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Are regression weights in SEM the same thing as in say, a weight in linear regression (for each 1 more of this predictor, there's 2 more of y)? And how should you decide which weight should be fixed to 1? Does it even matter?

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Regression weights in SEM are the same as regression weights in linear regression.

In R, if you run:

library(lavaan)
data(attitude)

summary(glm(rating ~ complaints + privileges, data = attitude))

m <- 'rating ~ complaints + privileges'

summary(sem(m, attitude))

You'll find that the results of the two models are close to identical.

I don't think you should fix any weight to 1. But you should often fix a factor loading to 1. It doesn't make any difference empirically which is fixed - it rescales the loadings. Sometimes it makes theoretical sense to choose one of the variables to have its loading fixed to one - this is the variable with the closest conceptual relationship to the latent variable of interest.

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