deltamethod {msm} | R Documentation |
Delta method for approximating the standard error of a transformation g(X) of a random variable X = (x1, x2, ...), given estimates of the mean and covariance matrix of X.
deltamethod(g, mean, cov, ses=TRUE)
g |
A formula representing the transformation. It must have
arguments labelled x1, x2,... For example,
~ 1 / (x1 + x2)
If the transformation returns a vector, then a list of formulae g1, g2, ... can be provided, for example list( ~ x1 + x2, ~ x1 / (x1 + x2) ) |
mean |
The estimated mean of X |
cov |
The estimated covariance matrix of X |
ses |
If TRUE , then the standard errors of g1(X), g2(X),... are
returned. Otherwise the covariance matrix of g(X) is returned. |
The delta method expands a differentiable function of a random variable about its mean, usually with a first-order Taylor approximation, and then takes the variance. For example, an approximation to the covariance matrix of g(X) is given by
Cov(g(X)) = g'(mu) Cov(X) [g'(mu)]^T
where mu is an estimate of the mean of X.
A vector containing the standard errors of g1(X), g2(X),... or a matrix containing the covariance of g(X).
C. H. Jackson chris.jackson@imperial.ac.uk
Oehlert, G. W. A note on the delta method. American Statistician 46(1), 1992
## Simple linear regression, E(y) = alpha + beta x x <- 1:100 y <- rnorm(100, 4*x, 5) toy.lm <- lm(y ~ x) estmean <- coef(toy.lm) estvar <- summary(toy.lm)$cov.unscaled ## Approximate standard error of (1 / (alphahat + betahat)) deltamethod (~ 1 / (x1 + x2), estmean, estvar)