# here we want standard error of G(b) for females in prog2 with math = 50 # G(b) = b0 + b_female1*female1 + b_prog2*prog2 + b_prog3*prog3 + b_math*math M2 <- lm(write ~ female + prog + math, data=d) # Delta method standard error for predicted value of Y at set values of We then take the sqrt of the variance to get the standard error of the conditional mean. Now we apply the delta method: var(G(B)) = dG/db’ %*% var(b) %*% dG/db. Example 1: Delta method standard error for conditional mean of Y at mean of Xįirst let’s make up some data and run a very simple linear regression. The predict() function calculates delta-method standard errors for conditional means, but it will not quite work for marginal means. Var(G(B)) = dG/db’ %*% var(b) %*% dG/db,where dG/db is a vector of partial derivatives of G(b) with respect toĮach b coefficient, also known as the Jacobian matrix, and var(b) is the variance-covariance matrix of theī coefficients. For a function G(b) of a random variable vector, b, the variance of G(b) by the delta method is: As model coefficients are themselves random variables, we can use the delta method to get the variance of conditional and marginal means, because they are functions of the model ceofficients. We can use the delta method to get the variance of a function of random variable. Both conditional and marginal means are functions of the model coefficients. (NOT SURE ABOUT THIS) Marginal means are often calculated to isolate the effect of a single predictor by averaging the predicted response over various levels of the predictor of interest while holding the values of other predictors constant. Additionally, this page will not be updated in the near future.Īdjusted predictions are often calculated to predict the response at a given set of predictor values, usually to get an idea of the response value at representative predictor values.
Calculate standard error from variance covariance matrix code#
Please note that this page is incomplete and there may be inconsistencies in the code or explanations.
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