vc_comb {qgcomp}

Calculate covariance matrix between one random variable and a linear combination of random variables

Description

This function uses the Delta method to calculate a covariance matrix of linear functions of variables and is used internally in qgcomp. Generally, users will not need to call this function directly.

Usage

vc_comb(aname = "(Intercept)", expnms, covmat, grad = NULL)

Arguments

aname

character scalar with the name of the first column of interest (e.g. variable A in the examples given in the details section)

expnms

a character vector with the names of the columns to be of interest in the covariance matrix for a which a standard error will be calculated (e.g. same as expnms in qgcomp fit)

covmat

covariance matrix for parameters, e.g. from a model or bootstrap procedure

grad

not yet used

Details

This function takes inputs of a name of random variable (character), as set of exposure names (character vector) and a covariance matrix (with colnames/rownames that contain the indepdendent variable and the full set of exposure names). See se_comb for details on variances of sums of random variables. Briefly, for variables A, B and C with covariance matrix Cov(A,B,C), we can calculate the covariance Cov(A,B+C) with the formula Cov(A,B) + Cov(A,C), and Cov(A,B+C+D) = Cov(A,B) + Cov(A,C) + Cov(A,D), and so on.

Value

A covariance matrix

Examples

vcov = rbind(c(0.010051348, -0.0039332248, -0.0036965571),
             c(-0.003933225,  0.0051807876,  0.0007706792),
             c(-0.003696557,  0.0007706792,  0.0050996587))
colnames(vcov) <- rownames(vcov) <- c("(Intercept)", "x1", "x2")
expnms <- rownames(vcov)[2:3]
aname = rownames(vcov)[1]
vc_comb(aname, expnms, vcov) # returns the given covariance matrix