## Reproducing stderr of difference of lsmeans

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# Reproducing stderr of difference of lsmeans

Hi,

I am trying to reproduce lsmeans from proc GLM in R and with the help of the online docs and through matrix algebra I can recreate everything but the standard error of the difference of lsmeans.

From the SAS doc:
for LS-means defined by the linear combinations li'b and lj'b of the parameter estimates, Sij^2=MSE*li'*inv(X'X)*lj

This is giving me a negative number.

For balanced data I could get the standard error by taking the square root of the sum of the variances (or sqrt(2)*se of the individual lsmean) but most of the time my data will be unbalanced so this does not hold.

Is there a nice closed form of the relationship between the se for individual lsmeans and their contrasts?

Rick Message was edited by: RickM
Regular Contributor
Posts: 165

## Re: Reproducing stderr of difference of lsmeans

Ok I figured out how to get it. Really simple too. Instead of li and lj I needed L=li-lj and then do Sij^2=MSE*L'*inv(X'X)*L

Have a nice weekend.
Regular Contributor
Posts: 171

## Re: Reproducing stderr of difference of lsmeans

Yes, because using the vector li on the left and lj on the right of inv(X'X) just returns the covariance of the two lsmeans that are obtained from li*beta and lj*beta. But the standard error of the difference is the sum of the variances of the lsmeans minus 2 times the covariance of the lsmeans. By using the matrix L, you get all the necessary terms for computing the variance of the difference.
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