Package 'risdr'

Description

The package implements SIR, SAVE, DR, and pHd for continuous responses, together with covariance regularisation, information-theoretic structural dimension selection, prediction, resampling, simulation, and diagnostic utilities.

Main interface

Use fit_risdr() to estimate an SDR model and predict.risdr() to obtain predictions for new observations. Use select_dimension_cv(), select_dimension_cv_icomp(), or select_dimension_ladle() for complementary structural-dimension diagnostics.

Scope

fit_risdr() retains its continuous-response scope. Use fit_risdr_sparse() for joint dimension and sparsity selection with continuous, categorical, and right-censored survival responses, or fit_risdr_dual() for sample-space PCA reduction when predictors outnumber observations. fit_risdr_sparse_realdata() adds variance screening. See the sparse-survival vignette for the frozen thesis conventions.

Author(s)

Maintainer: Kabir Olorede [email protected]

See Also

Useful links:

• https://github.com/ilovemaths/risdr

• https://ilovemaths.github.io/risdr/

• Report bugs at https://github.com/ilovemaths/risdr/issues

Description

Adjusted coefficient of determination

Usage

adjusted_r_squared(y_true, y_pred, d)

Arguments

Value

Numeric adjusted R-squared.

Examples

adjusted_r_squared(
  c(2, 4, 6, 8, 10),
  c(2.2, 3.8, 5.7, 8.1, 9.8),
  d = 1
)

Description

AR(1) covariance matrix

Usage

ar1_covariance(p, rho)

Arguments

Value

Covariance matrix.

Examples

ar1_covariance(p = 4, rho = 0.5)

Description

Computes cumulative scale-invariant covariance complexity from leading eigenvalues and converts the complexity profile to relative weights.

Usage

C1F(evals, positive_only = TRUE, cumulative = TRUE, tol = 1e-10)

Arguments

Value

A list with C1F values, induced weights, and processed eigenvalues.

Description

Choose dimension from criteria table

Usage

choose_dimension(
  d_table,
  selector = c("cicomp", "icomp", "bic", "caic", "aic")
)

Arguments

Value

Selected structural dimension.

Examples

scores <- as.matrix(mtcars[, c("wt", "hp", "disp")])
dimension_table <- select_dimension(scores, mtcars$mpg, d_max = 2)
choose_dimension(dimension_table, selector = "bic")

Description

Computes Directional Regression using the canonical pairwise-slice formulation.

Usage

compute_dr(
  X,
  y,
  Sigma = NULL,
  nslices = 6,
  slice_type = c("quantile", "equal_width"),
  stabilize_slices = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  eps = 1e-08
)

Arguments

Details

Directional Regression is computed using the pairwise-slice formulation.

$M_{DR} = \sum_h \sum_k p_h p_k (2I_p - A_{hk}) (2I_p - A_{hk})^\top$

where

$A_{hk} = \Sigma_h + \Sigma_k + (\mu_h - \mu_k) (\mu_h - \mu_k)^\top$

Value

A list containing DR kernel, eigenvalues, directions, scores, and slices.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
fit <- compute_dr(X, y = mtcars$mpg, nslices = 4)
head(fit$eigenvalues)

Description

Compute one reduced-model information criterion

Usage

compute_ic(
  y,
  Z,
  criterion = c("cicomp", "icomp", "aic", "caic", "bic"),
  response_type = c("continuous", "categorical", "survival"),
  delta = NULL,
  n_active = NULL,
  support_penalty = FALSE,
  tol = 1e-10
)

Arguments

Value

Scalar criterion value.

Description

Compute all reduced-model information criteria

Usage

compute_ic_values(
  y,
  Z,
  response_type = c("continuous", "categorical", "survival"),
  delta = NULL,
  n_active = NULL,
  support_penalty = FALSE,
  tol = 1e-10
)

Arguments

Value

Named numeric vector containing AIC, BIC, CAIC, ICOMP, CICOMP, log-likelihood, effective df, and C1F.

Description

Computes AIC, BIC, CAIC, ICOMP, and CICOMP for a fitted linear model.

Usage

compute_information_criteria(fit, complexity = c("C1", "C1F"), eps = 1e-10)

Arguments

Value

Named numeric vector of criteria.

Examples

fit <- stats::lm(mpg ~ wt + hp, data = mtcars)
compute_information_criteria(fit)

Description

For mode = "c1f", the regularised covariance matrix is decomposed into original-coordinate C1F contributions. Variables with larger contribution receive smaller soft-threshold weights, matching the direction of the historical C1F weighting rule while avoiding the invalid mapping of eigenvalue indices directly to predictor indices. inverse_c1f reverses that weighting. uniform returns equal weights.

Usage

compute_penalty_weights(
  Sigma,
  mode = c("c1f", "inverse_c1f", "uniform"),
  tol = 1e-10
)

Arguments

Value

Numeric vector of variable-level penalty weights with mean one.

Description

Compute Principal Hessian Directions

Usage

compute_phd(X, y, Sigma = NULL, eps = 1e-08)

Arguments

Value

A list containing pHd kernel, eigenvalues, directions, scores.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
fit <- compute_phd(X, y = mtcars$mpg)
head(fit$eigenvalues)

Description

Compute Sliced Average Variance Estimation

Usage

compute_save(
  X,
  y,
  Sigma = NULL,
  nslices = 6,
  slice_type = c("quantile", "equal_width"),
  stabilize_slices = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  eps = 1e-08
)

Arguments

Value

A list containing SAVE kernel, eigenvalues, directions, scores, and slices.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
fit <- compute_save(X, y = mtcars$mpg, nslices = 4)
head(fit$eigenvalues)

Description

Projects new predictor observations onto estimated SDR directions.

Usage

compute_scores(newX, directions)

Arguments

Value

Matrix of SDR scores.

Examples

X <- as.matrix(mtcars[1:5, c("wt", "hp", "disp")])
directions <- diag(3)[, 1:2, drop = FALSE]
compute_scores(X, directions)

Description

General SDR kernel dispatcher

Usage

compute_sdr(
  X,
  y,
  method = c("dr", "sir", "save", "phd"),
  Sigma = NULL,
  nslices = 6,
  ...
)

Arguments

Value

SDR fit components.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
Sigma <- cov_oas(X)
fit <- compute_sdr(
  X,
  y = mtcars$mpg,
  method = "sir",
  Sigma = Sigma,
  nslices = 4
)
dim(fit$scores)

Description

Compute Sliced Inverse Regression

Usage

compute_sir(
  X,
  y,
  Sigma = NULL,
  nslices = 6,
  slice_type = c("quantile", "equal_width"),
  eps = 1e-08
)

Arguments

Value

A list containing SIR kernel, eigenvalues, directions, scores, and slices.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
fit <- compute_sir(X, y = mtcars$mpg, nslices = 4)
head(fit$eigenvalues)

Description

Computes Bozdogan-type maximal covariance complexity.

Usage

cov_complexity_C1(Sigma, eps = 1e-10)

Arguments

Value

Numeric complexity value.

Description

Computes the scale-invariant C1F covariance complexity measure.

Usage

cov_complexity_C1F(Sigma, eps = 1e-10)

Arguments

Value

Numeric complexity value.

Description

Computes the spectral condition number of a covariance matrix.

Usage

cov_condition_number(Sigma, eps = 1e-12)

Arguments

Value

Numeric condition number.

Examples

Sigma <- cov(mtcars[, c("disp", "hp", "wt")])
cov_condition_number(Sigma)

Description

Provides diagnostic eigenvalue summaries for a covariance matrix.

Usage

cov_diagnostics(Sigma, tol = 1e-06)

Arguments

Value

A list of covariance diagnostics.

Examples

Sigma <- cov(mtcars[, c("disp", "hp", "wt")])
cov_diagnostics(Sigma)

Description

Computes the number of eigenvalues exceeding a threshold.

Usage

cov_effective_rank(Sigma, tol = 1e-06)

Arguments

Value

Effective rank.

Examples

Sigma <- cov(mtcars[, c("disp", "hp", "wt")])
cov_effective_rank(Sigma)

Description

Computes a practical Ledoit-Wolf type shrinkage estimator toward a scaled identity target.

Usage

cov_lw(X)

Arguments

Value

A covariance matrix.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
Sigma <- cov_lw(X)
attr(Sigma, "shrinkage")

Description

Computes a maximum-entropy motivated covariance estimator for SDR.

Usage

cov_mec(
  X,
  y,
  nslices = 6,
  response_type = c("continuous", "categorical", "survival"),
  delta = NULL,
  alpha = NULL,
  eps = 1e-06,
  ...
)

Arguments

Details

The estimator uses response slicing to obtain slice-specific covariance matrices, selects the covariance matrix with maximum log-determinant entropy, and combines it with the pooled covariance matrix through convex shrinkage.

For censored survival responses, the function accepts delta and applies a survival-aware response construction before slicing.

Value

A covariance matrix with attributes containing the shrinkage weight and entropy diagnostics.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
Sigma <- cov_mec(X, y = mtcars$mpg, nslices = 4)
attr(Sigma, "alpha")
attr(Sigma, "entropy_slice")

Description

Computes a simplified Oracle Approximating Shrinkage (OAS) covariance estimator for stabilising the sample covariance matrix.

Usage

cov_oas(X)

Arguments

Value

A covariance matrix.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
Sigma <- cov_oas(X)
attr(Sigma, "shrinkage")

Description

Computes a convex shrinkage covariance estimator of the form

$\Sigma_{\lambda} = (1 - \lambda)S + \lambda T,$

where $S$ is the sample covariance matrix and $T$ is a scaled identity target.

Usage

cov_ridge(X, lambda = 0.1)

Arguments

Value

A covariance matrix.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
cov_ridge(X, lambda = 0.2)

Description

Computes the usual unbiased sample covariance matrix.

Usage

cov_sample(X)

Arguments

Value

A covariance matrix.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
cov_sample(X)

Description

Computes relative weights from any information criterion column.

Usage

criterion_weights(
  d_table,
  criterion = c("AIC", "BIC", "CAIC", "ICOMP", "CICOMP")
)

Arguments

Value

Data frame with criterion differences and weights.

Examples

scores <- as.matrix(mtcars[, c("wt", "hp", "disp")])
dimension_table <- select_dimension(scores, mtcars$mpg, d_max = 2)
criterion_weights(dimension_table, criterion = "BIC")

Description

Constructs low-rank sample-space scores without forming a p by p covariance matrix. This is useful when the number of predictors is very large.

Usage

dual_pca_scores(
  X,
  dual_rank = NULL,
  variance_explained = NULL,
  center = TRUE,
  scale_X = TRUE,
  eps = 1e-10
)

Arguments

Value

A list containing scores, loadings, singular values, centre, scale, and retained rank.

Description

Dispatches to the requested covariance estimator. For MEC, the function supports continuous, categorical, and censored survival responses by passing response_type and delta to cov_mec().

Usage

estimate_cov(
  X,
  y = NULL,
  method = c("sample", "ridge", "oas", "lw", "mec"),
  nslices = 6,
  response_type = c("continuous", "categorical", "survival"),
  delta = NULL,
  ...
)

Arguments

Value

A covariance matrix.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])

estimate_cov(X, method = "oas")
estimate_cov(
  X,
  y = mtcars$mpg,
  method = "mec",
  nslices = 4
)

Description

Computes common prediction metrics.

Usage

evaluate_prediction(y_true, y_pred, d = NULL)

Arguments

Value

A data frame of prediction metrics.

Examples

evaluate_prediction(
  y_true = c(2, 4, 6, 8, 10),
  y_pred = c(2.2, 3.8, 5.7, 8.1, 9.8),
  d = 1
)

Description

Repeats V-fold cross-validation for a fixed SDR and covariance-estimator combination. Failed folds are retained with diagnostic messages.

Usage

evaluate_prediction_cv(
  X,
  y,
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("sample", "ridge", "oas", "lw", "mec"),
  d,
  v = 5,
  repeats = 10,
  nslices = 6,
  standardize = TRUE,
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  seed = NULL,
  cov_args = list(),
  stabilization_args = list(),
  sdr_args = list(),
  ...
)

Arguments

Value

A list containing a one-row summary and fold-level results.

Description

Extract SDR loadings

Usage

extract_loadings(directions, variables = NULL)

Arguments

Value

A data frame of loadings.

Description

Removes predictors with variance below a specified quantile.

Usage

filter_low_variance(X, variance_quantile = 0.25)

Arguments

Value

Filtered matrix.

Description

Fits a linear regression model using the first d SDR scores.

Usage

fit_downstream_lm(scores, y, d)

Arguments

Value

A fitted lm object.

Examples

scores <- as.matrix(mtcars[, c("wt", "hp")])
fit_downstream_lm(scores, y = mtcars$mpg, d = 2)

Description

Fits sufficient dimension reduction models with optional covariance regularisation and information-theoretic structural dimension selection.

Usage

fit_risdr(
  X,
  y,
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("sample", "ridge", "oas", "lw", "mec"),
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  nslices = 6,
  d = NULL,
  d_max = 10,
  selector = c("cicomp", "icomp", "bic", "caic", "aic"),
  standardize = TRUE,
  complexity = c("C1", "C1F"),
  cov_args = list(),
  stabilization_args = list(),
  sdr_args = list(),
  ...
)

Arguments

Value

An object of class "risdr".

Examples

simulated <- simulate_risdr_data(
  n = 60,
  p = 6,
  d = 2,
  seed = 2026
)

fit <- fit_risdr(
  X = simulated$X,
  y = simulated$y,
  sdr_method = "sir",
  cov_method = "oas",
  nslices = 4,
  d = 1,
  d_max = 3
)

fit

Description

Constructs a low-rank PCA score representation, fits the unified RISDR core in that score space, maps the dense and selected sparse SDR directions back to the original predictor coordinates, and ranks variables using the Euclidean loading norm across only the selected sparse directions.

Usage

fit_risdr_dual(
  X,
  y,
  delta = NULL,
  response_type = c("continuous", "categorical", "survival"),
  dual_rank = 100L,
  variance_explained = NULL,
  d = NULL,
  d_max = 10L,
  nslices = 4L,
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("mec", "oas", "lw", "sample", "ridge"),
  selector = c("cicomp", "icomp", "aic", "caic", "bic"),
  lambda_grid = seq(0, 0.3, length.out = 10L),
  adapt_weights = TRUE,
  weight_mode = c("c1f", "inverse_c1f", "uniform"),
  support_penalty = FALSE,
  standardize_dual = TRUE,
  gene_select_top = NULL,
  gene_select_quantile = 0.99,
  center = TRUE,
  scale_X = TRUE,
  verbose = TRUE,
  ...
)

Arguments

Details

The inner RISDR standardisation scale is explicitly undone before mapping directions through the PCA loadings. The returned reduced predictors are taken directly from the fitted core and are therefore exactly aligned with the model used for information-criterion selection.

This entry point uses the frozen sparse thesis engine. The existing fit_risdr() and fit_risdr_realdata() interfaces retain their continuous-response behaviour from version 0.3.1. Survival fits use Efron Cox partial likelihood. Apparent fit statistics and loading ranks are exploratory and do not establish external predictive validity.

Value

An object of class risdr_dual.

Examples

set.seed(2026)
X <- matrix(rnorm(80 * 6), 80)
colnames(X) <- paste0("G", 1:6)
time <- rexp(80, rate = exp(0.5 * X[, 1]))
delta <- rep(c(0L, 1L), 40)
fit <- fit_risdr_dual(
  X, time, delta = delta, response_type = "survival",
  sdr_method = "sir", cov_method = "oas", nslices = 4,
  dual_rank = 4, verbose = FALSE, d_max = 2, lambda_grid = c(0, 0.05)
)
fit$d
predict(fit, X[1:2, , drop = FALSE], type = "risk")

Description

Fit RISDR to real high-dimensional data

Usage

fit_risdr_realdata(
  X,
  y,
  delta = NULL,
  response_type = c("continuous", "binary", "multiclass", "survival"),
  variance_quantile = 0.25,
  d = NULL,
  ...
)

Arguments

Value

Fitted RISDR workflow object.

Description

Fits an SDR model using a regularised covariance estimator, a selected inverse-regression kernel, adaptive sparse direction estimation, and information-criterion profiling jointly over structural dimension and sparsity tuning parameter.

Usage

fit_risdr_sparse(
  X,
  y,
  delta = NULL,
  response_type = c("continuous", "categorical", "survival"),
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("mec", "oas", "lw", "sample", "ridge", "user"),
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  nslices = 6L,
  d = NULL,
  d_max = 10L,
  selector = c("cicomp", "icomp", "bic", "caic", "aic"),
  standardize = TRUE,
  complexity = "C1F",
  lambda_grid = seq(0, 0.3, length.out = 10L),
  adapt_weights = TRUE,
  weight_mode = c("c1f", "inverse_c1f", "uniform"),
  penalty_weights = NULL,
  support_penalty = FALSE,
  cov_fun = NULL,
  shrinkage = 1e-04,
  tol = 1e-10,
  ...
)

Arguments

Details

For d = NULL, every candidate dimension from 1 through d_max is evaluated over the complete lambda_grid. The requested selector then chooses the final ⁠(d, lambda)⁠ pair. For explicit d, the same audit grid is retained but the final dimension is fixed and only lambda is selected within that dimension.

This entry point uses the frozen sparse thesis engine. The existing fit_risdr() and fit_risdr_realdata() interfaces retain their continuous-response behaviour from version 0.3.1. Survival fits use Efron Cox partial likelihood. Apparent fit statistics and loading ranks are exploratory and do not establish external predictive validity.

Value

An object of class risdr containing the complete ⁠(d, lambda)⁠ selection grid, profiled dimension table, selected sparse directions, reduced predictors, covariance diagnostics, and compatibility fields.

Examples

set.seed(2026)
X <- matrix(rnorm(80 * 6), 80)
colnames(X) <- paste0("G", 1:6)
time <- rexp(80, rate = exp(0.5 * X[, 1]))
delta <- rep(c(0L, 1L), 40)
fit <- fit_risdr_sparse(
  X, time, delta = delta, response_type = "survival",
  sdr_method = "sir", cov_method = "oas", nslices = 4,
  d_max = 2, lambda_grid = c(0, 0.05)
)
fit$d
predict(fit, X[1:2, , drop = FALSE], type = "risk")

Description

Fit RISDR to real high-dimensional data

Usage

fit_risdr_sparse_realdata(
  X,
  y,
  delta = NULL,
  response_type = c("continuous", "binary", "multiclass", "categorical", "survival"),
  variance_quantile = 0.25,
  ...
)

Arguments

Details

This entry point uses the frozen sparse thesis engine. The existing fit_risdr() and fit_risdr_realdata() interfaces retain their continuous-response behaviour from version 0.3.1. Survival fits use Efron Cox partial likelihood. Apparent fit statistics and loading ranks are exploratory and do not establish external predictive validity.

Value

Fitted RISDR workflow object. Fit RISDR to a real-data predictor matrix

Applies outcome cleaning, low-variance screening, the unified RISDR core, and descriptive loading-based variable ranking. The wrapper returns the reduced predictors computed by the core itself so that centring and standardisation are not silently bypassed.

"multiclass", "categorical", or "survival". low-variance screen.

An object of class risdr_realdata.

Description

Accepts either an explicit dense direction matrix or a historical kernel object containing directions or vectors.

Usage

fit_sparse_grid(
  kernel_obj = NULL,
  directions = NULL,
  d = 2L,
  lambda_grid = seq(0, 0.5, length.out = 25L),
  penalty_weights = NULL,
  adapt_weights = FALSE,
  Sigma = NULL,
  weight_mode = c("c1f", "inverse_c1f", "uniform"),
  tol = 1e-10
)

Arguments

Value

Sparse-grid object.

Description

Mean absolute error

Usage

mae(y_true, y_pred)

Arguments

Value

Numeric MAE.

Examples

mae(c(2, 4, 6, 8), c(2.2, 3.8, 5.7, 8.1))

Description

Create cross-validation folds

Usage

make_cv_folds(n, v = 5, seed = NULL)

Arguments

Value

Integer vector of fold memberships.

Description

Constructs response slices for inverse regression-based sufficient dimension reduction methods.

Usage

make_slices(y, nslices = 6, type = c("quantile", "equal_width"))

Arguments

Value

Integer vector of slice memberships.

Examples

slices <- make_slices(mtcars$mpg, nslices = 4)
table(slices)

Description

Mean absolute percentage error

Usage

mape(y_true, y_pred)

Arguments

Value

Numeric MAPE.

Examples

mape(c(2, 4, 6, 8), c(2.2, 3.8, 5.7, 8.1))

Description

Plot cross-validation dimension selection result

Usage

plot_cv_dimension(cv, metric = NULL, ...)

Arguments

Value

Invisibly returns the CV table.

Description

Plot dimension selection criteria

Usage

plot_dimension_selection(
  fit,
  criteria = c("AIC", "BIC", "CAIC", "ICOMP", "CICOMP"),
  ...
)

Arguments

Value

Invisibly returns dimension table.

Description

Plot ladle dimension diagnostic

Usage

plot_ladle(ladle, ...)

Arguments

Value

Invisibly returns ladle table.

Description

Displays the largest absolute loadings for a selected SDR direction.

Usage

plot_loadings(fit, direction = 1, top = 15, ...)

Arguments

Value

Invisibly returns loading table.

Description

Plots observed versus predicted values.

Usage

plot_prediction(y_true, y_pred, ...)

Arguments

Value

Invisibly returns plotted data.

Description

Plots residuals against predicted values.

Usage

plot_residuals(y_true, y_pred, ...)

Arguments

Value

Invisibly returns plotted data.

Description

Scree plot of SDR eigenvalues

Usage

plot_scree(fit, n_eigen = 20, type = "b", ...)

Arguments

Value

Invisibly returns eigenvalues plotted.

Description

Plots the response against a selected SDR direction.

Usage

plot_sufficient(fit, direction = 1, ...)

Arguments

Value

Invisibly returns plotted data.

Description

Plots the first two selected SDR scores, optionally coloured by response.

Usage

plot_sufficient2d(
  fit,
  directions = c(1, 2),
  colour_by_y = TRUE,
  groups = 4,
  ...
)

Arguments

Value

Invisibly returns plotted data.

Description

Predict from downstream SDR regression model

Usage

predict_downstream_lm(fit_lm, scores_new, d)

Arguments

Value

Numeric vector of predictions.

Description

Predict method for risdr objects

Usage

## S3 method for class 'risdr'
predict(object, newX, d = NULL, ...)

Arguments

Value

Numeric vector of predictions.

Examples

simulated <- simulate_risdr_data(
  n = 60,
  p = 6,
  d = 2,
  seed = 2026
)

fit <- fit_risdr(
  X = simulated$X,
  y = simulated$y,
  sdr_method = "sir",
  cov_method = "oas",
  nslices = 4,
  d = 1,
  d_max = 3
)

predict(fit, newX = simulated$X[1:5, , drop = FALSE])

Description

Projects new observations using the training centring, scaling, and selected directions. Survival predictions are Cox linear predictors or relative risks; they are not predicted survival times.

Usage

## S3 method for class 'risdr_sparse'
predict(
  object,
  newX,
  type = c("response", "scores", "link", "risk", "class", "probs"),
  ...
)

## S3 method for class 'risdr_dual'
predict(
  object,
  newX,
  type = c("response", "scores", "link", "risk", "class", "probs"),
  ...
)

Arguments

Value

Predictions or a score matrix, according to type.

Description

Prediction correlation

Usage

prediction_correlation(y_true, y_pred)

Arguments

Value

Pearson correlation.

Examples

prediction_correlation(
  c(2, 4, 6, 8),
  c(2.2, 3.8, 5.7, 8.1)
)

Description

Prepare survival response

Usage

prepare_survival_response(time, delta)

Arguments

Value

Cleaned survival response list.

Description

Print risdr object

Usage

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

Arguments

Value

Invisibly returns x.

Description

Print method for dual RISDR objects

Usage

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

Arguments

Description

Print real-data RISDR workflow

Usage

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

Arguments

Value

Invisibly returns x.

Description

Print risdr object

Usage

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

Arguments

Value

Invisibly returns x.

Description

Print real-data RISDR workflow

Usage

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

Arguments

Description

Print summary of risdr object

Usage

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

Arguments

Value

Invisibly returns x.

Description

Print summary of risdr object

Usage

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

Arguments

Value

Invisibly returns x.

Description

Projection matrix

Usage

projection_matrix(B)

Arguments

Value

Projection matrix.

Examples

B <- matrix(c(1, 0, 0, 0, 1, 0), nrow = 3)
projection_matrix(B)

Description

Coefficient of determination

Usage

r_squared(y_true, y_pred)

Arguments

Value

Numeric R-squared.

Examples

r_squared(c(2, 4, 6, 8), c(2.2, 3.8, 5.7, 8.1))

Description

Root mean squared error

Usage

rmse(y_true, y_pred)

Arguments

Value

Numeric RMSE.

Examples

rmse(c(2, 4, 6, 8), c(2.2, 3.8, 5.7, 8.1))

Description

Run one SDR simulation replication

Usage

run_one_simulation(
  n = 200,
  p = 50,
  d = 2,
  rho = 0.6,
  sigma = 1,
  model = "linear_quadratic",
  beta_type = "coordinate",
  sdr_method = "dr",
  cov_method = "oas",
  nslices = 6,
  selector = "cicomp",
  d_max = 10,
  seed = NULL
)

Arguments

Value

A data frame with simulation results.

Description

Run SDR simulation study

Usage

run_risdr_simulation(
  R = 200,
  rho_values = c(0.3, 0.6, 0.9),
  methods = c("sir", "save", "dr", "phd"),
  cov_methods = c("sample", "oas", "mec"),
  seed = NULL,
  ...
)

Arguments

Value

Data frame of simulation results.

Description

Fits linear models on SDR scores for candidate dimensions and computes information criteria.

Usage

select_dimension(
  scores,
  y,
  d_max = 10,
  complexity = c("C1", "C1F"),
  eps = 1e-10
)

Arguments

Value

A data frame of criteria by candidate dimension.

Examples

scores <- as.matrix(mtcars[, c("wt", "hp", "disp")])
dimension_table <- select_dimension(
  scores = scores,
  y = mtcars$mpg,
  d_max = 2
)
dimension_table

Description

Selects structural dimension by V-fold cross-validation. For each candidate dimension, SDR is fitted on the training folds, a downstream linear regression is fitted using the reduced predictors, and prediction error is evaluated on the validation fold.

Usage

select_dimension_cv(
  X,
  y,
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("sample", "ridge", "oas", "lw", "mec"),
  d_max = 10,
  v = 5,
  nslices = 6,
  standardize = TRUE,
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  metric = c("RMSE", "MAE"),
  seed = NULL,
  cov_args = list(),
  stabilization_args = list(),
  sdr_args = list(),
  ...
)

Arguments

Value

A list containing the CV table, selected dimension, and fold-level results.

Description

Combines out-of-fold prediction error with rescaled BIC, CAIC, or CICOMP penalties. The tuning constant lambda controls the contribution of the information-criterion component.

Usage

select_dimension_cv_icomp(
  X,
  y,
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("sample", "ridge", "oas", "lw", "mec"),
  d_max = 10,
  v = 5,
  nslices = 6,
  standardize = TRUE,
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  complexity = c("C1", "C1F"),
  lambda = 1,
  seed = NULL,
  cov_args = list(),
  stabilization_args = list(),
  sdr_args = list(),
  ...
)

Arguments

Value

A list containing selected dimensions, the aggregated cross-validation table, and fold-level results.

Description

Computes a simple ladle-type diagnostic by combining normalised eigenvalue information with a bootstrap-based subspace instability measure.

Usage

select_dimension_ladle(
  X,
  y,
  sdr_method = c("dr", "sir", "save", "phd"),
  cov_method = c("sample", "ridge", "oas", "lw", "mec"),
  d_max = 10,
  B = 100,
  nslices = 6,
  standardize = TRUE,
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  seed = NULL,
  cov_args = list(),
  stabilization_args = list(),
  sdr_args = list(),
  ...
)

Arguments

Value

A list containing ladle table, selected dimension, and bootstrap distances.

Description

Simulates data from a sufficient dimension reduction model with an autoregressive covariance structure. The function returns the true orthonormal central subspace basis, which allows simulation studies to evaluate both prediction accuracy and subspace recovery.

Usage

simulate_risdr_data(
  n = 200,
  p = 50,
  d = 2,
  rho = 0.6,
  sigma = 1,
  signal_strength = 1,
  model = c("linear_quadratic", "symmetric", "interaction", "linear"),
  beta_type = c("coordinate", "random_sparse", "random_dense"),
  beta = NULL,
  seed = NULL
)

Arguments

Value

A list containing the simulated predictors, response, true basis, latent sufficient predictors, population covariance matrix, signal, error, and simulation settings.

Examples

simulated <- simulate_risdr_data(
  n = 60,
  p = 6,
  d = 2,
  rho = 0.4,
  seed = 2026
)

dim(simulated$X)
head(simulated$y)
crossprod(simulated$beta)

Description

Computes slice-specific covariance matrices.

Usage

slice_covariances(
  X,
  slices,
  stabilize = TRUE,
  stabilization = c("eigenfloor", "ridge", "nearest_pd"),
  eps = 1e-06
)

Arguments

Value

A list of covariance matrices.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
slices <- make_slices(mtcars$mpg, nslices = 4)
covariances <- slice_covariances(X, slices)
names(covariances)

Description

Computes slice-specific means of predictors.

Usage

slice_means(X, slices)

Arguments

Value

Matrix of slice means with rows corresponding to slices.

Examples

X <- as.matrix(mtcars[, c("disp", "hp", "wt")])
slices <- make_slices(mtcars$mpg, nslices = 4)
slice_means(X, slices)

Description

Computes empirical slice probabilities.

Usage

slice_proportions(slices)

Arguments

Value

Numeric vector of slice proportions.

Examples

slices <- make_slices(mtcars$mpg, nslices = 4)
slice_proportions(slices)

Description

Constructs slice labels for continuous, categorical, or censored survival responses. For censored survival data, double slicing is used by first splitting on censoring status and then slicing observed time within each status group.

Usage

slice_response(
  y,
  nslices = 5L,
  response_type = c("continuous", "categorical", "survival"),
  delta = NULL
)

Arguments

Value

A list containing integer slice labels and metadata.

Description

Produces a summary table of slice frequencies and response ranges.

Usage

slice_summary(y, slices)

Arguments

Value

A data frame summarising slices.

Examples

slices <- make_slices(mtcars$mpg, nslices = 4)
slice_summary(mtcars$mpg, slices)

Description

Stabilises a covariance matrix using one of several available methods.

Usage

stabilize_cov(
  Sigma,
  method = c("eigenfloor", "ridge", "nearest_pd"),
  eps = 1e-06,
  lambda = 1e-04,
  keep_diag = TRUE
)

Arguments

Value

A stabilised covariance matrix.

Examples

Sigma <- matrix(c(1, 1, 1, 1), nrow = 2)
stabilize_cov(Sigma, method = "eigenfloor")

Description

Stabilises a symmetric covariance matrix by replacing eigenvalues smaller than a positive threshold with that threshold.

Usage

stabilize_eigenfloor(Sigma, eps = 1e-06)

Arguments

Value

A symmetric positive definite covariance matrix.

Examples

Sigma <- matrix(c(1, 1, 1, 1), nrow = 2)
eigen(stabilize_eigenfloor(Sigma))$values

Description

Stabilises a covariance matrix by projecting it to the nearest positive definite matrix using Matrix::nearPD().

Usage

stabilize_nearest_pd(Sigma, keep_diag = TRUE)

Arguments

Value

A symmetric positive definite covariance matrix.

Examples

Sigma <- matrix(c(1, 1, 1, 1), nrow = 2)
eigen(stabilize_nearest_pd(Sigma))$values

Description

Stabilises a covariance matrix by adding a positive multiple of the identity matrix.

Usage

stabilize_ridge(Sigma, lambda = 1e-04)

Arguments

Value

A symmetric positive definite covariance matrix.

Examples

Sigma <- matrix(c(1, 1, 1, 1), nrow = 2)
eigen(stabilize_ridge(Sigma))$values

Description

Computes Frobenius distance between projection matrices.

Usage

subspace_distance(B_hat, B)

Arguments

Value

Numeric subspace distance.

Examples

B <- matrix(c(1, 0, 0, 0, 1, 0), nrow = 3)
transformed <- B %*% diag(c(2, 3))
subspace_distance(transformed, B)

Description

Summarise simulation results

Usage

summarise_simulation(sim_results)

Arguments

Value

Summary data frame.

Description

Summarise sparsity pattern

Usage

summarise_sparsity(V, tol = 1e-08)

Arguments

Value

Sparsity summary.

Description

Summarise risdr object

Usage

## S3 method for class 'risdr'
summary(object, ...)

Arguments

Value

A list summary.

Description

Summary method for dual RISDR objects

Usage

## S3 method for class 'risdr_dual'
summary(object, top_n = 20L, ...)

Arguments

Description

Summarise risdr object

Usage

## S3 method for class 'risdr_sparse'
summary(object, ...)

Arguments

Value

A list summary.

Description

Weighted soft-threshold operator

Usage

weighted_soft_threshold(z, lambda, weights = NULL, tol = 1e-10)

Arguments

Value

Thresholded vector.

Description

Weighted sparse directions from dense SDR directions

Usage

weighted_sparsify_directions(V, lambda, weights = NULL, tol = 1e-10)

Arguments

Value

Sparse direction matrix.