate screening coefficient based on marginal likelihood in univariate GLMs

Description

Generate screening coefficient based on marginal likelihood in univariate GLMs

Usage

generate_scrcoef_marglik(y, x, object)

Arguments

Value

vector of screening coefficients of length p

Sparse random projection matrix

Description

Sparse random projection matrix

Usage

generate_sparse(rp, m, included_vector, x = NULL, y = NULL)

Arguments

Value

(possibly sparse) matrix with m rows and length(included_vector) columns.

Extractor for model coefficients from 'coefspar' object

Description

Extractor for model coefficients from 'coefspar' object

Usage

get_coef(x)

Arguments

Value

A numeric vector or matrix of coefficients.

See Also

coef.spar, coef.spar.cv, print.coefspar, summary.coefspar

Extractor for model intercept from 'coefspar' object

Description

Extractor for model intercept from 'coefspar' object

Usage

get_intercept(x)

Arguments

Value

Intercept (numeric or vector).

Extractor for (cross-)validation measure from 'spar' or 'spar.cv' object

Description

Extractor for (cross-)validation measure from 'spar' or 'spar.cv' object

Usage

get_measure(object)

Arguments

Value

data.frame containing the (cross-)validation measure for the considered threshold and number of model combinations. For 'spar' objects it contains information about the measure calculated on the validation set (or on the training sample if xval and yval are missing) and the number of active variables. For 'spar.cv' objects it contains information on the average measure obtained across folds together with the standard deviation across the folds and the average number of active variables. the nfolds of the training set.

See Also

spar, spar.cv, get_model

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
get_measure(spar_res)

Extractor of model from a 'spar' or 'spar.cv' object

Description

Extractor of model from a 'spar' or 'spar.cv' object

Usage

get_model(object, opt_par = c("best", "1se"))

Arguments

Value

A 'spar' or 'spar.cv' object where the beta and intercept elements are the ones which correspond to the best or the 1se model.

Examples

example_data <- simulate_spareg_data(n = 100, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
best_model <- get_model(spar_res, opt_par = "best")

spar_cv <- spar.cv(example_data$x, example_data$y,
  nummods = c(5, 10, 15, 20, 25, 30), nfolds = 4)
best_model_cv <- get_model(spar_cv, opt_par = "best")
onese_model_cv <- get_model(spar_cv, opt_par = "1se")

plot.spar

Description

Plot values of validation measure or number of active variables over different thresholds or number of models for 'spar' object, or residuals vs fitted

Usage

## S3 method for class 'spar'
plot(
  x,
  plot_type = c("val_measure", "val_numactive", "res_vs_fitted", "coefs"),
  plot_along = c("nu", "nummod"),
  nummod = NULL,
  nu = NULL,
  xfit = NULL,
  yfit = NULL,
  prange = NULL,
  coef_order = NULL,
  digits = 2L,
  ...
)

Arguments

Value

'ggplot2::ggplot' object

plot.spar.cv

Description

Plot cross-validation measure or number of active variables over different thresholds or number of models of 'spar.cv' object, produce a residuals vs fitted plot, or a plot of the estimated coefficients in each marginal model, sorted by their absolute value.

Usage

## S3 method for class 'spar.cv'
plot(
  x,
  plot_type = c("val_measure", "val_numactive", "res_vs_fitted", "coefs"),
  plot_along = c("nu", "nummod"),
  nummod = NULL,
  nu = NULL,
  xfit = NULL,
  yfit = NULL,
  opt_par = c("best", "1se"),
  prange = NULL,
  coef_order = NULL,
  digits = 2,
  ...
)

Arguments

Value

'ggplot2::ggplot' object

predict.spar

Description

Predict responses for new predictors from 'spar' object

Usage

## S3 method for class 'spar'
predict(
  object,
  xnew = NULL,
  type = c("response", "link"),
  avg_type = c("link", "response"),
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median"),
  ...
)

Arguments

Value

Vector of predictions

predict.spar.cv

Description

Predict responses for new predictors from 'spar.cv' object

Usage

## S3 method for class 'spar.cv'
predict(
  object,
  xnew = NULL,
  type = c("response", "link"),
  avg_type = c("link", "response"),
  opt_par = c("best", "1se"),
  nummod = NULL,
  nu = NULL,
  aggregate = c("mean", "median"),
  ...
)

Arguments

Value

Vector of predictions

Print method for coefspar objects

Description

Print method showing the basic components of a 'coefspar' object.

Usage

## S3 method for class 'coefspar'
print(x, digits = 4L, show = 6L, ...)

Arguments

Value

Invisibly returns the input object x.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
coef(spar_res)
coef(spar_res, aggregate = "median")
coef(spar_res, aggregate = "none")
print(coef(spar_res), show = 10L, digits = 6L)

print.randomprojection

Description

Print method for a 'randomprojection' object

Usage

## S3 method for class 'randomprojection'
print(x, ...)

Arguments

Value

text summary

print.screencoef

Description

Print method for a 'screencoef' object

Usage

## S3 method for class 'screencoef'
print(x, ...)

Arguments

Value

text summary

print.spar

Description

Print summary of 'spar' object

Usage

## S3 method for class 'spar'
print(x, ...)

Arguments

Value

text summary

print.spar.cv

Description

Print summary of 'spar.cv' object

Usage

## S3 method for class 'spar.cv'
print(x, ...)

Arguments

Value

text summary

Sparse embedding matrix

Description

Creates an object class 'randomprojection' using arguments passed by user which in turn can be employed to generate a sparse embedding matrix as in (Clarkson and Woodruff 2013).

Usage

rp_cw(..., control = list())

Arguments

Details

The entries of the matrix are generated based on (Clarkson and Woodruff 2013). This matrix is constructed as \Phi=BD\in \mathbb{R}^{m\times p}, where B is a (p\times p) binary matrix, where for each column j an index is uniformly sampled from \{1,\ldots,m\} and the corresponding entry is set to one, and D is a (p\times p) diagonal matrix, with entries d_j \sim \text{Unif}(\{-1, 1\}). If specified as rp_cw(data = TRUE), the random elements on the diagonal are replaced by the ridge coefficients with a small penalty, as introduced in (Parzer et al. 2024).

Value

object of class 'randomprojection' which is a list with elements name, generate_fun, update_fun, control

References

Clarkson KL, Woodruff DP (2013). “Low Rank Approximation and Regression in Input Sparsity Time.” In Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, STOC '13, 81–90. ISBN 9781450320290, doi:10.1145/2488608.2488620.

Parzer R, Filzmoser P, Vana-Gür L (2024). “Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models.” Technical Report 2410.00971, arXiv.org E-Print Archive. doi:10.48550/arXiv.2410.00971..

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_cw(data = TRUE))

Gaussian random projection matrix

Description

Creates an object class 'randomprojection' using arguments passed by user which in turn can be employed to generate a random matrix with normally distributed entries (mean 0 and standard deviation 1 by default).

Usage

rp_gaussian(..., control = list())

Arguments

Details

Arguments related to the random projection procedure can be passed to the rp_gaussian() function through ..., and will be saved as attributes of the 'randomprojection' object. The following attributes are relevant for spar and spar.cv:

• mslow: integer giving the minimum dimension to which the predictors should be projected; defaults to \log(p).

• msup: integer giving the maximum dimension to which the predictors should be projected; defaults to n/2.

Value

object of class 'randomprojection' which is a list with elements name, generate_fun, update_fun, control

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_gaussian(control = list(sd = 1/sqrt(ncol(example_data$x)))))

Sparse random projection matrix

Description

Creates an object class 'randomprojection' using arguments passed by user which in turn can be employed to generate a sparse embedding matrix as in (Achlioptas 2003).

Usage

rp_sparse(..., control = list())

Arguments

Details

The sparse matrix used in (Achlioptas 2003) with entries equal to \Psi_{ij} = \pm 1/\sqrt{\psi} with probability \psi/2 and zero otherwise for \psi\in (0,1]. Default is psi = 1.

Arguments related to the random projection procedure can be passed to the rp_gaussian() function through ..., and will be saved as attributes of the 'randomprojection' object. The following attributes are relevant for spar and spar.cv:

• mslow: integer giving the minimum dimension to which the predictors should be projected; defaults to \log(p).

• msup: integer giving the maximum dimension to which the predictors should be projected; defaults to n/2.

Value

object of class 'randomprojection' which is a list with elements name, generate_fun, update_fun, control

References

Achlioptas D (2003). “Database-Friendly Random Projections: Johnson-Lindenstrauss with Binary Coins.” Journal of Computer and System Sciences, 66(4), 671-687. ISSN 0022-0000, doi:10.1016/S0022-0000(03)00025-4, Special Issue on PODS 2001.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  rp = rp_sparse(control = list(psi = 1/3)))

Screening coefficient based on correlation

Description

Creates an object class 'screencoef' using arguments passed by user, where the screening coefficient should be computed based on the correlation coefficient of response and each predictor separately.

Usage

screen_cor(..., control = list())

Arguments

Details

Creates an object class 'screencoef' using arguments passed by user.

The function generate_fun relies on cor.

Arguments related to the screening procedure can be passed to the screen_cor() function through ..., and will be saved as attributes of the 'screencoef' object. The following attributes are relevant for spar and spar.cv:

• nscreen integer giving the number of variables to be retained after screening; if not specified, defaults to $2n$.

• split_data_prop, double between 0 and 1 which indicates the proportion of the data that should be used for computing the screening coefficient. The remaining data will be used for estimating the marginal models in the SPAR algorithm; if not specified, the whole data will be used for estimating the screening coefficient and the marginal models.

• type character - either "prob" (indicating that probabilistic screening should be employed) or "fixed" (indicating that a fixed set of nscreen variables should be employed across the ensemble); defaults to type = "prob".

• reuse_in_rp logical - indicates whether the screening coefficient should be reused at a later stage in the construction of the random projection. Defaults to FALSE.

Value

object of class 'screencoef' which is a list with elements

• name (character)

• control (list of controls passed as an argument)

• generate_fun for generating the screening coefficient. This function should have arguments and y (vector of (standardized for Gaussian) responses), x (the matrix of standardized predictors) and a 'screencoef' object.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_cor(control = list(method = "kendall")))

Screening coefficient based on glmnet coefficients

Description

Creates an object class 'screencoef' using arguments passed by user, where the screening coefficient should be computed based on penalized coefficients.

Usage

screen_glmnet(..., control = list())

Arguments

Details

Creates an object class 'screencoef' using arguments passed by user.

The function generate_fun relies on glmnet.

Arguments related to the screening procedure can be passed to the screen_glmnet() function through ..., and will be saved as attributes of the 'screencoef' object. The following attributes are relevant for spar and spar.cv:

• nscreen integer giving the number of variables to be retained after screening; if not specified, defaults to $2n$.

• split_data_prop, double between 0 and 1 which indicates the proportion of the data that should be used for computing the screening coefficient. The remaining data will be used for estimating the marginal models in the SPAR algorithm; if not specified, the whole data will be used for estimating the screening coefficient and the marginal models.

• type character - either "prob" (indicating that probabilistic screening should be employed) or "fixed" (indicating that a fixed set of nscreen variables should be employed across the ensemble); defaults to type = "prob".

• reuse_in_rp logical - indicates whether the screening coefficient should be reused at a later stage in the construction of the random projection. Defaults to FALSE.

Value

object of class 'screencoef' which is a list with elements

• name (character)

• control (list of controls passed as an argument)

• generate_fun for generating the screening coefficient. This function should have arguments and y (vector of (standardized for Gaussian) responses), x (the matrix of standardized predictors) and a 'screencoef' object.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_glmnet(control = list(alpha = 0.1)))

Screening coefficient based on marginal GLMs

Description

Creates an object class 'screencoef' using arguments passed by user, where the screening coefficient should be computed based on the marginal likelihood of the univariate GLM where the response is regressed on each predictor separately.

Usage

screen_marglik(..., control = list())

Arguments

Details

The function generate_fun relies on glm.

Arguments related to the screening procedure can be passed to the screen_marglik() function through ..., and will be saved as attributes of the 'screencoef' object. The following attributes are relevant for spar and spar.cv:

• nscreen integer giving the number of variables to be retained after screening; if not specified, defaults to $2n$.

• split_data_prop, double between 0 and 1 which indicates the proportion of the data that should be used for computing the screening coefficient. The remaining data will be used for estimating the marginal models in the SPAR algorithm; if not specified, the whole data will be used for estimating the screening coefficient and the marginal models.

• type character - either "prob" (indicating that probabilistic screening should be employed) or "fixed" (indicating that a fixed set of nscreen variables should be employed across the ensemble); defaults to type = "prob".

• reuse_in_rp logical - indicates whether the screening coefficient should be reused at a later stage in the construction of the random projection. Defaults to FALSE.

Value

object of class 'screencoef' which is a list with elements:

• name (character)

• control (list of controls passed as an argument)

• generate_fun for generating the screening coefficient. This function should have arguments and y (vector of (standardized for Gaussian) responses), x (the matrix of standardized predictors) and a 'screencoef' object.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30),
  screencoef = screen_marglik(nscreen = 500))

Simulate Sparse Regression Data

Description

Generates synthetic data for sparse linear regression problems. Returns training and test sets along with model parameters.

Usage

simulate_spareg_data(
  n,
  p,
  ntest,
  a = min(100, p/4),
  snr = 10,
  rho = 0.5,
  mu = 1,
  beta_vals = NULL,
  seed = NULL
)

Arguments

Value

A list with the following components:

x

Training design matrix (n x p).

y

Training response vector (length n).

xtest

Test design matrix (ntest x p).

ytest

Test response vector (length ntest).

mu

Intercept used in data generation.

beta

True coefficient vector (length p).

sigma2

Noise variance used in data generation. Equals beta' Sigma beta / snr.

Examples

set.seed(123)
data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
str(data)

Sparse Projected Averaged Regression

Description

Apply Sparse Projected Averaged Regression to high-dimensional data by building an ensemble of generalized linear models, where the high-dimensional predictors can be screened using a screening coefficient and then projected using data-agnostic or data-informed random projection matrices. This function performs the procedure for a given grid of thresholds \nu and a grid of the number of marginal models to be employed in the ensemble. This function is also used in the cross-validated procedure spar.cv.

Usage

spar(
  x,
  y,
  family = gaussian("identity"),
  model = NULL,
  rp = NULL,
  screencoef = NULL,
  xval = NULL,
  yval = NULL,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  inds = NULL,
  RPMs = NULL,
  seed = NULL,
  ...
)

spareg(
  x,
  y,
  family = gaussian("identity"),
  model = NULL,
  rp = NULL,
  screencoef = NULL,
  xval = NULL,
  yval = NULL,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  inds = NULL,
  RPMs = NULL,
  seed = NULL,
  ...
)

Arguments

Value

object of class 'spar' with elements

• betas p x max(nummods) sparse matrix of class 'Matrix::dgCMatrix' containing the standardized coefficients from each marginal model

• intercepts used in each marginal model

• scr_coef vector of length p with coefficients used for screening the standardized predictors

• inds list of index-vectors corresponding to variables kept after screening in each marginal model of length max(nummods)

• RPMs list of projection matrices used in each marginal model of length max(nummods)

• val_res data.frame with validation results (validation measure and number of active variables) for each element of nus and nummods

• val_set logical flag, whether validation data were provided; if FALSE, training data were used for validation

• family a character corresponding to family object used for the marginal generalized linear model e.g., "gaussian(identity)"

• nus vector of \nu's considered for thresholding

• nummods vector of numbers of marginal models considered for validation

• ycenter empirical mean of initial response vector

• yscale empirical standard deviation of initial response vector

• xcenter p-vector of empirical means of initial predictor variables

• xscale p-vector of empirical standard deviations of initial predictor variables

• avg_type character, averaging type for computing the validation measure

• measure character, type of validation measure used

• rp an object of class "randomprojection"

• screencoef an object of class "screeningcoef"

• x_rows_for_fitting_marginal_models vector of row indicators from x which were used for fitting the marginal models, if screening was performed using screencoef with split_data_prop argument. Is NULL otherwise.

If a parallel backend is registered and parallel = TRUE, the foreach function is used to estimate the marginal models in parallel.

References

Parzer R, Filzmoser P, Vana-Gür L (2024). “Sparse Data-Driven Random Projection in Regression for High-Dimensional Data.” Technical Report 2312.00130, arXiv.org E-Print Archive. doi:10.48550/arXiv.2312.00130.

Parzer R, Filzmoser P, Vana-Gür L (2024). “Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models.” Technical Report 2410.00971, arXiv.org E-Print Archive. doi:10.48550/arXiv.2410.00971.

Clarkson KL, Woodruff DP (2013). “Low Rank Approximation and Regression in Input Sparsity Time.” In Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, STOC '13, 81–90. ISBN 9781450320290, doi:10.1145/2488608.2488620.

Achlioptas D (2003). “Database-Friendly Random Projections: Johnson-Lindenstrauss with Binary Coins.” Journal of Computer and System Sciences, 66(4), 671-687. ISSN 0022-0000, doi:10.1016/S0022-0000(03)00025-4, Special Issue on PODS 2001.

See Also

spar.cv, coef.spar, predict.spar, plot.spar, print.spar

Examples

example_data <- simulate_spareg_data(n = 200, p = 400, ntest = 100)
spar_res <- spar(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
coefs <- coef(spar_res)
pred <- predict(spar_res, xnew = example_data$x)
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest)
plot(spar_res, plot_type = "coefs", prange = c(1,400))

spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))

Sparse Projected Averaged Regression

Description

Apply Sparse Projected Averaged Regression to High-Dimensional Data, where the number of models and the threshold parameter is chosen using a cross-validation procedure.

Usage

spar.cv(
  x,
  y,
  family = gaussian("identity"),
  model = spar_glmnet(),
  rp = NULL,
  screencoef = NULL,
  nfolds = 10,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  seed = NULL,
  ...
)

spareg.cv(
  x,
  y,
  family = gaussian("identity"),
  model = spar_glmnet(),
  rp = NULL,
  screencoef = NULL,
  nfolds = 10,
  nnu = 20,
  nus = NULL,
  nummods = c(20),
  measure = c("deviance", "mse", "mae", "class", "1-auc"),
  avg_type = c("link", "response"),
  parallel = FALSE,
  seed = NULL,
  ...
)

Arguments

Value

object of class 'spar.cv' with elements

• betas p x max(nummods) sparse matrix of class 'Matrix::dgCMatrix' containing the standardized coefficients from each marginal model computed with the spar algorithm on the whole training data.

• intercepts used in each marginal model, vector of length max(nummods) computed with the spar algorithm on the whole training data.

• scr_coef p-vector of coefficients used for screening for standardized predictors

• inds list of index-vectors corresponding to variables kept after screening in each marginal model of length max(nummods)

• RPMs list of projection matrices used in each marginal model of length max(nummods)

• val_res a data.frame with CV results for each fold and for each element of nus and nummods

• nus vector of \nu's considered for thresholding

• nummods vector of numbers of marginal models considered for validation

• family a character corresponding to family object used for the marginal generalized linear model e.g., "gaussian(identity)"

• measure character, type of validation measure used

• avg_type character, averaging type for computing the validation measure

• rp an object of class 'randomprojection'

• screencoef an object of class 'screeningcoef'

• model an object of class 'sparmodel'

• ycenter empirical mean of initial response vector

• yscale empirical standard deviation of initial response vector .

• xcenter p-vector of empirical means of initial predictor variables

• xscale p-vector of empirical standard deviations of initial predictor variables

See Also

spar, coef.spar.cv, predict.spar.cv, plot.spar.cv, print.spar.cv

Examples

example_data <- simulate_spareg_data(n = 200, p = 400, ntest = 100)
spar_res <- spar.cv(example_data$x, example_data$y, nfolds = 3L,
  nummods = c(5, 10, 15, 20, 25, 30))
spar_res
coefs <- coef(spar_res)
pred <- predict(spar_res, example_data$x)
plot(spar_res)
plot(spar_res, plot_type = "val_measure", plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_measure", plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nummod", nu = 0)
plot(spar_res, plot_type = "val_numactive",  plot_along = "nu", nummod = 10)
plot(spar_res, plot_type = "res_vs_fitted",  xfit = example_data$xtest,
  yfit = example_data$ytest, opt_par = "1se")
plot(spar_res, "coefs", prange = c(1, 400))


spar_res <- spareg.cv(example_data$x, example_data$y,
  nummods=c(5, 10, 15, 20, 25, 30))

GLM marginal models

Description

Creates an object class 'sparmodel' using arguments passed by user.

Usage

spar_glm(..., control = list())

Arguments

Details

Relies on glm.

Value

object of class 'sparmodel' which is a list with elements

• name (character)

• control (list of controls passed as an argument)

• model_fun function for estimating the model coefficients and the intercept. This function should have arguments y, vector of standardized responses, z, a matrix of projected predictors in each marginal model, and object, which is a 'sparmodel' object. Returns a list with two elements: gammas which is the vector of regression coefficients for the projected predictors and intercept which is the intercept of the model

Penalized GLM marginal models

Description

Creates an object class 'sparmodel' using arguments passed by user.

Usage

spar_glmnet(..., control = list())

Arguments

Details

Relies on glmnet.

Value

object of class 'sparmodel' which is a list with elements

• name (character)

• control (list of controls passed as an argument)

• model_fun for generating the screening coefficient. This function should have arguments y, vector of standardized responses, z, a matrix of projected predictors in each marginal model, and object, which is a 'sparmodel' object. Returns a list with two elements: gammas which is the vector of regression coefficients for the projected predictors and intercept which is the intercept of the model.

• update_fun optional function for updating the 'sparmodel' object before the start of the algorithm.

Summary method for coefspar objects

Description

Provides a summary of a coefspar object.

Usage

## S3 method for class 'coefspar'
summary(object, digits = 4L, ...)

Arguments

Value

Invisibly returns object.

Examples

example_data <- simulate_spareg_data(n = 200, p = 2000, ntest = 100)
spar_res <- spareg(example_data$x, example_data$y, xval = example_data$xtest,
  yval = example_data$ytest, nummods=c(5, 10, 15, 20, 25, 30))
summary(coef(spar_res))
summary(coef(spar_res, aggregate = "none"))