sSDR (version 1.2.0)

sOLS.comp.d: Structured OLS (sOLS) outer level BIC criterion to estimate dimension with eigen-decomposition

Description

Structured OLS (sOLS) outer level BIC criterion to estimate dimension with eigen-decomposition

Usage

sOLS.comp.d(X, sizes)

Arguments

X

A matrix containing directions estimated from all subpopulations.

sizes

A vector with the sample sizes of all subpopulation.

Value

sOLS.comp.d returns a list containning at least the following components: "d", the dimension estimated across subpopulations; "u", the "d" linearly independent directions among the matrix X.

Details

This function estimates dimension across the subpopulations using eigen-decomposition. The order of the subpopulations in the "sizes" vector should match the one in the "X" matrix. Also, this function returns the linearly independent directions among all subpopulations.

References

Liu, Y., Chiaromonte, F., and Li, B. (2015). Structured Ordinary Least Squares: a sufficient dimension reduction approach for regressions with partitioned predictors and heterogeneous units. Submitted.

Examples

v1 <- c(1, 1, 0, 0)
v2 <- c(0, 1, 1, 0)
v3 <- c(0, 0, 1, 1)
v4 <- c(1, 1, 1, 1)
m1 <- cbind(v1, v2)
sizes1 <- c(100, 200)
sOLS.comp.d(m1, sizes1)
m2 <- cbind(v1, v2, v3)
sizes2 <- c(100, 200, 500)
sOLS.comp.d(m2, sizes2)
m3 <- cbind(v1, v3, v4)
sizes3 <- c(100, 500, 1000)
sOLS.comp.d(m3, sizes3)