madness (version 0.2.0)

vcov.madness: Calculate Variance-Covariance Matrix for a model.

Description

Returns the variance-covariance matrix of the parameters computed by a madness object.

Usage

"vcov"(object, ...)

Arguments

object

a madness object. A varx matrix must have been set on the object, otherwise an error will be thrown.

...

additional arguments for method functions. Ignored here.

Value

A matrix of the estimated covariances between the values being estimated by the madness object. While $Y$ may be multidimensional, the return value is a square matrix whose side length is the number of elements of $Y$

Details

Let $X$ represent some quantity which is estimated from data. Let $Sigma$ be the (known or estimated) variance-covariance matrix of $X$. If $Y$ is some computed function of $X$, then, by the Delta method (which is a first order Taylor approximation), the variance-covariance matrix of $Y$ is approximately $$\frac{\mathrm{d}Y}{\mathrm{d}{X}} \Sigma \left(\frac{\mathrm{d}Y}{\mathrm{d}{X}}\right)^{\top},$$ where the derivatives are defined over the 'unrolled' (or vectorized) $Y$ and $X$.

Note that $Y$ can represent a multidimensional quantity. Its variance covariance matrix, however, is two dimensional, as it too is defined over the 'unrolled' $Y$.

See Also

vcov.

Examples

y <- array(rnorm(2*3),dim=c(2,3))
dy <- matrix(rnorm(length(y)*2),ncol=2)
dx <- crossprod(matrix(rnorm(ncol(dy)*100),nrow=100))
obj <- madness(val=y,dvdx=dy,varx=dx)
print(vcov(obj))