create_monomials {TSCI}

Monomials as Violation Space Candidates

Description

Monomials as Violation Space Candidates

Usage

create_monomials(Z, degree, type = c("monomials_main", "monomials_full"))

Arguments

Z

observations of the instrumental variable(s). Either a numeric vector of length n or a numeric matrix with dimension n by s.

degree

The degree up to which monomials should be created. Either a single positive integer or a vector of length s containing positive integers.

type

One out of monomials_main or monomials_full.
monomials_main creates the monomials for the polynomials of each instrumental variable up to degree degree.
monomials_full creates the monomials for the polynomials of a combination of all instrumental variables up to degree degree.
Default is monomials_full.

Details

assuming there are 3 instrumental variables Z1, Z2, and Z3 and degree = c(d1, d2, d3) with d1 < d2 < d3, monomials_main creates the monomials of the polynomials (Z1 + 1)^d1, (Z2 + 1)^d2, (Z3 + 1)^d3 without the constants and monomials_full creates the monomials (Z1 + Z2 + Z3), (Z1 + Z2 + Z3)^2, ..., (Z1 + Z2 + Z3)^d3 without the constants and excluding monomials that are products of Z1^d or Z2^d with d > d1 resp. d > d2. Thus type = monomials_main does not include interactions between the instrumental variables.

Value

A list. Each element is a matrix consisting of the monomials to be added to the next violation space candidate.

Examples

Z <- matrix(rnorm(100 * 3), nrow = 100, ncol = 3)
vio_space <- create_monomials(Z = Z, degree = 4, type = "monomials_full")