How is the standard error of the least squares means found in Fit Model multiple regression

[#1]

JMP supplies a standard error for its least squares means in the Least Squares Mean Table. How is this standard error calculated given that the least squares mean is a constant using the rules that JMP follows for calculating the least squares means? That is, JMP  fixes background continuous variables at their mean and sums over background categorical variables using equal weighting (which is equivalent to ignoring them because they always sum to zero under this approach).

[#2]

Hello, and welcome to the site. First of all, the LS mean is not a constant. It is a random variable (the observed LS mean is a realization of that random variable) and as such, has a variance/standard error. The following link may be a good place to start.

 https://communities.sas.com/t5/Statistical-Procedures/How-to-interpret-SE-for-lsmeans/td-p/257989

[#3]

Hi, Many thanks for this. I can do the linear algebra in that link you sent but am not sure what the L is in this sentence:

"The approximate standard errors for the LS-mean is computed as the square root of L*(X'*(V_hat)^-1*X)^-1*L'. "

I am assuming X is the data, V is the V-C matrix, but what is L? Is it the linear constraints matrix or ??

However JMP is calculating the SEs for the least squares means they have the undesirable (and potentially misleading) property that they get smaller the fewer the number of observations on which they are based.

Any help greatly appreciated.

[#4]

Hard to address the "undesirable property"  issue without knowing more about the data....but, for the question about L; here ya go!

https://documentation.sas.com/doc/en/statcdc/14.2/statug/statug_glm_details41.htm#:~:text=To%20const....

[#5]

Thanks again, this is going to take a bit of studying, but I think the answer to the standard error might indeed lurk in the maths in that link -- thank you!