stillenter.blogg.se

1. #HOW TO CALCULATE STANDARD ERROR OF THE REGRESSION CODE#
2. #HOW TO CALCULATE STANDARD ERROR OF THE REGRESSION SERIES#

For a random variable \(X\) with known variance-covariance matrix \(Cov(X)\), the variance of the transformation of \(X\), \(G(X)\) is approximated by:

Variance of this approximation to estimate the variance of \(G(X)\) and thus the standard error ofĪ transformed parameter. Where \(\nabla G(\mu_X)\) is the gradient of \(G(X)\) at \(X = \mu_X\), or a vector of partial derivatives of \(G(X)\) at point \(\mu_X\). The first two terms of the Taylor expansion are then an approximation for \(G(X)\), Let \(G\) be the transformation function and \(\mu_X\) be the mean vector of random variables (X=(x1,x2,…)).

#HOW TO CALCULATE STANDARD ERROR OF THE REGRESSION SERIES#

We, thus, first get the Taylor series approximation of the function using the first two terms of the Taylor expansion of the transformation function about the mean of of the random variable. Although the delta method is often appropriate to use with large samples, this page is by no means an endorsement of the use of the delta method over other methods to estimate standard errors, such as bootstrapping.Įssentially, the delta method involves calculating the variance of the Taylor series approximation of a function. Regression coefficients are themselves random variables, so we can use the delta method to approximate the standard errors of their transformations. The delta method approximates the standard errors of transformations of random variable using a first-order Taylor approximation. Well approximated using the delta method. Point estimates of our desired values, but the standardĮrrors of these point estimates are not so easily calculated. Often in addition to reporting parameters fit by a model, we need to report

#HOW TO CALCULATE STANDARD ERROR OF THE REGRESSION CODE#

Version info: Code for this page was tested in R version 3.1.1 ()