R FAQ: How can I estimate the standard error of a transformed parameter in R using the delta method?
Often we do not wish to directly report parameters fit by a model but rather some transformation of these parameters. The transformation can generate the point estimates of our desired values, but the standard errors of these point estimates are not so easily calculated. They can, however, be well approximated using the delta method. This is based on the first two terms of the Taylor expansion of the transformation function. Let f be the transformation function and u be the mean of a random variable X. The first two terms of the Taylor expansion are then an approximation for f(X), f(X) = f(u) + (X – u)f'(u) where f’ is the first derivative of f. We can then take the variance of this approximation to find the variance of f(X) to find the standard error of a transformed parameter. For example, we may fit a multinomial logit model and want to report odds ratios. However, R fits and displays the linear coefficients. We can use the deltamethod in the msm package to find the standard errors
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