spca_est: Scaled PCA factor extraction
In sdim: An R Package for Supervised Dimension Reduction

spca_est

R Documentation

Scaled PCA factor extraction

Description

Implements scaled principal component analysis (sPCA): predictors are first standardized, then each standardized predictor is scaled by its univariate predictive slope on the target, and finally principal components are extracted from the scaled predictors.

Usage

spca_est(target, X, nfac, winsorize = FALSE, winsor_probs = c(0, 99))

Arguments

`target`	A numeric vector of length `T_reg` (`T_reg <= T`).
`X`	A numeric matrix or data frame with `T` rows and `N` columns. When `length(target) < nrow(X)`, the first `length(target)` rows of the standardized `X` are used for the scaling regression while all `T` rows are used for standardization and factor extraction. This matches the out-of-sample workflow in Huang et al. (2022), where the predictive regression `y_{t+1} ~ X_t` uses fewer rows than the full training window.
`nfac`	A positive integer giving the number of factors to extract.
`winsorize`	Logical; if `TRUE`, winsorize absolute slope estimates before scaling predictors.
`winsor_probs`	Numeric vector of length 2 giving winsorization percentiles. Used only when `winsorize = TRUE`.

Details

The function follows the MATLAB implementation of Huang, Jiang, Li, Tong, and Zhou (2022).

Value

An object of class "sdim_spca" with components:

factors: A T x nfac matrix of extracted sPCA factors.
beta: A numeric vector of predictor-specific predictive slopes.
beta_scaled: A numeric vector of scaling coefficients actually used.
col_means: Column means of X (used by predict).
col_sds: Column standard deviations of X (used by predict).
Xs: The standardized predictor matrix.
scaleXs: The scaled standardized predictor matrix.
lambda: The estimated loading matrix.
residuals: Residual matrix from the PCA reconstruction step.
ve2: Average squared residual by row.
eigvals: Singular values from the decomposition of scaleXs %*% t(scaleXs).
call: The matched function call.

References

Huang, D., Jiang, F., Li, K., Tong, G., and Zhou, G. (2022). Scaled PCA: A New Approach to Dimension Reduction. Management Science, 68(3), 1678–1695. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1287/mnsc.2021.4020")}

Examples

set.seed(123)
X <- matrix(rnorm(200 * 10), nrow = 200, ncol = 10)
y <- rnorm(200)

fit <- spca_est(target = y, X = X, nfac = 3)
dim(fit$factors)
head(fit$beta)

# Predictive alignment: target has fewer rows than X
fit2 <- spca_est(target = y[1:199], X = X, nfac = 3)
dim(fit2$factors)  # 200 x 3 (factors for all T rows)

sdim documentation built on July 15, 2026, 1:10 a.m.