cta (version 1.3.0)

check.zero.order.homog: Zero-Order \(Z\) Homogeneity Check

Description

Checks whether the estimand function \(S(\cdot)\) is zero-order \(Z\) homogeneous.

Usage

check.zero.order.homog(S.fct, Z, tol = 1e-9)

Arguments

S.fct

An R function object, indicating the estimand function \(S(\cdot)\) for zero-order \(Z\) homogeneity check.

Z

Population (aka strata) matrix \(Z\).

tol

The pre-set tolerance with which norm(diff.LRHS) is to be compared with.

Value

check.zero.order.homog returns a character string check.result that states whether \(S(\cdot)\) is zero-order \(Z\) homogeneous. If check.result = "", it means that we cannot state that \(S(\cdot)\) is not zero-order \(Z\) homogeneous based on the result of the check.

Details

The main idea:

\(S(\cdot)\) is zero-order \(Z\) homogeneous if \(S(Diag(Z\gamma) x) = S(x)\), for all \(\gamma > 0\), and for all \(x\) within its domain. This program randomly generates gam (\(\gamma\)) and x (\(x\)), and computes $$\texttt{diff.LRHS} = S(Diag(Z\gamma) x) - S(x).$$ It returns a warning if norm(diff.LRHS) is too far from \(0\).

References

Lang, J. B. (2004) Multinomial-Poisson homogeneous models for contingency tables, Annals of Statistics, 32, 340--383.

See Also

check.homog, check.HLP

Examples

# NOT RUN {
# EXAMPLE 1
S.fct <- function(m) {(m[1] - m[2]) / (m[1] + m[2])}
Z <- matrix(c(1, 1, 1, 1), nrow = 4)
check.zero.order.homog(S.fct, Z)

# EXAMPLE 2
S.fct.2 <- function(m) {m[1] - m[2]}
Z <- matrix(c(1, 1, 1, 1), nrow = 4)
check.zero.order.homog(S.fct.2, Z)
# }