fetch.rho.v: Function to transform var(theta) back to var(rho)

In lleemann/StratSel: Strategic Selection Estimator

Function to transform var(\theta) back to var(\rho)

Description

The model has a correlation parameter which is estimated and theoretically bound between -1 and +1. To ensure that the estimated parameters are within the theoretical bounds a transformation is necessary. The chosen transformation is:

f(\rho): \rho = \frac{2}{(1-exp(-\theta))}- 1

Whereas \rho is the actual correlation coefficient and \theta is the parameter we estimate in the model. This parametrization has been worked into the likelihood function and ensures that \rho will be between -1 and +1.

The variance covariance matrix thus contains entries based on \theta but not \rho. Hence, this function takes the variance of the transformed correlation parameter (\theta) and produces the value correct for \rho.

To create the correct measure of var(\rho) this function simulates 1,000 \theta's and then transforms them to \rho's. The variance of these \rho's is then reported. Note, this means that the variance-covariance returned by StratSel is only correct for all diagonals and off-diagonals for the parameters (\beta) but for the correlation coefficient only the variance is correct. Given that there is no reason to use the full variance-covariance for post-estimation commands this is not a problem.

Usage

fetch.rho.v(v, b)

Arguments

v	Variance-covariance matrix based on the regular parameters (\beta) and \theta.
b	Coefficient vector, first n elements are for the regular parameter estimates and the last element is \theta.

Details

This function is for internal use but documented as a regular function to enable any user to assess the estimator and its functionality.

Value

Returns the correct variance estimate for the estimate of the correlation coefficient \rho.

Author(s)

Lucas Leemann [e-mail]

See Also

StratSel

Examples

fetch.rho.v(matrix(c(1,0,0,1),2,2),c(0,0))
fetch.rho.v(matrix(c(1,0,0,2),2,2),c(0,0))

lleemann/StratSel documentation built on Aug. 19, 2023, 7:58 p.m.