sSDR (version 1.2.0)

gOLS.comp.d: Groupwise OLS (gOLS) BIC criterion to estimate dimensions with eigen-decomposition

Description

Groupwise OLS (gOLS) BIC criterion to estimate dimensions with eigen-decomposition

Usage

gOLS.comp.d(X, y, groups)

Arguments

X

A covariate matrix of n observations and p predictors.

y

A univariate response.

groups

A vector with the number of predictors in each group.

Value

gOLS.comp.d returns a list containning at least the following components: "d", the estimated dimension (at most 1) for each predictor group; "crit", the BIC criterion from each iteration.

Details

This function estimates dimension for each predictor group using eigen-decomposition. Predictors need to be organized in groups within the "X" matrix, as the same order saved in "groups". We only allow continuous covariates in the "X" matrix; while categorical covariates can be handled outside of gOLS, e.g. structured OLS.

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

data <- gen.data(n=1000, binary=FALSE) # generate data
dim(data$X) # covariate matrix of 1000 observations and 15 predictors
dim(data$y) # univariate response
groups <- c(5, 10) # two predictor groups and their numbers of predictors
dim_gOLS<-gOLS.comp.d(data$X,data$y,groups)
names(dim_gOLS)