qgcomp (version 2.17.4)

se_comb: Calculate standard error of weighted linear combination of random variables

Description

This function uses the Delta method to calculate standard errors of linear functions of variables (similar to lincom in Stata). Generally, users will not need to call this function directly.

Usage

se_comb(expnms, covmat, grad = NULL)

Arguments

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

the "weight" vector for calculating the contribution of each variable in expnms to the final standard error. For a linear combination, this is equal to a vector of ones (and is set automatically). Or can be calculated via the grad_poly procedure, in the case of coming up with proper weights when the combination of expnms derives from a polynomial function (as in qgcomp.glm.boot with degree>1).

Details

This function takes inputs of a set of exposure names (character vector) and a covariance matrix (with colnames/rownames that contain the full set of exposure names), as well as a possible grad parameter to calculate the variance of a weighted combination of the exposures in expnms, where the weights are based off of grad (which defaults to 1, so that this function yields the variance of a sum of all variables in expnms)

Here is simple version of the delta method for a linear combination of three model coefficients:

\(f(\beta) = \beta_1 + \beta_2 + \beta_3\) given gradient vector $$G = [d(f(\beta))/d\beta_1 = 1, d(f(\beta))/d\beta_2 = 1, d(f(\beta))/d\beta_3 = 1]$$ \(t(G) Cov(\beta) G\) = delta method variance, where t() is the transpose operator

Examples

vcov = rbind(c(1.2, .9),c(.9, 2.0))
colnames(vcov) <- rownames(vcov) <- expnms <- c("x1", "x2")
se_comb(expnms, vcov, c(1, 0))^2 # returns the given variance
se_comb(expnms, vcov, c(1, 1)) # default linear MSM fit: all exposures
# have equal weight
se_comb(expnms, vcov, c(.3, .1)) # used when one exposure contributes
  # to the overall fit more than others  = d(msmeffect)/dx