# delta.sum and se.sum

Returns the standard error, calculated by the delta method, of the sum of the elements of theta. This is a convenience function that calls into the deltamethod function in the msm package to do the actual calculation.

# Arguments

delta.sum <- function(theta, v)
se.sum <- function(fit, m=NULL)

• theta: Vector of coefficients.
• v: Covariance matrix corresponding to the elements of theta.
• fit: lm output.
• m: Vector holding the indexes of the coefficients to sum. If NULL, it identifies all coefficients.

# Examples

fit is the output of a regression with three coefficients. You need the standard error of the sum of all three coefficients.

delta.sum(coefficients(fit), vcov(fit))

fit2 is the output of a regression with five coefficients. You need the standard error of the sum of the second and fourth coefficients.

# Grab the relevant coefficients
b <- coefficients(fit)[c(2,4)]

# This will grab the right submatrix
# Keeps the elements in the right place
v <- vcov(fit)[c(2,4), c(2,4)]
delta.sum(b, v)

The second example is pretty verbose. You have to call the coefficients function and pull out the elements you want. You have to pull the appropriate elements out of vcov, and you might not even be aware of how to do it. Therefore a further convenience function se.sum is included for cases where you’re working with linear regression output. Note that delta.sum works with any estimation output, as long as you have the covariance matrix.

This achieves the same thing as the previous example:

se.sum(fit, c(2,4))

If you want the standard error of the sum of all coefficients in the regression, you can omit the second argument:

se.sum(fit)

Please keep in mind that, while this is the most convenient case, it only works with lm output.